Mindy awoke coughing again. Her eyes broke out from their shells faster than a bullet, aching from the air that hit them. Blinking rapidly, Mindy turned and coughed into her pillow.
Mindy startled when she felt a hand on her shoulder. "Are you okay?"
Mindy gasped for air as she turned to look at the voice. Breathing a sigh of a relief, she noticed that it was Tom. Slumping into her pillow, she tried to recall the last twelve hours. Nothing came. The stupid antibiotics were messing with her memory.
"What.... what are you doing here?" She asked, trying to re-catch her breath.
Tom raised an eyebrow. "You asked me to stay a few hours ago,"
Mindy looked over at her alarm clock. It was only four a.m. Scooting uncomfortably up to the headboard, Mindy breathed out slowly.
Tom scooted up next to her, about a foot apart. He sighed, rolling his head over to look at Mindy.
Mindy nodded, trying her best to not let out the cough that was pressing against her chest and lips. She tried desperately not to let it out. Each cough felt like thousands of needles embedding themselves in her flesh, and she had no intention on feeling it again.
Tom's breath caught in his throat. Mindy raised an eyebrow, looking over at him. He was looking down at her pillow, which she had put on her lap when she had replaced her positioning. Mindy glanced down at it, and saw what he was staring at.
There, in the shallow lamp light, blood was splattered on her white pillow case. Mindy gasped, causing her to cough again. More blood spurted from her mouth, dribbling down her chin. She bit her lip, wiping her mouth with the back of her hand.
Her hand came away red, and Mindy tried her hardest not to gag. She slipped out of bed quickly, moving to the bathroom. She heard Tom following behind, his soft footsteps reassuring her fast pacing thoughts.
She was coughing up blood. Mindy's heart raced as she turned on the faucet, the cold water running smoothly over her hand. She scrubbed hard, afraid that the blood would stain her forever. She would have to walk around all the time, covering her bloody hand. She would look like a murdering psychopath idiot.
She coughed suddenly into he sink, leaning over to stop the blood from spreading across the counter. She felt her long hair tangle with her hand and tickle in front of her face.
Tom reached out and brushed the hair back, bringing it back behind her back. He rubbed her back in circles, comforting her in every way possible. The light flickered on and she had to blink to get used to it.
Tom stood slightly behind her, his left foot near her side. His eyes were filled with concern, and locked with hers in the mirror. Mindy smiled weakly - causing her to hack out another cough. Groaning, she leaned over the sink, trying not to think of the splatters she would have to clean off of the mirror. It would look like a murder scene.
Mindy mentally shook herself, clearing her thoughts. Tom squeezed her shoulder, keeping his other hand wrapped around her messy and knotted hair.
"Hey, it's okay," he soothed quietly.
Mindy nodded, almost hitting her head on the faucet. Squeezing her eyes shut, she begged herself to stop coughing.
Finally, the hacking stopped, and she was able to open her eyes. The sink was covered in a sleek layer of pink, mixing into the water that was still running from the faucet.
Mindy breathed deeply, slowly regaining her balance and standing up straight. She looked into the mirror and almost went back to the sink to vomit.
There was spots of blood covering the surface of the mirror. The only area that she was able to see anything decipherable was the top of Tom's head. His eyes were visible, but one of them had a red dot in the center. Mindy almost laughed to herself. Almost.
"This hurts more than it looks," she groaned, leaning up against Tom with a huff.
Tom gave her a half smile. "I bet,"
He lead her back to her bed to sit down, handing her an old popcorn bowl from the ground. She got the point of it, and sat upright against her headboard. Tom smiled softly and exited the room, returning a few moments later with some paper towels from the kitchen. Tom went straight to the bathroom.
Mindy closed her eyes, silently thanking the heavens for the wonderful guy they put in her life. She listened to the rapid beating of her heart, trying to slow the adrenaline coursing through her. She unsteadily breathed, keeping a short pace - trying her best to repeat it for as long as possible without coughing.
The contest between herself and her lungs gave out after a minute or two, when she felt her chest heave uncontrollably. She leaned down into the plastic bowl on her hands, letting the cough come out.
A few seconds after the first wheeze came out, Tom was by her side. He was like a faithful puppy. Always at her side when she needed him. He was cute, bright, playful, caring.... and she was coughing again.
Tom moved Mindy's hair out of the way while she basically puked out all of the blood in her body.
"This needs to stop." She mumbles when she is able to take a breath.
Tom rubbed her back. "Hey, relax. I'm glad I get to be here to take care of you. It's nice,"
Mindy's heart squeezes, making her cheeks blush. A tingle runs down her spine and a flame kindles in her belly. Ignoring the blood on her lips, she presses her mouth to Tom's cheek.
Mindy could feel Tom's grin before she saw it. It was the cutest thing with his dimples. Mindy had tried her best not to be all mushy over him, but she wasn't sure how else to be. He was nice and comforting, the least she could do was admit her feelings to him.
"I like you. A lot," Mindy muttered, fighting off another cough.
Tom wasn't bothered by the blood. He didn't even move to wipe it off his cheek, which made Mindy cringe. She wiped it off his slight stubble, her hand tingling from the contact.
Tom stopped her hand before it could rub his jawline any more. "You're driving me insane,"
Mindy looked at him, confused, as Tom wiped the blood off of Mindy's mouth with the rag he had given her earlier.
Tom grinned at Mindy's confused expression as he leaned down and pressed his lips firmly to hers.
Mindy's heart might've leaped or of her chest right then and there if it wasn't for the way it longed to be kissing Tom back. Her lips moved on their own accord, wanting to continue whatever it was they were doing.
"I like you too, Mindy. And I always will. I can never get you off my mind - and I don't want you to ever leave my thoughts," Tom admitted into Mindy's tingly lips.
Author Notes: Hey guys! Sorry for such a long wait! It is here! And it will be followed by a few more chapter that I've completed! I love you guys!!


text:
Clash of Champions
John Lineker: The Weight is Over
2014/07/20 By CombatFiled in Hot fight articles
The fact that John Lineker was willing to sit for an interview on weigh-in day should tell you all you need to know about how the cut for his Wednesday fight against Alptekin Ozkilic was going, and as he predicted, he not only hit the mark on Tuesday, he came in at 125.5 pounds, a half-pound under the limit.
It's a new day for "Hands of Stone."
"The first part of the fight is done," said Lineker through translator Michele Spinelli Davis. Now all that's left is the part with the gloves on, and that's always been the easiest part for the 23-7 flyweight contender, who has gone 4-2 in the UFC despite missing weight in three of those bouts. But the 24-year-old insists that those days are over.
"For sure," he said. "I have made a great job this time cutting weight, and I will keep working like this in the future."
If not for his battles with the scale – and a February loss to Ali Bagautinov – Lineker might have already secured a shot at champion Demetrious Johnson. But there were too many red lights around him to put him in a fight he might not even make weight for. He admits that he thought about moving to 135 pounds, but after this smooth cut, he's going to stay put and begin his quest for a title anew. And it starts with Ozkilic.
"I think we will both do a great fight," said Lineker. "He is great on the ground and is also a great wrestler, but I don't want to worry about difficulties right now; I will only worry about imposing my game."
That game includes the kind of knockout power that is rivaled only by John Dodson at 125 pounds. You don't see a flyweight changing the course of a fight with a single punch like Lineker does, and he's done it three times in the UFC against Azamat Gashimov, Jose Maria, and Phil Harris.
"I think that the reason for that is that I am usually the heaviest fighter in this division, and I am the one that cuts more weight," said Lineker, and that's certainly a good reason for remaining at 125 pounds. But it takes more than pure power to win four times in the UFC, and for this he doesn't hesitate to reveal the trio of reasons why he believes he's a major player in the division.
"The secret is a lot of training, focus, and faith in God," said the Paranagua native, who can also point to determination for his success. Remember, this is the same kid who had no team with him when he came to the U.S. for his UFC debut against Louis Gaudinot due to visa issues, and didn't even have a mouthpiece or cup. He's come a long way since then, in and out of the Octagon.
"I can say that since I have started fighting in the UFC I gained a lot of experience and I look forward to always getting better," he said. "Everything changes after you become a UFC fighter. My life has gone from 40% to 100%."
Title shot or not, that's a success story already, but Lineker – like any fighter – is hungry for more, and with John Dodson sidelined until next year, a big win from "Hands of Stone" could propel him up the flyweight ladder, something he's aiming for.
"I think now that Dodson got injured, if I win this fight I might be closer to the title shot."
And weight won't be an issue.
www.ufc.com
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Ricky and his parents would like to thank all the sponsors for their help. Without their help, Ricky would not be able to train or compete as much as he is able to do now.
Ricky has ongoing sponsorships and event sponsors. On going sponsors provide financial and service type help for Ricky year round.
Event sponsors provide financial help for individual events that would otherwise be out of reach for him and his parents.
If you would like to sponsor Ricky, you can make contact with him at the address below. All donations will be acknowledged and appreciated. Make checks payable to: Ricky Olson P.O. Box 5254 Lake Station, IN 46405-0254
Tyson Fury pulls out of fight with Alexander Ustinov
Fight Night at Broadripple Place
DZ Action! Action! Action!
THE LAST EYADA FILE
Freestyle Combat Challenge
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redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Relation between product and user in opencart? How to identify which product added by which user(not customers) in opencart? any table or data in database related to user and product?
Thanks in advance..

A: There is no such relation. But you can create a field in oc_products table named as add_by_user_id and can insert the id using session by $this->user->getId().

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}

The problem we address is the estimation of latent sub-population mean
and covariance curves when only populational aggregated data is available. By
aggregated data we mean that each sample consists of linear
combinations of functional data that cannot be observed individually
for each sub-population.

Certainly, there are many methods of fitting curves to data. A
collection of techniques known as nonparametric regression, for
example, allows great flexibility in the possible form of the
regression curve $\alpha$. In particular, it assumes no parametric form for
it. In fact, a nonparametric regression model only makes the assumption
that the regression curve belongs to some infinite collection of
curves. Consequently, in order to propose a nonparametric model one
may just need to choose an appropriate space of functions where he/she
believes that the regression curve lies. This choice, usually, is
motivated by the degree of smoothness of $\alpha$. Then, one uses the
data to determine an element of this function space that can represent
the unknown regression curve. Consequently, nonparametric techniques
rely more heavily on the data for information about $\alpha$ than their
parametric counterparts. Also, this flexibility on the form of the
curve allows one  to incorporate prior information.  The literature on nonparametric
regression is vast, for the interested reader we refer to the book of
\citeasnoun{euba:1999}.

The set up for  nonparametric regression assumes that an
unknown function $\alpha$ of one or more variables and a set of
measurements $y_1, \ldots, y_n$ are such that:
\[y_{i}={\cal L}_{i}\alpha + \varepsilon_{i}, \]
where ${\cal L}_{1},\ldots,{\cal L}_{n}$ are linear functionals defined on some
linear space $\cal H$ containing $\alpha$, and
$\varepsilon_{1},\ldots,\varepsilon_{n}$ are measurement errors usually
assumed to be independent, with common, zero mean normal distributions
with unknown variance $\sigma^{2}$. Typically, the ${\cal L}_{i}$ will be
point evaluations of the function $\alpha$. That is, ${\cal
  L}_{i}g=g(x_i)$ and $y_i=y(x_i)$, where $x_i$ are the explanatory
variables for $i=1,\ldots,n$.

