text:
Advertising on our site helps support our mission. We do not endorse non-CTCA products or services.
Speak up: The chemotherapy patient's first step toward finding relief from treatment-related nerve damage
May 17, 2016 | by CTCA
When vulnerable nerves far from the brain and spine become damaged by drugs meant to attack cancer, it may signal a need for a dose change.
Chemotherapy is known for causing a number of side effects that may affect patient's quality of life. Many of them, like fatigue, nausea and hair loss, are often temporary. Peripheral neuropathy is different. Characterized by nerve damage that may impair patients' ability to walk, maintain balance, hold objects and perform other key functions, it has the potential to become permanent, affecting not only patients' quality of life but, sometimes, their ability to continue treatment.
Nerve damage may affect patients in a number of ways—triggering pain, numbness, tingling sensations, reduced fine-motor skills and mobility limitations, for example. Addressing these symptoms the moment they flare may help prevent them from worsening and compounding patients' physical and mental challenges, says Shayma Kazmi, MD Medical Oncologist and Hematologist-Oncologist at our Philadelphia hospital. Still, some patients are hesitant to open up, for fear of "bothering" others with their complaints, so they suffer silently.
Talk to your doctor
Dr. Kazmi says it's important that doctors hear from patients about all their symptoms—from difficulty picking up coins or buttoning a shirt to limited reflexes and sensitivity to cold or heat. Even seemingly minor changes, like tingling in the fingertips, deserve mention and attention, Dr. Kazmi says, because they may signal more serious issues to come. They may also be an indication that the chemotherapy dose, timing or duration may need to be adjusted. "Never feel, 'This is just normal.' Always speak up about it," Dr. Kazmi says.
What the medical world refers to as chemotherapy-induced peripheral neuropathy (CIPN) is caused when vulnerable nerves far from the brain and spine become damaged by drugs meant to attack cancer. Symptoms of CIPN may depend on the type of nerves affected. Most often, symptoms develop equally on both sides of the body, usually affecting the hands and feet. They may include shooting and stabbing pains, pin-prick sensations, cold sensitivity or numbness, indicating sensory nerve damage. Less common feelings of weakness or imbalance may signify damage to motor nerves, while constipation or dizziness may indicate damage to autonomic nerves. Often, CIPN symptoms appear slowly and may worsen over time. Acute CIPN, on the other hand, may develop suddenly, then subside.
"If there is numbness to the point where I cannot pick up my coffee cup anymore, numbness where I am tripping, losing my balance? We're getting to moderate and severe CIPN," Dr. Kazmi says. "At some point, it may become irreversible and permanent."
Who's at risk
The risk of developing peripheral neuropathy may be higher for patients who take stronger chemotherapy doses for a longer period of time, are older, have diabetes or use tobacco. Genetics and nutritional deficiencies may play a role, too. The drugs most commonly associated with CIPN are those in the taxane family, such as paclitaxel, and platinum-based drugs, including cisplatin, oxaliplatin and carboplatin—all first-line chemotherapy drugs for breast, ovarian and colorectal cancers. Alkaloids like vincristine, which is often used to treat lymphoma, have also been associated with peripheral neuropathy.
Besides changing how the drugs are administered, a variety of supportive therapies may help prevent and manage severe CIPN. Therapies that may help address pain include supplements and other naturopathic remedies, prescription pain relievers and antidepressants, acupuncture, massage and meditation. Physical therapy may help cancer patients adapt to balance impairments and other challenges that may result from sensory changes, says Carolyn Lammersfeld, Vice President of Integrative Medicine at Cancer Treatment Centers of America® (CTCA). "The most important message is that the minute you have any numbness or tingling, speak up."
Learn more about how integrative care can help cancer patients manage peripheral neuropathy.
Available 24/7 to discuss treatment options
Call us today Chat online now
Integrative cancer treatment's role in the whole-patient journey
Using integrative therapies to help manage side effects of cancer treatment
Dangerous drug interactions: Common medicines to avoid while undergoing oral chemotherapy

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Setting up logging with PHP official docker image I'm using the official PHP docker image but don't quite know how to setup logging to work. I want to view my error_log() results in a file.
Update: I renamed /usr/src/php/php.ini-development to /usr/src/php/php.ini but I only see truncated logs using docker logs.

redpajama_set_name: RedPajamaStackExchange


text:
\section{Introduction}

{T}{raditionally} the bulk of the responsibility of maintaining the (real-time) balance between load and generation has rest upon the conventional generators, e.g. spinning reserves, which provide various forms of grid ancillary services such as inertia support, regulation and ramping. As the power systems transition towards a greener grid with larger penetration of renewable generation, a large fraction of which is expected to be \textit{distributed}, there is a general consensus that various forms of distributed energy resources (DERs), including flexible and responsive electrical loads, need to be coordinated and controlled in real-time to provide grid support. This requires an appropriate understanding of the loads behavior, including their physical models, at the details useful for real-time coordination. It is important that such models capture the necessary information, such as the associated dynamics (thermal dynamics of a residential air-conditioner), measure of the available flexibility (reactive power capacity of a grid-connected inverter), the end-user constraints (desired state-of-charge of an electric vehicle battery), etc., while being tractable for real-time operation.