The problem we address here is more general. We have several unknown
functions $\alpha_{c}, c=1, \ldots, C$ of one or more variables and the set of
measurements are given by
\begin{equation}
\label{eq:ourmodel}
y_{i}= \sum_{c=1}^{C}{\cal L}_{ic}\alpha_{c} + \varepsilon_{i}
\end{equation}
where
${\cal L}_{ic},i = 1,\ldots, I, c=1,\ldots, C$ are the linear
functionals. The problem is to estimate the functions $\alpha_c, c=1,
\ldots, C$ based on the measurements $y_i, i=1, \ldots, I$.

More specifically, in our model we assume each aggregated curve $y_i$
is an independent partial realization of a Gaussian process with mean
modeled through a weighted linear combination of the disaggregated
curves $\alpha_c$s. Following \citeasnoun{dias:garcia:martarelli:2009}
we model the mean of the Gaussian process as a smooth function
approximated by a function belonging to a finite dimensional space
${\cal H}_K$ which is spanned by $K$ B-splines basis functions.  This
is not the only choice, other basis could be used such as Fourier
expansion, wavelets, natural splines. See, for example,
\citeasnoun{silv:1986}, \citeasnoun{koop:ston:1991},
\citeasnoun{vida:1999}, \citeasnoun{dias:1998a} and
\citeasnoun{dias:2000}.

In this work, differently from
\citeasnoun{dias:garcia:martarelli:2009}, we consider two different
structures for the covariance function of the Gaussian process
postulating models that impose positive definiteness condition on the
function. The first one assumes a uniform structure across the domain
of the process, the second one models the covariance itself as a
smooth function providing a nonstationary behaviour. Our model is
going to be applied for two practical situations. In both of them it
is reasonable to consider that the experts in the field have prior
information on the disaggregated curves. Therefore, in order to incorporate
this opinion,  inference procedure will be performed following the Bayesian
paradigm. As a by-product, we naturally obtain the uncertainty associated
with the parameters estimates, and fitted values.

This paper is organized as follows. Section \ref{sec:ex} presents two
motivating examples: calibration problem for NIR spectroscopy data
and an analysis of distribution of energy among different types of
consumers.  Section \ref{sec:model} describes our proposed hierarchical
model to estimate latent disaggregate curves when only aggregated
population observations are available.  Therein we also propose a
non-stationary covariance function allowing the variance of the
underlying process to smoothly change across the domain of the
function. Next section analyzes different sets of artificial data. The
aim is to check the ability of the model in recovering the true
disaggregated functions under different scenarios. Then Section
\ref{sec:realdata} discusses the analysis for the two motivating
examples described in subsections \ref{sec:nir} and
\ref{sec:traficload}. Finally, Section \ref{sec:conclusion} concludes.

\section{Motivating examples} \label{sec:ex}

\subsection{Near-infrared (NIR) spectroscopy data: a calibration
problem \label{sec:nir} }

Analyzing materials to determine their chemical composition is a basic
tool of science. It is used in many applications such as food safety
testing, protein detection, pharmaceutical purposes, forensics, to
mention just a few.  This analysis can be done directly in the
laboratory by usually expensive and time-consuming techniques. An
alternative is to determine the chemical composition through NIR
spectroscopy which is a low cost technique, relatively simple to use
and provides adequate accuracy in many practical situations. Some
references with practical applications of NIR spectroscopy are
\citeasnoun{cand:mass:etal:1999}; \citeasnoun{rodriguez-saona:2001};
\citeasnoun{mara:catt:gian:2002}; \citeasnoun{tewa:mehr:iru:2003};
\citeasnoun{cozzo:flood:etal:2006};
\citeasnoun{scho:mohl:wint:reic:2006}; Saranwong and Kawano (2008a,
2008b); \nocite{sara:kawa:2008a} \nocite{sara:kawa:2008b}
\citeasnoun{wood:dow:don:2008}; \citeasnoun{boto:bow:lamo:tsa:2009};
and \citeasnoun{romia:berna:2010}. For introductory material on the
subject see Shenk and Westerhaus (1991), Brereton (2003), and Burns
and Ciurczac (2007).

When atoms or molecules absorb light, the energy input excites a
quantized structure to a higher energy level. The type of excitation
depends on the wavelength of the light. NIR spectroscopy technology is
based on the fact that each of the major chemical components of a
sample has near infrared red absorption properties in the region
700-2500 nm. An absorption spectrum is the absorption of light as a
function of wavelength. The NIR spectrum of a sample is the summation
of these absorption properties for each chemical sample resulting in a
continuous curve measured by modern scanning instruments at hundreds
of equally spaced wavelengths.  The information contained in this
curve can be used to predict the chemical composition of the
sample. The problem lies in extracting the relevant information from
possibly thousands of overlapping peaks. This can be accomplished by
applying the Beer-Lambert Law. The Beer-Lambert law is the linear
relationship between absorbance and concentration of absorbing
species.

Analysing a training set of different samples with distinct
compositions allow us to calibrate the analysis. Osborne, Fearn, and
Hindle (1993) described applications in food analysis and reviewed
some of the standard approaches to the calibration problem.
Multivariate calibration techniques are widely used in the literature
for this kind of problem. We propose a different approach by treating
this problem in the framework of functional data analysis. We regard
the response of interest as an aggregated continuous curve observed
only at a set of discrete points.  Therefore, having measurements of
the NIR spectrum for several chemical samples, with distinct
compositions, will allow us to estimate the typical curve for each
constituint of the sample. Figure \ref{PAHI_dados} shows the
absorbance curves measured for a dataset of 10 polyaromatic hydrocarbons
(PAH) obtained by Electronic Absorption Spectroscopy. The sample
consists of 25 chemical samples, each sample composed of varying
compositions of 10 different constituents (pyrene, acenaphthene,
anthracene, acenaphthylene, chrysene, benzanthracene, uoranthene,
uorene, naphthalene, phenanthracene). Each sample was submitted to 27
wavelengths (220nm--350nm). This dataset was presented by
\citeasnoun{brer:2003} to illustrate multivariate calibration
techniques.

\begin{figure}[!bpth]
\centering
\includegraphics[height=7cm,width=9cm]{PAHI_dados.ps}
\caption{Polyaromatic hydrocarbons spectra}
\label{PAHI_dados}
\end{figure}

\subsection{Electric load \label{sec:traficload}}

The distribution of electric energy is done in several stages: first
substations provide energy for regions in the city. This energy
arrives at power transformers ({\it trafo}, an usual acronym for
transformer) that redistributes it to micro-regions. Each micro-region
is composed of different types of consumers, residential, commercial,
industrial, among others. For each type of consumer, there are peaks
of consumption at certain hours of the day. In Brazil, for example, it
is empirically known that residential consumers have a peak on energy
consumption between 6--8pm (due partially to the use of electric
showers) and commercial and industrial consumers have their peak
between 8am--6pm. To avoid overload, trafos have to be designed to
deal with the maximum load of the day. Ideally, the distribution of
electric energy should be done in such a way that there is a constant
load during the whole day, all days of the week, all over the year for
all power plants, substations and transformers. Therefore, to have a
more efficient and uniform distribution of electricity, it is
necessary to know the profile of the consumption for each type of
consumer.  For each type of consumer, this typical curve is called the
{\it typology}. The empirical evidence described before might be used
as prior information when modeling the typology for each type of
consumer.

From a practical point of view, it is very difficult and expensive to
obtain samples from individual consumers. Commonly, the data available
are aggregated data from power transformers (trafos). Typically each
trafo comprises around 50 consumers. Notice that this data is the sum
of all load demanded by the {\it market} (the number of consumers of
each type) of this trafo. Moreover, due to billing issues, the
market of each trafo is known. Therefore, having measurements of the
electric load for several different trafos, with distinct markets,
provides us with the information to estimate the individual curves for
each type of consumer. Figure \ref{fig:a1} shows the data from two trafos, that we analyse in Section \ref{sec:ex}

\begin{figure}[!htb]
\begin{center}
\includegraphics[scale=0.55]{ObservedElectricLoadCrop.eps}
\caption{Observed curves for two trafos.}
\label{fig:a1}
\end{center}
\end{figure}

Both problems described above can be viewed as examples of samples
obtained from aggregated data; that is, the observed data might be
described as a linear combination of individual functional processes
and the aim is to estimate their individual mean and covariance
functions.

\section{Proposed Model \label{sec:model}}

Let $Y_{ij}(t)$ be the $j$-th replication of curve $i$ observed at
point $t$, $t \in [0,T_F]$. We decompose $Y_{ij}(\cdot)$ as the sum of
two components. The first one is described as a weighted sum of $C$
smooth curves, each representing the mean curve of a category  $c$
($c=1,\cdots,C$). For example, in the electric load example, each
disaggregated curve represents the typical curve of consumer type
$c$.
 The second component represents measurement error, described by a zero
mean Gaussian process with some covariance function. More
specifically, we assume
\begin{equation}
\label{model1} Y_{ij}(t)=\sum_{c=1}^{C} r_{ic} \alpha_{c}(t) +
\sum_{c=1}^C {\boldmath{\textbf{$\varepsilon$}}}_{ijc}(t), \quad
i=1, \ldots, I,\, \, j=1, \ldots, J,
\end{equation}
\noindent where $\alpha_1(t), \ldots, \alpha_C(t)$ are the mean curves
related to category $c=1,2,\cdots,C$, respectively. The $r_{ic}$s are assumed known and are
related to the problem being investigated. These will be discussed
in detail in Section \ref{sec:realdata}. We assume
${\boldmath{\textbf{$\varepsilon$}}}_{ijc}(\cdot)$ follows independent
zero mean Gaussian processes with covariance function given by
$Z_{ic}(t,s)$, for $t,s \in [0,T_F]$.

In general, the required degree of smoothness depends on the problem
under study. However, it is common to require that the functions
$\alpha_c$ belong to the Sobolev space ${\cal H}_{2}^{2}=\{f:[x_a,x_b]
\rightarrow {\mathbb R}, \sum_{j=0}^{2} \int (f^{(j)})^2 < \infty\} $.  To
consider the class ${\cal H}_{2}^{2}$ as the set of possible mean
curves is natural and desirable for this particular situation since it
can be well approximated by a finite-dimensional approximating space
generated by cubic B-splines, see \citeasnoun{boor:1978}. Therefore, the
second level of hierarchy expands the mean curves, $\alpha_c(\cdot)$,
as a linear combination of B-spline basis. We assume there exists a
positive integer $K$ and a knot sequence $\xi=(\xi_1,\cdots,\xi_K)$
such that
\begin{equation}
\label{eq:e3} \alpha_c(t)\,=\,\sum_{k=1}^{K} \beta_{ck} B_{k}(t),
\end{equation}
\noindent where $B_k(t)$, $k=1, \ldots, K$ are cubic
B-splines. Consider the function is evaluated at $T$ points, with $t_1
< t_2 < \cdots < t_T$, following equation (\ref{eq:e3}), we can write
\begin{eqnarray}\label{eq:ee3}
\left( \begin{array}{c} \alpha_{c}(t_1) \\ \vdots \\
    \alpha_c(t_T)\end{array} \right)\, = \,  \left( \begin{array}{c c c} B_1(t_1) & \cdots & B_K(t_1) \\ \vdots & & \vdots \\ B_1(t_T)& \cdots & B_K(t_T) \end{array} \right)\,
\left( \begin{array}{c} \beta_{c1} \\ \vdots \\
\beta_{cK}\end{array} \right)
\end{eqnarray}
for $c=1,2,\cdots,C$.