Modeling of an ensemble of flexible loads for ancillary services (in particular, frequency regulation and ramping) have been explored in the literature in recent years \cite{Callaway:2009, Kundu:2012CDC, Perfumo:2012, Mathieu:2013, Zhang:2013, Hao:2015, Sanandaji:16, Zhao:2016}. The methods proposed in these articles are applicable to ensembles of similar loads (albeit with heterogeneous parameters), such as a collection of residential air-conditioners, or a collection of plug-in electric vehicles. Such types of aggregate flexibility models are suitable for a transmission system operator which views the net demand flexibility available at the distribution-level as a lumped-model. Aggregation at this level (tens of thousands of loads) do not explicitly take into account the operational constraints (line-flow and voltage limits) at the mid/low-voltage distribution systems. As the fraction of flexible loads increase, however, chances of violation of operational constraints due to control of flexible demand will increase.

In order to efficiently coordinate tens of thousands of flexible loads in distribution systems, while also satisfying line-flow and node voltage constraints, hierarchical modeling and control frameworks \cite{Callaway:2011,Bernstein:2015} become attractive. Load aggregators, referred to as \textit{aggregate device controller} (or ADC), help in keeping the size of control problem tractable by aggregating the neighboring DERs locally. This aggregation can be done at the level of a couple of service transformers (tens of residential customers). It is the responsibility of the ADC to capture the aggregated flexibility, in terms of active and reactive power, of the local DERs which are likely to be of different types (e.g. a collection of air-conditioners, electric water-heaters, batteries, solar photovoltaic inverers wind inverters) and ratings.

The rest of the paper is organized as follows. In Section\,\ref{S:problem} we describe the problem of aggregating flexibility of heterogeneous DERs. Section\,\ref{S:back} presents some key concepts that form the basis of our work. In Section\,\ref{S:method} we discuss in details the geometric programming approach to the aggregation of flexibility, while exploring the metrics of quality of approximation in Section\,\ref{S:metric}. Numerical results illustrating the concept are presented in Section\,\ref{S:result}, before concluding the article in Section\,\ref{S:concl}.

\section{Problem Description}\label{S:problem}

Consider a hierarchical distribution system operation framework in which a distribution system operator (DSO) communicates with aggregate device controllers (ADCs) at every control period and solves an optimal dispatch problem to schedule the DERs. It is assumed that the ADCs are so placed that the operational constraints (line-flow and voltage limits) are trivially satisfied at the ADC-level. The primary responsibilities of the ADC are two-fold: 1) before the start of each control period (5-15\,min), the ADC estimates the net flexibility (in active and reactive power) available among the DERs under its control, and exchanges that information to the DSO; 2) during the control period, the ADC coordinates the DERs in real-time to track the active and reactive power set-points dispatched by the DSO. In this paper we restrict our discussion only on the first part, i.e. the problem of estimating the net flexibility in a group of (dissimilar) DERs.

\begin{figure*}[thpb]
\centering
\captionsetup{justification=centering}
\subfigure[batteries]{
\includegraphics[scale=0.35]{battery.eps}\label{F:battery}
}
\hspace{0.1in}
\subfigure[switching loads]{
\includegraphics[scale=0.35]{hvac.eps}\label{F:hvac}
}
\hspace{0.1in}
\subfigure[PV inverters]{
\includegraphics[scale=0.35]{pv.eps}\label{F:pv}
}
\hspace{0.1in}
\subfigure[wind inverters]{
\includegraphics[scale=0.35]{wind.eps}\label{F:wind}
}
\caption[Optional caption for list of figures]{Representation of continuous and discrete flexibility domains for an individual DER of certain types.}
\label{F:domains}
\end{figure*}
For the purpose of this article, any energy (consuming or generating) resource which offers certain flexibility in active ($p$) and/or reactive ($q$) power, possibly over a reasonably short time window (such as a 5-15\,min long control period), is considered as a DER. We use the notation $\mathcal{F}$ to represent the flexibility domain as a collection of $(p,q)$-points that are physically admissible by the DER (possibly via some local device-level control). Note that the flexibility domain ($\mathcal{F}$) could be a continuous or a discrete domain. For example, a solar photovoltaic (PV) inverter that can modulate its active and reactive power over a continuous range will have a continuous flexibility domain, while the flexibility domain for switching loads, such as an air-conditioner or electric water-heater, will be discrete. Moreover this flexibility is time-varying, and depends on exogenous parameters as well as end-user preferences.