Notice that the design matrix in equation \reff{eq:ee3} does not
depend on the category $c$ since we are using the same number of
basis and same knot allocation for all categories. Moreover, in this
model the coefficients do not depend on the sampled points and all
$N$ points of all aggregated curves can be used to estimate the same
$C \times K$ coefficients. Therefore, following equation
\reff{model1} and the discussion above,  we have the following
linear model
\begin{equation}\label{eq:e4}
Y_{ij}(t)=\sum_{c=1}^{C} \sum_{k=1}^{K} r_{ic} \beta_{ck} B_{k}(t)+
{\boldmath{\textbf{$\varepsilon$}}}_{ij}(t),
\end{equation}
where ${\boldmath{\textbf{$\varepsilon$}}}_{ij}(t) = \sum_{c=1}^C
{\boldmath{\textbf{$\varepsilon$}}}_{ijc}(t)$, because of the
independence assumption of $\epsilon_{ijc}(\cdot)$ for $i=1,\cdots,I$,
$j=1,\cdots,J$, and $c=1,\cdots,C$. We now discuss in detail the
covariance structure among the $\epsilon_{ij}(\cdot)$s.

\subsection{Covariance structure of the measurement error \label{sec:covariance}}

The measurement error captures any structure left after adjusting
the data to the sum of the latent disaggregated curves $\alpha_c(.)$. As we
are estimating functions we assume the errors are correlated across the domain of $Y_{ij}(\cdot)$.

We expect the correlation between points $Y_{ij}(t)$ and
$Y_{ij}(s)$ to decay exponentially,
as $|t-s|$ increases. For each category $c$, we assign an exponential correlation function with
decay parameter $\phi_c>0$ for the Gaussian process associated to each $\epsilon_{ijc}(\cdot)$. Our main contribution lies on the
specification of the variance structure. For the $i$-th curve, let
$Z_{i}(t,s) = {\rm Cov
}({\boldmath{\textbf{$\varepsilon$}}}_{ij}(t),
{\boldmath{\textbf{$\varepsilon$}}}_{ij}(s))$, be the covariance
between points $t$ and $s$. Notice that we assume the same covariance
structure across replicates $j=1,\cdots, J$. We propose
the following general structure for $Z_i(t,s)$,
\begin{equation}
\label{eq:e3a} Z_{i}(t,s) = \sum_{c=1}^C C_{ic} \eta_c(t) \,
\eta_c(s) \exp(-\phi_c|t-s|),
\end{equation}
where $C_{ic}, c=1, \cdots, C$, $i=1, \cdots, I$ are known
constants. Like the constants $r_{ic}$ in equation \reff{eq:e4}, the $C_{ic}$s
assume values related to the problem being studied.  For every $i$, we
allow the variances to change with $t$, such that $Z_i(t,t)= \sum_{c=1}^C
C_{ic} \eta_c(t)^2$. More generally, the covariance function is
allowed to change along the domain of the function. Because of the
product $\eta_c(t) \, \eta_c(s)$ in equation (\ref{eq:e3a}) we do not
need to impose any particular restriction on the $\eta_c(\cdot)$s to
guarantee that we have a valid covariance function. It is worth noting
that this covariance function might assume negative values, depending
solely on the function $\eta_c(\cdot)$.

We consider three different models for the components $\eta_c(\cdot)$s:
\begin{itemize}
\item[(a)] {\bf Uniformly homogeneous case}: In this case we assume
$$
\eta_c(t) = \sigma, \, \, \forall \, t \quad \mbox{ and } \quad \phi_c=\phi,
$$
implying that  $Z_{i}(t,s) =
(\sum_{c=1}^C C_{ic}) \sigma^2 \exp(-\phi|t-s|)$, for all $c = 1,
\ldots, C$.

\item[(b)] {\bf Homogeneous case}: Here we relax the assumption of
  common $\sigma^2$ and $\phi$ by assuming
$$
\eta_c(t) = \sigma_c, \, \, \forall \, t,
$$
which leads to $Z_{i}(t,s) = \sum_{c=1}^C C_{ic} \sigma_c^2 \exp(-\phi_c|t-s|)$, i.e.

\item[(c)] {\bf Heterogenous case}: The more general case expands
  $\eta_c(\cdot)$ in B-splines basis functions, such that
\begin{equation}
\label{eq:e3b} \eta_c(t)\,=\,\sum_{\ell=1}^{L} \theta_{c\ell}
B_{\ell}(t),
\end{equation}
\noindent where $B_\ell(t)$, $\ell=1, \cdots, L$ are cubic B-splines
with (possibly) a different knot sequence from that for
$\alpha_c(\cdot)$, say $\xi_{\eta}$,  and the covariance function follows the general structure shown in Equation (\ref{eq:e3a}).
\end{itemize}

\subsection{Likelihood function and Prior specification \label{sec:likel}}

Assume ${\bf y}$ represents the $IJT$-dimensional vector of
observations, with components ${\bf y}=(y_{11}(t_1),\cdots,\newline
y_{1J}(t_1),
\cdots,y_{11}(t_T),\cdots,y_{1J}(t_T),\cdots,y_{IJ}(t_T))$.
Considering the more general case, denote by
${{\boldsymbol{\Theta}}}$  the parameter vector
for the model. We will specify this vector for the three covariance
structures considered.  Notice that
for each $i=1,\cdots,I$, and $j=1,\cdots,J$, conditioned on the
parameter vector, ${\bf Y}_{ij}=(Y_{ij}(t_1),\cdots,Y_{ij}(t_T))'$
follows independent normal distributions such tha
\begin{equation}
  \label{eq:n1}
   {\bf Y}_{ij} \sim N_T(X_i {{\boldsymbol{\beta}}}, Z_i),
\end{equation}
where $X_i$ are $T \times CK$ matrices given by
$$
X_i = \left( \begin{array}{ccccccc}
               r_{i1} B_1(t_1) & \ldots &  r_{i1}B_K(t_1) & \ldots &
               r_{iC}B_1(t_1)& \ldots & r_{iC} B_K(t_1) \\
               \vdots & \ldots & \vdots &  \ldots & \vdots & \ldots &
               \vdots \\
               r_{i1} B_1(t_T) & \ldots &  r_{i1}B_K(t_T) & \ldots &
               r_{iC}B_1(t_T)& \ldots & r_{iC} B_K(t_T)
               \end{array}
         \right),
$$
${{\boldsymbol{\beta}}}=({{\boldsymbol{\beta}}}_1,\cdots,{{\boldsymbol{\beta}}}_C)'$, with
${{\boldsymbol{\beta}}}_c=(\beta_{c1},\cdots,\beta_{cK})'$, is the $CK$
dimensional vector of coefficients, and $Z_i = Z_i({\boldsymbol{\Theta}})$ are covariance
matrices of order $T$ with elements given by Equation \reff{eq:e3a}.
Therefore, based on the observed vector ${\bf y}$, the likelihood
function for ${{\boldsymbol{\Theta}}}$ can be written as
\begin{equation}
  \label{eq:n2}
   L({{\boldsymbol{\Theta}}};{\bf y}) \propto \prod_{i=1}^{I} \, \prod_{j=1}^{J}  |Z_i|^{-1/2}
\exp \left\{ -\frac{1}{2} ({\bf y}_{ij} - X_i {{\boldsymbol{\beta}}})' Z_i^{-1} ({\bf
y}_{ij} - X_i {{\boldsymbol{\beta}}}) \right\}.
\end{equation}
As our inference procedure follows the Bayesian paradigm, we now
specify the prior distribution of the parameter vector
${{\boldsymbol{\Theta}}}$ depending on the covariance structure.

\paragraph{Prior specification}
We assume prior independence among the components of the parameter vector ${{\boldsymbol{\Theta}}}$.
In particular, for the coefficients ${\boldsymbol{\beta}}_c$ we assign
$K$-dimensional multivariate normal distributions with known mean vector
${\bf b}_c$ and covariance matrice $\Omega_c$, $c=1,2,\cdots,C$.
In Section \ref{sec:realdata} we assume a
zero mean prior for ${{\boldsymbol{\beta}}}_c$. However, experts in the field
of interest might provide useful information about the shape of each
function, and this can be induced through the mean of the prior
distributions of the respective ${{\boldsymbol{\beta}}}_c$s. For the covariance
matrices $\Omega_c$ we assume diagonal matrices, with the
diagonal elements fixed at some large value to let the observed data
drive the inference procedure. The prior specification of the parameters in the covariance function is related to the choice of the covariance structure proposed in Section \ref{sec:covariance}.

\begin{description}
\item [(a)] {\bf Uniformly homogeneous case:}
in this case the parameter vector is defined as ${\boldsymbol{\Theta}}^U=({{\boldsymbol{\beta}}},\sigma^2,\phi)$.
For $\sigma^2$ we assume an inverse gamma
distribution with shape parameter $d$ and rate parameter $l$. For
$\phi$, we assign a gamma prior distribution with
  shape parameter $p$ and rate parameter $q$ fixed at some reasonable
  value.  For example, we can use the idea
of practical range. The mean of the prior, $p/q$ can be fixed such
that at a reasonable distance, the correlation is close to zero, say
0.05. More specifically, we fix the mean at the value that solves
$0.05=\exp(-\phi^* dist)$, where $\phi^*$ is the prior mean guess we
need, and $dist$ is a fixed distance.

\item [(b)] {\bf Homogeneous case:} for the homogenous covariance structure we define the parameter vector as ${\boldsymbol{\Theta}}^H=({\boldsymbol{\beta}},\sigma^2_1,\sigma^2_2,\cdots,\sigma^2_C,\phi_1,\phi_2,\cdots,\phi_C)$.
We suggest independent inverse gamma prior distributions, each with parameters $(d_c,l_c)$,  for each $\sigma_c^2$.
We also assume prior independence among the decay parameters $\phi_c$ of the exponential correlation function; and each one is assumed to follow a gamma prior distribution with parameters $p_c$ and $q_c$, $c=1,\cdots, C$, with $p_c$ and $q_c$ fixed at some reasonable values.  The same idea of practical range discussed in the uniformly homogenous case can be used here.