Fig.\,\ref{F:domains} shows examples of flexibility domains for certain types of DERs, with positive (negative) values of $p$ and $q$ denoting consumption (generation). Discrete flexibility domain of a switching load (e.g. air-conditioner) that operates in two discrete operational states (`on' and `off') is shown in Fig.\,\ref{F:hvac}, while the rest of the plots represent continuous flexibility domains. Batteries (Fig.\,\ref{F:battery} offer full four-quadrant flexibility, while PV (Fig.\,\ref{F:pv}) and wind (Fig.\,\ref{F:wind}) inverters offer flexibility only on the left half-plane (active power generation). It must be noted that the flexibility offered by the DERs is dynamic, and change based on end-usage and exogenous influence. For example, if there is a cloudy sky, the PV inverter output might only be restricted to a small fraction of its rated generation. Similarly, the air-conditioner may be forced to operate mostly in `on'-state, if the outside air-temperature is high. Finally, the flexibility domains should be able to capture DER uncertainties, which could be modeled in the robust sense via a conservative estimate of the available flexibility.

In this article, we will focus our discussion on the challenges of aggregating the flexibility of a heterogeneous mix of DERs at the ADC, while the issues regarding the dynamic evolution of flexibility and the associated uncertainties will be addressed in future work. Let us assume that there are $N$ DERs with an ADC. The flexibility domain of the $i$-th DER is denoted by $\mathcal{F}_i$\,, such that its active and reactive power consumption (with negative value signifying net generation)
\begin{align*}
(p_i,q_i)\in\mathcal{F}_i\,,\quad i\in\lbrace 1,2,\dots,N\rbrace\,.
\end{align*}
The goal of the flexibility aggregation task is to find the net flexibility domain $\mathcal{F}$ in the form of a Minkowski  sum of the individual DER flexibility domains ($\mathcal{F}_i$), such that,
\begin{align*}
\mathcal{F}&:=\biguplus_{i=1}^N\mathcal{F}_i=\left\lbrace (p,q)\,\left| \begin{array}{c} p=\sum_{i=1}^Np_i\\
q=\sum_{i=1}^Nq_i\\
\,(p_i,q_i)\in\mathcal{F}_i~\forall i\end{array}\right.\right\rbrace.
\end{align*}
Calculating the exact Minkowski sum of the individual flexibility domains is computationally complex, especially as the number of DERs increases. Thus, from a practical point-of-view, a desirable approach is to construct approximations of the aggregate flexibility domain at the ADC in a scalable way. In the rest of the paper, we will discuss methods of computing the approximated aggregate flexibility at the ADC using geometric optimization procedures.

\section{Background}\label{S:back}

\subsection{Homothetic Transformation}
In a recent work, \cite{Zhao:2016}, authors used a geometric optimization-based approach to compute the \textit{inner} and \textit{outer} polytopic approximation of the aggregated flexibility of an ensemble of thermostatically-controlled loads, in the two-dimensional space of control variable and active power consumption. We propose to apply a similar approach to approximate the aggregated flexibility ($\mathcal{F}_i$) in active and reactive power consumption. Before we explain the approach, let us first introduce the concept of \textit{homothets}.

\begin{definition}
\cite{Zhao:2016} A \textit{homothet} of a compact convex domain $\mathcal{F}\subset\mathbb{R}^n$ is defined as the family of domains which can be expressed as $\mathcal{H}[\alpha,\beta;\mathcal{F}]:=\alpha\,\mathcal{F}+\beta$, where $\alpha$ is a positive scalar and $\beta\in\mathbb{R}^n$. Henceforth, the scalar $\alpha$ will be referred to as the \textit{`scaling factor'} and $\beta$ as the \textit{`translational vector'}.
\end{definition}

Thus a \textit{homothetic} transformation is a transformation applied on the state-space ($\mathbb{R}^n$) using uniform scaling and translation. The following result is useful in computing the inner and outer approximations of a set of homothets of a given domain (extension of the following result for more than two homothets follows trivially),

\begin{theorem}\label{T:Minkowski}
\cite{Schneider:2013} Consider a compact convex domain $\mathcal{F}\subset\mathbb{R}^n$\,, and two of its homothets $\mathcal{H}[\alpha_i,\beta_i\;\mathcal{F}]$\,, $\alpha_i>0$\,, $\beta_i\in\mathbb{R}^n$ $\forall i\in\lbrace 1,2\rbrace\,$. The Minkowski sum of the homothets is given by
$\mathcal{H}[\alpha,\beta;\mathcal{F}]=\biguplus_{i}^{2}\mathcal{H}[\alpha_i,\beta_i;\mathcal{F}]$\,, with the \textit{scaling factor} as $\alpha=\alpha_1+\alpha_2$ and the \textit{translational vector} as $\beta=\beta_1+\beta_2$\,.
\end{theorem}