\item [(c)]{\bf Heterogeneous case:}
the parameter vector to be estimated is $\Theta^{NH}=({\boldsymbol{\beta}},{\boldsymbol{\theta}}_1,\cdots,{\boldsymbol{\theta}}_C,\phi_1,\cdots,\phi_C)$. We assume independent $K$-dimensional multivariate normal prior  distributions for the coefficients ${\boldsymbol{\theta}}_c$, each with known mean vector ${\bf d}_c$, and covariance matrix $\Lambda_c$.
Like in the mean values of ${\boldsymbol{\beta}}$, the  ${\bf d}_c$s can be obtained by experts in
  the field. However, it might be more challenging to elicitate these values as they are in the covariance structure of the process.  For the covariance
  matrices $\Lambda_c$ we assume diagonal matrices, with
  the diagonal elements fixed at some reasonably large value to let the observed
  data drive the inference procedure.
\end{description}

\paragraph{Posterior distribution and inference procedure}
Following the Bayesian paradigm, the posterior distribution,
$p({\boldsymbol{\Theta}} \mid {\bf y})$, is proportional to the likelihood
function times the prior distribution of $\Theta$.

The resultant posterior distributions under all different covariance functions do not have
closed forms. We use Markov chain Monte Carlo (MCMC) methods,
specifically, the Gibbs sampler with some steps of the Metropolis-Hastings (M-H)
algorithm to obtain samples from the target posterior distribution (see e.g.
\citeasnoun{game:lop:2006}). In particular, the
full conditional posterior distributions of ${\boldsymbol{\beta}}_c$ are normal distributions,
which are easy to sample from. Independent of the assumed covariance function, the  full conditional posterior distributions of each of the parameters involved in it do not result in known distributions.
For these parameters we make use of the Metropolis-Hastings algorithm with
log-normal proposals based on the current value of the chain, and some fixed variance, tuned to give reasonable acceptance rates. The MCMC
algorithm was implemented in {\tt R} \cite{Rproj},
and the codes are available from the authors upon request.

\subsection{Predictive inference \label{sec:predictive}}

From a Bayesian point of view, one can obtain the posterior predictive distribution of the function $Y_i(\cdot)$ at unobserved values of the domain of the function, ${\bf Y}_i^*=(Y_{i}(t_1^*),\cdots,Y_{i}(t_L^*))$, for $t_l^* \in [0,T_F], \, l=1,\cdots,L$, through
\begin{eqnarray}
p({\bf y}_i^* \mid {\bf y})=\int_{{{\boldsymbol{\Theta}}}} p({\bf y}_i^*\mid
{\bf y},  {{\boldsymbol{\Theta}}}) p({{\boldsymbol{\Theta}}} \mid {\bf y}) d{{\boldsymbol{\Theta}}}. \label{eq:predictive}
\end{eqnarray}

The model assumes that samples $Y_i(\cdot)$ are being generated from the multivariate normal distribution, $N(X_i {\boldsymbol{\beta}},Z_i)$. From the theory on the multivariate normal distribution
\cite{anderson:1984}, it follows that the joint distribution of
 ${\bf Y}$ and ${\bf Y}_i^*$, conditioned on ${{\boldsymbol{\Theta}}}$, is given by
\begin{eqnarray}
\left(
\begin{array}{c}
{\bf Y}_i^* \\
{\bf Y}
\end{array} \bigg\vert{{\boldsymbol{\Theta}}} \right) \sim N \left( \left(
\begin{array}{c}
X_i^* {\boldsymbol{\beta}} \\
X_i {\boldsymbol{\beta}}
\end{array} \right);
\left(
\begin{array}{cc}
Z_i^* & Z_{i_{12}}'\\
Z_{i_{12}} & Z_i
\end{array} \right)
\right),
\end{eqnarray}
where $X_i^*$ is a L-dimensional vector with elements equal to the cubic B-splines at point $t_l^*$; $X_i$ is a vector comprising the cubic B-splines at the  observed points $t_t$;
$Z_i^*$ is a covariance matrix of dimension $L$ and each of its element is
the covariance of the process between unobserved points. Each
line of the matrix $Z_{i_{12}}$, $T \times L$, represents the
covariance between the $i^{th}$ observed point and the $j^{th}$
unobserved one, $i=1,\cdots,T$ and $j=1,\cdots,L$. From the theory
of the multivariate normal distribution we have that
\begin{eqnarray}
{\bf Y}_i^* | {\bf y}_i,{{\boldsymbol{\Theta}}} \sim N_L
\left(X_i^* {\boldsymbol{\beta}}+Z_{i_{12}}'{Z_i}^{-1} \left( {\bf
y}_i-X_i {\boldsymbol{\beta}} \right);
Z_i^*-Z_{i_{12}}'Z_i^{-1}Z_{i_{12}} \right).
\label{preditivacondicional}
\end{eqnarray}
The integration in (\ref{eq:predictive}) does not have an analytical
solution, however approximations can be easily obtained through
Monte Carlo methods \cite{game:lop:2006}. For each sample
$s$, $s=1,\cdots, Q$, obtained from the MCMC algorithm, we can
obtain an approximation for (\ref{eq:predictive}), by sampling from the
distribution in (\ref{preditivacondicional}) and computing
\begin{eqnarray}
p({\bf y}_i^* | {\bf y}) \approx \frac{1}{Q}\sum_{s=1}^Q \,
p({\bf y}_i^* | {{\boldsymbol{\Theta}}}^s). \label{eq:predictivelik}
\end{eqnarray}
Once samples from the posterior distribution of ${\boldsymbol{\Theta}}$ are
available, realizations from the posterior predictive distribution can
be obtained by sampling from the distribution of ${\bf Y}_i^* \mid
{\bf y}, {\boldsymbol{\Theta}}^s$, with ${\boldsymbol{\Theta}}^s$ representing the $s$th sampled
parameter vector ${\boldsymbol{\Theta}}$.

\section{Analyzing artificial data sets \label{sec:artificial}}

Here we analyze six artificial sets of data to check the ability of
the model in estimating the disaggregated curves of interest when the
truth is known. All datasets assume $C=2$ population curves.  We
consider data are generated from
\begin{equation}
\label{ex1} Y_{ij}(t)= r_{i1} \alpha_1(t) + r_{i2} \alpha_2(t) +
\epsilon_{ij}(t), \quad i=1,2, 3,\, \, j=1, \cdots, J,
\end{equation}
where the true curves are given by
\begin{eqnarray*}
  \alpha_1(t) &=& 5 \exp\{-t\}  \sin(\pi\,t/2)  \cos(\pi\,t) \label{eq:alpha1.1} \\
\alpha_2(t) &=& 5 \exp\{-(t-0.2)\}  \cos(\pi\,t/2) \sin(\pi\,t),
\label{eq:alpha2.2}
\end{eqnarray*}
with $r_{11}= 1$, $r_{12}=4$, $r_{21}=4$, $r_{22}=1$, $r_{31} = 2.5$
and $r_{32}=2.5$. These curves were chosen because they have
interesting features to be captured by the model.
We explore 6 different scenarios by assuming different specifications for the  covariance structures of $\epsilon_{ij}(\cdot)$:

\paragraph{Case 1: Uniformly homogeneous case} In this case we assume all
  $C_{ic}=1$, $\sigma^2 = 1$ and $\phi = 0.5$. We concetrated on the
  case where there are no replicates for the aggregated curves, such that $J=1$ and we obtained samples for $I=10$ and $I=30$.

\paragraph{ Case 2: Homogeneous case}
Here we assume
\begin{equation}
\label{eq:e3a1} Z_{i}(t,s) =  C_{i1} \sigma_1^{2} \exp(-\phi_1|t-s|)
+ C_{i2} \sigma_{2}^2 \exp(-\phi_2|t-s|),
\end{equation}
and we fix the parameters at the following values: $\sigma_1^2 =
\sigma_2^2 = 1$, $\phi_1 = \phi_2 = 4$ and
$C_{11}= 1$, $C_{12}=1.3$, $C_{21}=1.4$, $C_{22}=1.3$, $C_{31} =
1.5$ and $C_{32}=1.5$.
Here we consider only the case $J=15$.

\paragraph{Case 3: Heterogeneous case}
Here we assume
\begin{equation}
\label{eq:e3a2} Z_{i}(t,s) =  C_{i1} \eta_1(t) \eta_1(s)
\exp(-\phi_1|t-s|) + C_{i2} \eta_2(t) \eta_2(s) \exp(-\phi_2|t-s|)
\end{equation}
with $\eta_1$ and $\eta_2$ curves generated as linear combinations
of B-splines, $\phi_1 = \phi_2 = 4$ and $C_{11}= 1$, $C_{12}=1.3$,
$C_{21}=1.4$, $C_{22}=1.3$, $C_{31} = 1.5$ and $C_{32}=1.5$.
For the heterogeneous covariance
structure we fit the model considering $J=15$, $J=50$ and $J=150$.
This is to investigate the effect of the number of replicates on the
estimates of the parameters when a more flexible  covariance
structure is assumed.

For all datasets we assumed 14 B-splines basis with $K=10$ internal
knots. In the heterogeneous case, we assumed this same set of knots to
estimate $\eta_1(.)$ and $\eta_2(.)$.  We let the MCMC algorithm run
for 100,000 iterations, considered the first 5,000 as burn-in and kept
every $95$-th sample to avoid autocorrelation between the sampled
values. Convergence of the chains was checked through the use of two
chains starting from very different values.

For the uniformly homogeneous case we notice that inspite of the value of $I$ the posterior distribution of $\sigma^2$ and $\phi$ seem to recover the true values used to generated the data. On the other hand, the value of $I$ seems to have influence on the magnitude of the ranges of the 95\% posterior credible intervals  of the disaggregated curves $\alpha_c(\cdot)$ (Figures \ref{fig:alphaUni} and \ref{fig:histUni}).

\begin{figure}[!h]
\begin{center}
\includegraphics[width=13cm]{alphaUniJ1Crop.ps}
\caption{Summary of the posterior distribution of the parameters for
  the uniformly homogeneous case with $J=1$, $I=10$ (first column) and
  $I=30$ (second column).  Posterior mean curves (solid lines) and
  limits (shaded area) of the 95\% posterior credible
  intervals. Dashed lines represent respective true
  values.} \label{fig:alphaUni}
\end{center}
\end{figure}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=13cm]{histUniJ1Crop.ps}
\caption{Summary of the posterior distribution of the parameters for
  the uniformly homogeneous case with $J=1$ and $I=10$ (first row) and
  $I=30$ (second row). Posterior distribution of $\sigma^2$ and and
  $\phi$. Dashed lines represent respective true
  values.} \label{fig:histUni}
\end{center}
\end{figure}

For the homogeneous case, even with only $J=15$
replicates, the model is able to recover the true structure of the
disaggregated functions $\alpha_1(.)$ and $\alpha_2(.)$.
The posterior mean of both curves are very close to their respective
true values and the range of the 95\% posterior credible intervals
are relatively narrow.  The parameters in the covariance structure
are also well estimated (Figure \ref{fig:GRhom}).

\begin{figure}[!h]
\begin{center}
\includegraphics[width=15.0cm]{SummaryJ15Homo.eps}
\caption{Summary of the posterior distribution of the parameters for
the homogeneous case with $J=15$.  Posterior mean curves (solid
lines) and limits (shaded area) of the 95\% posterior credible
intervals (1st row), posterior distribution of $\sigma_1^2$ and
$\sigma_2^2$ (2nd row), and $\phi_1$ and $\phi_2$ (3rd row). Dashed
lines represent respective true values.} \label{fig:GRhom}
\end{center}
\end{figure}

For the heterogenous case it is clear that the number of replicates
affect the range of the posterior credible intervals both for
$\alpha_c(.)$ and $\eta_c(.)$, $c=1,2$. Regardless of the value of $J$
the true values are recovered from the inference procedure, specially
for the disaggregated functions $\alpha_c(.)$ . The greater the number of
replicates the narrower the 95\% posterior credible intervals (Figures
\ref{fig:mediasNP} and \ref{fig:etasNP}). The true values of the decay
parameters $\phi_1$ and $\phi_2$ are also recovered from the inference
procedure, and similar to the results for $\alpha_c(.)$ and
$\eta_c(.)$, the magnitude of $J$ influences the range of the
posterior credible intervals (Figure \ref{fig:corr}).

\begin{figure}[!h]
\begin{center}
\includegraphics[width=15.0cm]{SummaryAlpha.eps}
\caption{Posterior mean curves (solid lines) and limits (shaded
  area) of the 95\% posterior credible intervals for (a)
  $\alpha_1(.)$, $J=15$, (b) $\alpha_2(.)$, $J=15$, (c) $\alpha_1(.)$,
  $J=50$, (d) $\alpha_2(.)$, $J=50$, (e) $\alpha_1(.)$, $J=150$, (f)
  $\alpha_2(.)$, $J=150$. In all panels the dashed line is the
  respective true curve.} \label{fig:mediasNP}
\end{center}
\end{figure}

\begin{figure}[!h]
\begin{center}
\includegraphics[width=15.0cm]{SummaryEta.eps}
\caption{Posterior mean (solid line) of the variance functions
  $\eta_1(.)$ and $\eta_2(.)$ (rows) and limits (shaded area) of the
  95\% posterior credible intervals for the heterogeneous case with
  $J=15$, $J=50$ and $J=150$ (columns). The dashed lines represent the
  true curves used to generate the data.}
\label{fig:etasNP}
\end{center}
\end{figure}

\clearpage

\begin{figure}[!htb]
\begin{center}
\includegraphics[width=8.0cm]{SummaryPhis.eps}
\caption{Posterior summary (solid circle: posterior mean and lines represent the limits of the 95\% posterior credible intervals) of the decay parameters $\phi_1$ and $\phi_2$ in equation (\ref{eq:e3a}). Dashed line represents true value used to generate the data.  \label{fig:corr} }
\end{center}
\end{figure}

\section{Applications \label{sec:realdata}}

\subsection{NIR Spectroscopy data - Polyaromatic hydrocarbons}

The Beer-Lambert law for $K$ constituents plus noise states that for
the $i$th chemical sample the measurement at wavelength $t$ is given
by
\begin{equation}
  \label{eq:modelchemo}
  Y_{i}(t)=\sum_{\ell=1}^{C} r_{\ell,i} \alpha_{\ell}(t) +
  \sum_{\ell=1}^{C} e_{\ell,i}(t), \quad
t \in [220,350], \quad i=1,\ldots,25.
\end{equation}
where $r_{\ell,i}$ is the concentration of the $\ell$ constituent in
the $i$th chemical sample , $\alpha_{\ell}(t)$ is the absorbance at
wavelength $t$ of the $\ell$th pure constituent and $e_{\ell,i}$ is a
random noise.

Notice that the Beer-Lambert formula leads exactly to the functional
model of aggregated data given by Equation \reff{eq:ourmodel}.

In this example, we used 14 B-spline basis with 10 internal knots
equally spaced in the interval (220,350) to estimate the latent absorbance
curves of each constituint, $\alpha_c(\cdot)$.

Since there are no replicates of the population curves available and
we have $C=10$ constituints, we chose to fit the model considering a
homogeneous covariance structure. In this case, we used a gamma prior
for $\phi_c$, and an inverse gamma with parameters 2 and 0.2 for
$\sigma_c^2$, $c=1, \ldots, 10$.  We let the MCMC algorithm run
for 100,000 iterations, considered the first 5,000 as burn-in and kept
every $100$-th sample to avoid autocorrelation between the sampled
values.

 \begin{figure}[!htb]
\begin{center}
   {\includegraphics[width=12.0cm]{AbsorbanceCurvesCrop.eps}}
 \caption{Estimated absorbance curves for the constituints,
   for the PAH dataset under the uniformly homogeneous model.}\label{fig:abs}
 \end{center}
 \end{figure}

Figure \ref{fig:abs} shows the estimated individual curves for each of
the constituints. However, to see how good these estimates are we
should compare the aggregated observed curves with the weighted sum of
these estimates using the Beer-Lambert formula. These comparisons are
made in Figures \ref{fig:comp} and \ref{fig:comppred}. The confidence
bands for Figure \ref{fig:comp} are the quantiles weighted sum of the
estimates whereas  Figure \ref{fig:comppred} compares the data
obtained in some chemical samples with the predictive 95\% confidence
intervals. Both figures show that we have an excelent
fit for the data.

\begin{figure}[!htb]
\centerline{ {\includegraphics[width=7.0cm]{EstimatedCurvesSamplesCrop.eps}}}
\caption{Estimated curves for chemical samples 6, 12 ,21 and 24}
\label{fig:comp}
\end{figure}

\begin{figure}[!htb]
\centerline{ {\includegraphics[width=7.0cm]{PredictiveChemoCrop.eps}}}
\caption{Predictive 95\% confidence intervals for chemical samples 6, 12 ,21 and 24}
\label{fig:comppred}
\end{figure}

\subsection{Electric load data}

Here we analyze electric load data as described in Section \ref{sec:traficload}.
In Brazil, for security reasons, houses are loaded with energy tension
either equal to 127V or 220V. For this reason, they are classified as
monophasic (single phase/ 127V) or biphasic (two phases/220V). Usually, more modest residencies are monophasic
suggesting that monophasic and biphasic consumers have different
typologies. We consider samples observed from $I=2$ trafos which
are denoted by TR07 and TR09.
The market for each trafo is small and
variable, consisting only of single phase and two phase
residential consumers.  The consumption of energy
during weekends is different than from weekdays (Figure \ref{fig:a1}). Therefore, we decide to analyse only the weekdays resulting that $J=5$ replicates.

Measurements from trafos TR07 and TR09 were stored at every 15
minutes, during 5 days of a particular week.  It is known that the electric load
of each trafo $i$ is equal to the sum of $N_i = N_{i1} + N_{i2}$
curves, where $N_{ic}$ is the number of consumers of type $c$ (monophasic or biphasic here), and
$(N_{i1}, N_{i2})$ is the market of trafo $i$. Table
\ref{tab:a1} presents the number of consumers (market) for each trafo.
\begin{table}[!h]
\begin{center}
\renewcommand{\arraystretch}{1}
\begin{tabular}{c|ccc} \hline \hline
Trafo & Single Phase & Two Phase   & Total \\ \hline
TR07      & 87                     & 5                    & 92    \\
TR09      & 25                     & 25                   & 50    \\
\hline  \hline
\end{tabular}
\end{center}
\caption{Distribution of the number of consumers (market) for trafos TR07 and TR09 in the electric load application.}
\label{tab:a1}
\end{table}

Following the general structure in equation (\ref{model1}), we model the traffic load of trafo $i$, at day $j$, observed at time $t$ as
\begin{equation}
  \label{eq:modelelectric}
  Y_{ij}(t)=\sum_{c=1}^{C} \sum_{n_c=1}^{N_{ic}} W_{cj n_c i}(t), \quad
t \in [0,24], \quad i=1,2, \quad j=1,\ldots,5,
\end{equation}
where $W_{c,j,n_c,i}(t)=\alpha_c(t)+\varepsilon_{c,j,n_c,i}(t)$. For this example the constants $r_{ic}$ and $C_{ic}$ (in equations (\ref{eq:e4}) and (\ref{eq:e3a})) coincide and are equal to $N_{ic}$.

We fitted the model assuming 14 B-spline basis, with $K=10$ internal knots located at the following points $\xi=\{4,6,8,10,12,14,16,18,19,20\}$. We fitted the model considering a heterogeneous covariance
structure. The prior specification of $\phi_c$ uses
the idea of practical range as discussed in Section \ref{sec:likel}.
{\em A priori}, we assume the correlation between measurements in a
day dies off, in average, after 3/4 of an hour. We assume a gamma
prior for $\phi_c$ with mean equals $3/0.75=4$, and variance 1.
Panels of figure \ref{fig:a4} show the posterior mean with
respective 95\% posterior credible intervals for the mean  and
variance curves for monophasic and
biphasic consumers. As expected  the single phase houses have a
smaller load than the two phase residencies. Both types have a peak
around 8pm, as this coincides with arriving home from work, taking
showers, etc. The basic difference is that for two phase residencies
there is an increase in the electric load from 8am to 12pm which is
not observed for the single phase consumers.

\begin{figure}[!h]
\begin{center}
{\includegraphics[scale=0.58]{Reais2cAlexCrop.eps}}
\caption{Posterior mean (solid line) and $95\%$ credible intervals
  (shaded area) for monophasic (single phase) and biphasic (two phase)
  consumers based on trafos TR07 and TR09 for the tipologies (first
  row) and variance (second row). The dotted lines in the first row show the
  estimate obtained under the frequentist approach proposed by Dias et
  al (2009). \label{fig:a4}}
  \end{center}
\end{figure}

Figure \ref{fig:repelectric} compares the posterior predictive distribution with the observations.
It is clear that the proposed model is capturing quite well the structure of the data, as most of the observations are within the limits of the
95\% posterior predictive interval.
\begin{figure}[!htb]
\begin{center}
\includegraphics[scale=0.56]{PredictiveElectricLoadCrop.eps}
\caption{Summary of the posterior predictive distribution (solid
  lines) and limits of the 0.025 and 0.975 quantile curves (shaded area)
  compared with the respective observed values (hollow circles), for trafos  TR07 and TR09. \label{fig:repelectric}}
  \end{center}
\end{figure}

\section{Concluding remarks \label{sec:conclusion}}
In this work our attention was focused on the Bayesian estimation of
latent sub-population (disaggregated) mean and covariance curves when
we only have available observations of the population (aggregated)
curves.  Although our proposed models are an extension of the model
initially proposed by \citeasnoun{dias:garcia:martarelli:2009}, we
propose more flexible nonstationary covariance structures for the
Gaussian process by allowing the variance of the process to change
across the domain of the function. The general non-parametric case
naturally imposes the positive definiteness of the covariance function
and can be restricted to accomodate many different situations. We
believe our proposed covariance structure might also be applied in
different areas, e.g. geostatistics.
\newpage

There are several advantages of using the Bayesian
paradigm:
\begin{itemize}
\item  It might naturally incorporate prior information that is available to experts
  in the field;
\item Estimates are obtained under a single framework;
\item and it naturally provides the uncertainties of the estimates of the
  latent sub-population curves, not only of the mean curves but also
  of the covariance curves.
\end{itemize}

To show the strength of our method, we analyzed two examples from
different areas in science: environmetrics and chemometrics.
In both examples it is clear, from comparing the observed
aggregated curves with the weighted sum of the estimated latent ones,
that the proposed model provide extremely reasonable estimates.

redpajama_set_name: RedPajamaArXiv


text:
Yunga cartwrighti är en insektsart som beskrevs av Young 1968. Yunga cartwrighti ingår i släktet Yunga och familjen dvärgstritar. Inga underarter finns listade i Catalogue of Life.

Källor

Dvärgstritar
cartwrighti

redpajama_set_name: RedPajamaWikipedia


text:
GreekReporter.comGreek NewsEconomyIMF's Lagarde: Still a Lot of Work Before Greek Deal
IMF's Lagarde: Still a Lot of Work Before Greek Deal
By Philip Chrysopoulos
Managing Director of the International Monetary Fund (IMF) Christine Lagarde said that there is still a lot of work to be done before Greece signs a deal with international creditors.
Lagarde was interviewed on German television's ARD on Thursday. She was asked about the progress of negotiations between Athens and the three lenders, the IMF, the European Central Bank and the European Commission.
"We are all in the process of working towards a solution for Greece and I would not say that we already have reached substantial results," Lagarde said.
"Things have moved, but there is still a lot of work to do," she added. She stated, however, that she believes Greece would fulfil its commitments to lenders.
The Lagarde statements came in the aftermath of several statements from the Greek government saying that negotiations are at the finish line and Athens is close to an agreement.
Corfu, Homer's Odyssey and Odysseus' Petrified Ship
New Test Could Detect Alzheimer's Years Before Diagnosis
5.9 Earthquake Strikes Off the Coast of Rhodes


text:
Q: Merge data from 2 tables I have two tables, both of which have a KEY and a few columns, I'd like to merge them into a single table when the key is the same
e.g:
Table 1: Key | Attr 1 | Attr 2 | Attr 3
Table 2: Key | Attr 1 | Attr 2 | Attr 4
I'm trying to end up with:
Table 3: Key | Attr 1 | Attr 2 | Attr 3 | Attr 4
I tried using this:
SELECT
  T1.KEY,
  T1.ATTR1,
  T1.ATTR2,
  T1.ATTR3,
  CASE
    WHEN T1.KEY = T2.KEY
    THEN T2.ATTR4
    ELSE 0
   END AS ATTR4
  FROM TABLE_1 AS T1, TABLE_2 AS T2

but for some reason, I get a ton of duplicates

A: I am guessing that you really want a LEFT JOIN:
SELECT T1.*, COALESCE(T2.ATTR4, 0) as ATTR4
FROM TABLE_1 T1 LEFT JOIN
     TABLE_2 AS T2
     ON T1.KEY = T2.KEY


Discussion in 'Archive' started by [GM]Ahri, Apr 9, 2019.
The servers will undergo maintenance and server update on Tuesday (04/09) starting at 18:00 server time. The downtime will be approximately 2 hours.
Apply OX Quiz new schedule. You can find full event details here.
Extend 3rd Anniversary Buff & Gift until April 23rd.
We'll update this post when the maintenance is complete, and servers are available. Additional Patch Notes including improvements and new features will be added after the maintenance.
The maintenance is now over, and servers will be open at 19:15 (7:15 PM PDT) server time.


text:
package jaea.optimization.tools;

import java.util.Random;
/**
 * Class for generating uniformly random numbers, using Random class (Java)
 * @author Le Minh Nghia, NTU-Singapore
 *
 */
public class RandomGenerator {
	Random rd = null;
	Random booleanRd = null;
	/**
	 * Constructor
	 */
	public RandomGenerator()
	{
		rd = new Random(System.currentTimeMillis());
		booleanRd = new Random(System.currentTimeMillis());
	}
	/**
     * Return a INTEGER random number between 0 and < upperBound
     */
    public int getRandom(int upperBound)
    {
        int iRandom = rd.nextInt(upperBound);
        return (iRandom);
    }

    /**
     * return a DOUBLE random number between 0 and < upperBound
     * @param upperBound
     * @return double
     */
    public double getRandom(double upperBound)
    {
        double dRandom = rd.nextDouble()* upperBound;
        return (dRandom);
    }
    /**
     * "Coin Toss" distribution - Return boolean value with probability P for TRUE, 1-P for FALSE
     */
    public boolean coinToss(double P)
    {
    	if (booleanRd.nextDouble() < P)
    		return true;
    	else
    		return false;
    }
}

redpajama_set_name: RedPajamaGithub


Give your skin, and your next selfie, a flawless filter with Laura Geller Filter Fix Baked Correcting Setting Powder. Ultra HD perfecting pigments and skin-brightening apricot pigments blur away imperfections, while the whisper-weight formula hydrates and regulates excess shine so touch-ups and selfie filters are unnecessary.
Laura Geller Filter Fix Baked Correcting Setting Powder leaves skin with a flawless, enhanced finish and sets makeup in place for up to 16 hours. Ultra HD perfecting pigments instantly blur away imperfections while Apricot Nano Pigments brighten dull, lackluster skin. Silica Microbeads absorb excess oils and help regulate shine throughout the day. Hyaluronic Acid hydrates and plumps skin, diminishing the appearance of fine lines. Get ready for flawless photos!
TALC, POLYMETHYLSILSESQUIOXANE, METHYL METHACRYLATE CROSSPOLYMER, SILICA, DIMETHICONE, TOCOPHERYL ACETATE, CENTELLA ASIATICA LEAF EXTRACT, CAMELLIA SINENSIS LEAF EXTRACT, BUTYROSPERMUM PARKII SHEA BUTTER EXTRACT, GLYCERIN, ETHYLHEXYL PALMITATE, CAPRYLYL GLYCOL, SODIUM HYALURONATE, 1,2HEXANEDIOL, DIMETHICONOL, TRIMETHYLSILOXYSILICATE, WATER AQUA,EAU, BUTYLENE GLYCOL, SILICA DIMETHYL SILYLATE, PHENOXYETHANOL, HEXYLENE GLYCOL, YELLOW 6 LAKE CI 19585, CARMINE CI75470.


text:
Q: axis numbers fall outside of the lattice plot in R When I plot my lattice graph, the x-axis value of 100000 falls outside of the plot. I don't want to make the number size smaller. Anything I could do to make this work?
code:
bwplot(dfmh2$Period~dfmh2$Intensity|dfmh2$microhabitat, #temperature difference low over day period
       par.settings = my_settings,
       par.strip.text = list(cex =1.7),
       scales = list(x = list(font=1,cex=2),y = list(cex = 1.8)),
       ylab= list(label = "Period of Day", fontsize = 25), xlab= list(label = "Light intensity", fontsize = 25),
       main= list(label  =  "B) Light intenstiy (lux)", cex= 2))

My plot looks like this now:

A: You could try tuning
> lattice.options("skip.boundary.labels")
$skip.boundary.labels
[1] 0.02


In India the Karnataka States' Biofuel Development Programme is set to get a boost in the form of $50 million dollars from International Fund for Agriculture Development (IFAD). The loan can be utilized in various activities such as plantation of biofuel crops and production.
Biofuel Development Board of Karnataka has been active in promoting biofuels and has established biofuel information and demonstration centres with about 100 l per day capacity in each district. These centres are being scaled up to 150-200 l capacity. The Board also owns a 500 litre biodiesel production plant at Hatti Gold Mines.
The loan conditions include 1% interest with a 50-year repayment period.


text:
Q: Converting a naive datetime column to a new timezone Pandas Dataframe I have the following dataframe, named 'ORDdataM', with a DateTimeIndex column 'date', and a price point column 'ORDprice'. The date column has no timezone associated with it (and is naive) but is actually in 'Australia/ACT'. I want to convert it into 'America/New_York' time.
                    ORDprice
date
2021-02-23 18:09:00 24.01
2021-02-23 18:14:00 23.91
2021-02-23 18:19:00 23.98
2021-02-23 18:24:00 24.00
2021-02-23 18:29:00 24.04
... ...
2021-02-25 23:44:00 23.92
2021-02-25 23:49:00 23.88
2021-02-25 23:54:00 23.92
2021-02-25 23:59:00 23.91
2021-02-26 00:09:00 23.82

The line below is one that I have played around with quite a bit, but I cannot figure out what is erroneous. The only error message is:
KeyError: 'date'
ORDdataM['date'] = ORDdataM['date'].dt.tz_localize('Australia/ACT').dt.tz_convert('America/New_York')
I have also tried
ORDdataM.date = ORDdataM.date.dt.tz_localize('Australia/ACT').dt.tz_convert('America/New_York')
What is the issue here?

A: Your date is index not a column, try:
df.index = df.index.tz_localize('Australia/ACT').tz_convert('America/New_York')

df
#                           ORDprice
#date
#2021-02-23 02:09:00-05:00     24.01
#2021-02-23 02:14:00-05:00     23.91
#2021-02-23 02:19:00-05:00     23.98
#2021-02-23 02:24:00-05:00     24.00
#2021-02-23 02:29:00-05:00     24.04
#2021-02-25 07:44:00-05:00     23.92
#2021-02-25 07:49:00-05:00     23.88
#2021-02-25 07:54:00-05:00     23.92
#2021-02-25 07:59:00-05:00     23.91
#2021-02-25 08:09:00-05:00     23.82


text:
Robert Lee Barker (born 1937) is a psychotherapist, author, editor, and professor of social work.  He is most noted as the creator and author of The Social Work Dictionary through its first five editions and has written 20 other textbooks in the fields of family therapy, behavioral dysfunctions, and legal-social issues.  He was an early advocate and systematizer for the case management approach to delivering social services, for private practice in social work, and for the emerging field of forensic social work.

Biography

Robert Lee Barker was born July 19, 1937 in Tacoma, Washington, the oldest of four children.  His mother worked as a waitress and his stepfather was a prison guard. During college and graduate school he worked in a variety of blue-collar jobs in canneries and paper mills.  In one of those jobs, he was employed in a Veteran's Administration hospital as a psychiatric aide, which inspired his interest in working with people with mental and behavioral distresses.  He graduated in 1959 from the University of Puget Sound in Tacoma, majoring in sociology and psychology before earning his Master of Social Work (MSW) from the University of Washington in Seattle.

In 1961 he became a 2nd Lieutenant in the U.S. Air Force where he worked as a social work officer at Travis Air Force Base.  He was a founder and first president of the Air Force Social Workers Association. The organization later published Barker's pamphlet, "Careers In Air Force Social Work."  In 1969 he completed his military service at Andrews Air Force Base in Washington D.C., attaining the rank of Major.  As part of his military duties in the hospital Department of Psychiatry, he had to personally inform hundreds of families of Vietnam casualties of the deaths of their loved ones.

Under an Air Force Institute of Technology scholarship he attended Columbia University in New York to earn his PhD, where his mentors included Robert K. Merton, Richard A. Cloward, Eveline M. Burns, and Florence Hollis.  In his doctoral dissertation research he studied personnel patterns in mental hospitals.  This work led to a grant from the  U.S. Veterans Administration to determine how to utilize social work personnel more efficiently.  His dissertation work led to his first published book, Differential Use of Social Work Manpower. In collaboration with Professor Thomas L. Briggs of Syracuse University, Barker wrote a series of books and monographs to deal with shortages in mental health personnel through more efficient intervention strategies, including teamwork and case management approaches.

In 1969 Barker co-founded, with psychiatrist-psychoanalyst Karl D. Hawver M.D., the Potomac Psychiatric Center in the Washington D.C. suburbs.  The clinic focused on treating individuals and families with mental health problems and family relationship issues.  Barker specialized in family therapy, couples therapy, and group psychotherapy.  In the clinic's Capitol Hill office in Washington, Barker treated the families of many U.S. Members of Congress and other government officials.

In 1979, Barker joined the faculty of The Catholic University of America, where he taught master's and doctoral students and guided their dissertation researches. During this time he wrote over 100 articles in professional journals, created and edited the Journal of Independent Social Work from 1986–1991, and produced textbooks on couples therapy.  He was consultant to the Ladies Home Journal column "Can This Marriage Be Saved" in 1987 through 1989 and its counselor-expert.  He wrote a best selling book "The Green Eyed Marriage" which led to his conducting a series of workshops for people and their families with jealousy problems.  Together with faculty at Catholic University he helped establish two new schools of social work in Santiago and Valparaíso, Chile, and he taught courses at the Escuela de Trabajo Social at the Pontificia Universidad Católica de Valparaíso for three years beginning in 1988.

Since 1990 he has focused his career to the development of The Social Work Dictionary and other publications.  He has also worked extensively as a consultant to organizations that write questions for professional state licensing boards, to testifying in courtrooms about family and custody issues, and as a researcher and advocate for homeless persons.

Barker is married to Dr. Mary Elizabeth Donovan, formerly of the education faculty at the University of Puget Sound. They have three sons and one daughter.

Case management innovations

Early in Barker's career in the 1960s, President Lyndon Johnson's Great Society programs necessitated tremendous increases in the numbers of social service and mental health workers.  The National Association of Social Workers (NASW) was awarded grants from government agencies to help find ways to remedy these shortages. Barker and Thomas Briggs were employed to conduct and administer these studies.  They observed numerous state and federal institutions and experimented with different ways staff members could help hospitalized clients and their families.  The Barker-Briggs model of using teams to provide these services was later used as a template for case management approaches is still used by the U.S. Department of Veterans Affairs, known as the Veteran's Administration at the time, and by many state mental hospital staffing patterns.  As originated, the model replaced the primary one-on-one relationship between client and helping professional with a team approach.  The leader of the team, usually a professional social worker or registered nurse assigned specific tasks to a staff of several ancillary workers.  The ancillary workers were experts in their own right at providing for the specific needs of the client.  For example, one worker could specialize in helping clients get jobs, or helping clients access post-discharge resources in the community.  The implication was that such clients needed help not only with psychotherapy or counseling but with life-skills problems, and when met, the client's psychotherapy goals were achieved more efficiently and effectively.

Private practice

Members of the social work profession have debated for decades about whether its mission is compatible with private practice.  Opponents of private practice argue that social workers should only be employed by governmental agencies or charitable organizations, and deal primarily with clients who are economically disadvantaged.  When Barker established his clinic in 1969 almost all of his social colleagues were employed by charity oriented.  He conducted workshops in private practice and a series of debates with social work advocates of the agency based model.  Eventually, more social workers entered private practice and it has become one of the primary ways these professionals are now employed.

Crisis intervention theory in couples therapy

When Barker left the military to establish his private practice he had been greatly influenced by the studies of Vietnam War veterans who suffered Post Traumatic Stress Disorder (PTSD) and related works about crisis intervention with PTSD victims.  He concluded that, while the severity of the trauma in Vietnam might be greater, the crisis facing dysfunctional family members could have similar consequences and might benefit from similar intervention strategies. He conducted a series of systematic research studies with such family members and, with several colleagues used an adapted version of the crisis intervention PTSD model to treat troubled families. Treating Couples In Crisis, has been subsequently used as an instructional textbook for graduate students in marital therapy classes.

The Social Work Dictionary

In the early 1980s Barker served on several panels of social work experts who wrote the questions and answers for the state licensing board examinations.  Many of these panels resulted in disagreements about what social workers actually mean when they use their unique terminology.  The researchers who conducted these panels wondered why the social work profession could not resolve disputes simply by consulting the dictionaries of their profession's nomenclature.  However, up to that point, the social work profession did not have such a dictionary and had never developed one of its own.  With most of the states in the process of developing professional licensing boards for social workers for the first time, the need for a uniform professional nomenclature and glossary became urgent.

With the help of the National Association of Social Workers, the major association of the profession, Barker called on hundreds of experts in the field and in related disciplines, to assist his efforts to create a dictionary.  Barker developed the list of the terms to be included in the Dictionary by reviewing the indexes of all the textbooks and journals used in the profession, and in related professions such as psychology, psychiatry, economics, administration, medicine, and other fields.  He then wrote succinct definitions for several thousand terms from this list.  A selection of these definitions was submitted to experts for corrections and clarifications. Eventually every term and definition had been reviewed by at least three experts before a final definition was established. Before publication, each of these definitions was reviewed for clarity and comprehensibility by graduate students in several of the schools of social work in the Washington, D.C. area.

The result was the original social work dictionary, first published by NASW in 1987 with about 4,000 terms defined.  With each revision, in 1991, 1995, 1999, and 2003 about 2000 additional definitions were added; the current edition has nearly 10,000 definitions in 493 pages.  The dictionary also contains thousands of acronyms commonly used in the profession, and a timeline of the historical events in the development of the profession.

The dictionary is now the definitive reference resource in the profession, used in agencies, universities, and social work organizations throughout the world.  It has been called  "a landmark in the continuing professionalization of social work—the development of a distinctive and unique vocabulary and the development of consensus by social work consultants (scholars and practitioners) on key terms."

Homeless advocacy

Perhaps because of his own humble origins, Barker has always had a strong interest in the problems of homelessness.  His close friendship and work with the famous urban anthropologist Elliot Liebow, author of "Tally's Corner" and " Tell Them Who I Am: The Lives of Homeless Women," motivated him to speak and write about problems of the homeless.  In 1989 he devoted several months to living as a homeless person in several cities throughout the United States.  He conducted extensive interviews with "other" homeless persons, and sent the findings by mail to Liebow.  These correspondences formed the basis of a series of lectures about homelessness given by Liebow and Barker to various government agencies, universities, and civic groups.

Forensic social work

After Barker retired from The Catholic University to devote more time to the dictionary and to homeless advocacy, he testified as an expert witness in courtroom trials, primarily involved in family dissolution disputes and custody issues. He conducted workshops for social workers on how to prepare for courtroom testimony and to conduct forensic investigations to be used in legal proceedings.  He developed a curriculum for universities for a new specialty, forensic social work, and with lawyer Douglas Branson of the University of Pittsburgh School of Law, published the first text on the subject, " Forensic Social Work", now in its second edition. This text is now used in many schools of social work for their courses on forensics and legal issues.

References

1937 births
Living people
American psychotherapists
American sociologists
University of Puget Sound alumni
University of Washington School of Social Work alumni
Columbia University School of Social Work alumni
National Catholic School of Social Service faculty
Writers from Tacoma, Washington


GREE Forum > Forums > Crime City > General > Is there any difference between armor and defense buildings?
View Full Version : Is there any difference between armor and defense buildings?
CC Mark You've said more then enough on these various subjects. Let the players do their research in the Forum archives. It's their homework shall we say.
I think that when you get attacked, your building defense total gets halved for it and when you get robbed, your armor defense total gets halved for that hit.
on par with oldest necro ever. wtg!
Shall we dig up a M4 thread now?


Set oven to 200°C or gas mark 6. Line a roasting tin with a non-stick Teflon sheet. Separate sausages and arrange in the tin. Roast for 30 mins (turning once), until brown.
Meanwhile, put the potatoes, parsnips and apples into a pan of salted water. Cover, bring to the boil and simmer for 15 mins.
Drain potatoes. Return to pan. Keep heat on gently to dry out potatoes for 1 min. Add milk and butter. Turn off heat. Mash apples, potatoes and parsnips until smooth.
Season and stir in nutmeg and parsley. Serve potatoes with sausages, and cranberry and caramelised red onion chutney.
Pan-fry apple slices in a nonstick pan for 1 min, turn and cook until golden. Add slices to plates, and garnish with a sprig of parsley, if you like.


We aim to offer customers a selection of genuine antique maps and topographical prints, in all price ranges, to meet their personal requirements whether for their own collection or for gifts. We hope you enjoy our catalogue and please do contact us if we can be of any assistance.
Customers are encouraged to make full use of our approval service to inspect items at leisure before deciding whether to keep them. We feel that no matter how good the description and illustration, there is no substitute for visual inspection.
All items are treated as 'on approval' for a period during which they may be returned if not entirely satisfactory. Please see below for information about Returns.
The catalogue offers a good selection from our stock. It does not, however, show everything we have so please let us know if you are looking for an item that is not listed. We may have one or be able to find one, although this can take some time.
A button on the Item Details page for each item allows you to add it to Your Enquiry List which can then be used as the basis of an enquiry or an order.
In most cases we have only one copy of the items in the catalogue so they are offered subject to being unsold. Whilst we attempt to update our catalogue regularly, there will always be items which have been sold or are on approval with another customer.
If you would like to enquire about or order one or more items from our catalogue please contact us by post, telephone or email.
We will need the reference number for each item, as shown in the catalogue, and your contact details. For an order, we will also need the name and address for posting and either a cheque or card details to cover the cost.
If you use the facility in the catalogue to select onto Your Enquiry List, this can then be used as the basis for our email Enquiry Form or our printable Order Form, and item descriptions, references and prices are filled in automatically.
If you prefer to print out a blank Order Form, you can find it here.
The Order Form is designed to be printed and sent by post. For reasons of security for card information, it is not to be saved on your computer or transmitted by email.
We can, of course, take orders by telephone.
If you order an item which is not available we will return the money or not take card payment for it.
Payment must be made in £ sterling either by personal cheque payable to 'Antique Maps and Prints' or by Visa, MasterCard or Maestro.
As explained above, to avoid security risks with card information, we are set up to take orders and payment by post or telephone but not email.
For customers based outside the UK, card payments may not clear our security procedures so please pay by sterling cheque drawn on a UK bank or contact us to make alternative payment arrangements.
For UK orders under £75 there is a charge of £5 towards postage and packaging costs but no charge is made for orders of £75 or over.
All overseas orders are subject to a charge of £10 towards postage and packaging - please adjust the UK Packing Charge and the Total to Pay by hand on the Order Form.
Most items are presented in a display mount for protection and to give an impression of how they might look when mounted and framed. They are then packed against hardboard. Large items are packed in a cardboard tube.
Delivery is by insured post which is also recorded.
This combination of packaging and delivery works well and problems are rare.
If you decide to return any items to us we recommend you use the same protective packaging and insured post – that way it is very unlikely that there will be a problem with safe return.
All items are treated as on approval for a period. Any items you do not wish to keep should be returned well packed by insured post and on receipt of them in good condition we will refund the purchase price in full (but excluding any postage / packaging charge). They should be posted within 20 days of our despatch date to you (within 30 days for overseas customers). Our use of a P.O.Box ensures that safe return is not dependent on our availability to receive deliveries and in practice this works very well.
We hold the name, address and contact details of customers and potential customers together with their interests in particular subjects or specific maps or prints.
We do not divulge this information to any other parties. We use it to respond to your queries and occasionally for instance, to inform you that our catalogue has been updated. We will not send you frequent emails or letters.
Where you provide credit or debit card details they are used for the transaction in question only and are not stored on our computer systems.
Items are as described in our catalogue. We do not stock modern copies or modern retakes.
Errors do occur but they are rare. If ever you have any questions or doubts please ask and we will always do our best to provide answers.
Items were published or on about the date stated in the catalogue. Generally the dates are known fairly precisely but in some cases the dates are unknown and we provide an estimate.
The illustrations in the catalogue give an overall impression of the map or print but photographs presented on a screen do have their limitations. Colour reproduction is sometimes not true from the camera and additionally customers screen settings vary greatly. Two copies of the same map or print can also show colour variation. Probably the biggest limitation is the loss of any feel for the texture and age of an item. These are all good reasons why customers should see items physically before deciding whether to keep them.
The description page for an item shows its size. The sizes are to the nearest centimetre width first, to about where the item might be mounted. The screen images do not attempt to reproduce actual sizes; for instance, a small print will be shown taking up screen area similar to that of a large map.


text:
Q: Android Studio - How to put Buttons in a ListView I have a problem. I want to put Buttons in a listview but I don't know how to do that. I searched a lot but I found nothing. The major problem is to have a button for each elements of the ListView. I think I have to precise that I'm a very beginner so If it's really hard I will not understand very well.
NB: Sorry for my bad english ;)


text:
In mathematics, a subset of a given set is closed under an operation of the larger set if performing that operation on members of the subset always produces a member of that subset. For example, the natural numbers are closed under addition, but not under subtraction:  is not a natural number, although both 1 and 2 are.

Similarly, a subset is said to be closed under a collection of operations if it is closed under each of the operations individually.

The closure of a subset is the result of a closure operator applied to the subset. The closure of a subset under some operations is the smallest superset that is closed under these operations. It is often called the span (for example linear span) or the generated set.

Definitions
Let  be a set equipped with one or several methods for producing elements of  from other elements of .
A subset  of  is said to be closed under these methods, if, when all input elements are in , then all possible results are also in . Sometimes, one say also that  has the .

The main property of closed sets, which results immediately from the definition, is that every intersection of closed sets is a closed set. It follows that for every subset  of , there is a smallest closed subset  of  such that  (it is the intersection of all closed subsets that contain ). Depending on the context,  is called the closure of  or the set generated or spanned by .

The concepts of closed sets and closure are often extended to any property of subsets that are stable under intersection; that is, every intersection of subsets that have the property has also the property. For example, in  a Zariski-closed set, also known as an algebraic set, is the set of the common zeros of a family of polynomials, and the Zariski closure of a set  of points is the smallest algebraic set that contains .

In algebraic structures
An algebraic structure is a set equipped with operations that satisfy some axioms. These axioms may be identities. Some axioms may contain existential quantifiers  in this case it is worth to add some auxiliary operations in order that all axioms become identities or purely universally quantified formulas. See Algebraic structure for details.

In this context, given an algebraic structure , a substructure of  is a subset that is closed under all operations of , including the auxiliary operations that are needed for avoiding existential quantifiers. A substructure is an algebraic structure of the same type as . It follows that, in a specific example, when closeness is proved, there is no need to check the axioms for proving that a substructure is a structure of the same type.

Given a subset  of an algebraic structure , the closure of  is the smallest substructure of  that is closed under all operations of . In the context of algebraic structures, this closure is generally called the substructure generated or spanned by , and one says that  is a generating set of the substructure.

For example, a group is a set with an associative operation, often called multiplication, with an identity element, such that every element has an inverse element. Here, the auxiliary operations are the nullary operation that results in the identity element and the unary operation of inversion. A subset of a group that is closed under multiplication and inversion is also closed under the nullary operation (that is, it contains the identity) if and only if it is non-empty. So, a non-empty subset of a group that is closed under multiplication and inversion is a group that is called a subgroup. The subgroup generated by a single element, that is, the closure of this element, is called a cyclic group.

In linear algebra, the closure of a non-empty subset of a vector space (under vector-space operations, that is, addition and scalar multiplication) is the linear span of this subset. It is a vector space by the preceding general result, and it can be proved easily that is the set of linear combinations of elements of the subset.

Similar examples can be given for almost every algebraic structures, with, sometimes some specific terminology. For example, in a commutative ring, the closure of a single element under ideal operations is called a principal ideal.

In topology

In topology and related branches, the relevant operation is taking limits.  The topological closure of a set is the corresponding closure operator.  The Kuratowski closure axioms characterize this operator.

Binary relations
A binary relation on a set  can be defined as a subset  of  the set of the ordered pairs of elements of . The notation  is commonly used for  Many properties or operations on relations can be used to define closures. Some of the most common ones follow:

Reflexivity
A relation  on the set  is reflexive if  for every  As every intersection of reflexive relations is reflexive, this defines a closure. The reflexive closure of a relation  is thus
Symmetry
Symmetry is the unary operation on  that maps  to  A relation is symmetric if it is closed under this operation, and the symmetric closure of a relation  is its closure under this relation.
Transitivity
Transitivity is defined by the partial binary operation on  that maps  and  to  A relation is transitive if it is closed under this operation, and the transitive closure of a relation is its closure under this operation.

A preorder is a relation that is reflective and transitive. It follows that the reflexive transitive closure of a relation is the smallest preorder containing it. Similarly, the reflexive transitive symmetric closure or equivalence closure of a relation is the smallest equivalence relation that contains it.

Other examples
 In matroid theory, the closure of X is the largest superset of X that has the same rank as X.
 The transitive closure of a set.
 The algebraic closure of a field.
 The integral closure of an integral domain in a field that contains it.
 The radical of an ideal in a commutative ring.
 In geometry, the convex hull of a set S of points is the smallest convex set of which S is a subset.
 In formal languages, the Kleene closure of a language can be described as the set of strings that can be made by concatenating zero or more strings from that language.
 In group theory, the conjugate closure or normal closure of a set of group elements is the smallest normal subgroup containing the set.
 In mathematical analysis and in probability theory, the closure of a collection of subsets of X under countably many set operations is called the σ-algebra generated by the collection.

Closure operator

In the preceding sections, closures are considered for subsets of a given set. The subsets of a set form a partially ordered set (poset) for inclusion. Closure operators allow generalizing the concept of closure to any partially ordered set.

Given a poset  whose partial order is denoted with , a closure operator on  is a function  that is increasing ( for all ), idempotent (), and monotonic ().

Equivalently, a function from  to  is a closure operator if  for all

An element of  is closed if it is its own closure, that is, if  By idempotency, an element is closed if and only if it is the closure of some element of .

An example of a closure operator that does not operate on subsets is given by the ceiling function, which maps every real number  to the smallest integer that is not smaller than .

Closure operator vs. closed sets
A closure on the subsets of a given set may be defined either by a closure operator or by a set of closed sets that is stable under intersection and includes the given set. These two definitions are equivalent.

Indeed, the defining properties of a closure operator  implies that an intersection of closed sets is closed: if  is an intersection of closed sets, then  must contain  and be contained in every  This implies  by definition of the intersection.

Conversely, if closed sets are given and every intersection of closed sets is closed, then one can define a closure operator  such that  is the intersection of the closed sets containing .

This equivalence remains true for partially ordered sets with the greatest-lower-bound property, if one replace "closed sets" by "closed elements" and "intersection" by "greatest lower bound".

Notes

References

Set theory
Closure operators
Abstract algebra


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27' Round Caribbean Overlap Pool Liner-20 Mil. At SPP , our Aboveground Pool Liners are made from the finest 100% virgin vinyl, and will stand up to years of wear & weather. The overlap liner is the most common type of aboveground pool liner.
Your liner simply folds over the corrugated metal wall and drapes down on the outside of the wall. It is held in place by plastic coping strips. Features of our SPP liner. Will work with either 48" or 52" Constant Depth swimming Pool. Will not work in expandable swimming pool.
Don't see your size liner, Give SPP a call! Standard 20 mil Above Ground Vinyl Material. Once the liner has been taken out of the box, the liner is not returnable. Please make sure you measure your pool before purchasing the liner.
We like to measure at the bottom of the wall in case the wall is not plumb from side to side. The wall at the bottom track location is your safest bet. On an Oval pool you do the same thing as a round except that you do it in the middle of the pool from side to side and at the ends at the longest point from end to end. All measurements are from inside the pool touching the wall at the base. On Rectangular pools like a Kayak® you measure from side to side and end to end in the middle location of the corresponding rectangle. In rectangular pools we also need to know the corner shape. Is it square 90-degree corners, radius (rounded) corners, or diagonal (45 degree) angle corners? We need to know the measurement of the radius and the diagonal to better fit your liner.
Depth of the pool can range from 36" to 54" deep. Most liners are for 48" or 52" sidewall pools. Our manufacturers also make provisions for the dirt, sand, wedge, or pool cove that is needed at the base perimeter inside the pool.
If your pool has water in it measure out at least 2 ft. From the sidewall with a measuring tape to the point at the top of the wall or where the liner is attached. Bear in mind that most round liners are made to be flat bottom and not a deeper middle. If your pool has a deeper area please contact one of our representatives to discuss. Some liners are what we call overlap.
Most pools can utilize the standard bead that is common in the industry. Better to be safe than sorry. Incidentally, you can change your overlap liner to accept a beaded liner by simply adding bead receiver strips to the order. This way, if you need to change the liner in the future, you do not have to remove the top seats of the pool. This is a real timesaver and is much easier to reinstall. J-Hook-V-Bead are liner types that have a thicker open flap top that inserts over the corrugated metal wall. It looks likes the plastic coping we use to hold an overlap liner over the metal wall except that, in this case, it is attached to the top of the liner. If you are using an overlap liner and your pool is a flat-bottom, you can use the V-Hook or the J-Hook type liner. Note: This information is intended to answer many questions you may have regarding the type and size liner you may need. We're happy to help! Customers who have shopped with us before can tell you - Specialty Pool Products offers the finest, most innovative and most effective items for your pool, spa, backyard and home. We only sell products that meet our strict standards for quality, function and value. Specialty Pool Products also promises you. We are unable to make changes or cancellations to orders after they are placed.
The item "27' ft Round Overlap CARIBBEAN Above Ground Swimming Pool Liner-20 Mill" is in sale since Wednesday, February 26, 2014. This item is in the category "Home & Garden\Yard, Garden & Outdoor Living\Pools & Spas\Pool Equipment & Parts\Pool Liners".com" and is located in United States. This item can be shipped to United States.