\subsection{Sum-of-Squares Programming}

\begin{definition}
Any n-variate polynomial that can be expressed as sum of squared polynomials, is called a sum-of-squares (SOS) polynomial. We denote the ring of all SOS polynomials in $x\in\mathbb{R}^n$ by $\Sigma[x]\,.$
\end{definition}

Positivstellensatz theorem allows one to translate a set of semi-algebraic constraints into SOS feasibility conditions. In particular, Putinar's Positivstellensatz theorem says:
\begin{theorem}\label{T:Putinar}
\cite{Putinar:1993,Lasserre:2009} Consider a compact domain $\mathcal{K}\!=\!\!\left\lbrace x\!\in\!\mathbb{R}^n\!\left|\, g_i(x)\!\geq\! 0\,\forall i\!=\!1,\dots,m\right.\right\rbrace$, where $g_i(x)\,\forall i$ are polynomials and $g_i(\cdot)\geq 0\,\forall i$ define compact domains. Then a polynomial $f(x)$ is positive on $\mathcal{K}$ if and only if there exist SOS polynomials $\sigma_i(x)$ such that
$f(x) - \sum_i \sigma_i(x)g_i(x)$ is SOS.
\end{theorem}

For every SOS polynomial $f(x)$ of degree $2d$ ($d$ is a positive integer), there exists a positive semi-definite matrix $\Xi$ such that the Gramm matrix representation $f(x)\!=\!z(x)^T\Xi\,z(x)$ holds, where $z(x)$ is a vector of monomials in $x$ of degree less than or equal to $d$ \cite{Parrilo:2000}. Thus each SOS problem can be cast into an equivalent semidefinite programming (SDP) problem and solved via SOSTOOLS \cite{sostools13}, in conjunction with SDP solvers such as SeDuMi \cite{Sturm:1999}. Next we demonstrate the application of SOS programming to compute the approximations of flexibility domains using prototypes.

\section{Aggregate Flexibility: Geometric Approach}\label{S:method}

In this section we describe how one can use Theorem\,\ref{T:Minkowski} to design an algorithm to compute the outer and inner approximation of the aggregated flexibility without explicitly computing their Minkowski sum. The idea is to first define a \textit{`prototype'} domain $\mathcal{F}^0\subset\mathbb{R}^2$, either as a polytope (e.g. a \textit{box} constraint) or a generic convex domain, and obtain the \textit{outer} and \textit{inner} approximations of the individual flexibility domains ($\mathcal{F}_i\subset\mathbb{R}^2$) of the $i$-th ADC as the \textit{homothets} of the \textit{prototype}. For each $i\in\lbrace 1,2,\dots,N\rbrace$\,, we seek to find positive scalars $\underline{\alpha_i}\,,\,\overline{\alpha_i}$\,, and vectors $\underline{\beta_i}\,,\,\overline{\beta_i}\in\mathbb{R}^2$, such that
\begin{align}\label{E:indiv_approx}
\mathcal{H}\!\left[\underline{\alpha_i},\underline{\beta_i};\mathcal{F}^0\right]\,\subseteq\,\mathcal{F}_i \,\subseteq\, \mathcal{H}\!\left[\overline{\alpha_i},\overline{\beta_i};\mathcal{F}^0\right].
\end{align}
Computation of the outer and inner approximations would be discussed in details in the following sub-section. Note that,
\begin{proposition} \label{prop:aggr}
If the flexibility domains of a set of DERs are outer and inner approximated by \textit{homothets} of a compact convex \textit{prototype} domain $\mathcal{F}^0\!\subset\!\mathbb{R}^2$ as in \eqref{E:indiv_approx}, then their aggregate flexibility domain $\mathcal{F}\!\subset\!\mathbb{R}^2$ is outer and inner approximated as follows,
\begin{subequations}\begin{align*}
&\mathcal{H}\!\left[\underline{\alpha},\underline{\beta};\mathcal{F}^0\right]\,\subseteq\,\mathcal{F} \,\subseteq\, \mathcal{H}\!\left[\overline{\alpha},\overline{\beta};\mathcal{F}^0\right]\,\\
\text{where }&\underline{\alpha}=\sum_{i=1}^N\underline{\alpha_i}\,,\,\underline{\beta}=\sum_{i=1}^N\underline{\beta_i}\,,\,\overline{\alpha}=\sum_{i=1}^N\overline{\alpha_i}\,,\,\overline{\beta}=\sum_{i=1}^N\overline{\beta_i}\,.
\end{align*}\end{subequations}
\end{proposition}
\begin{proof}
The proof follows trivially from Theorem\,\ref{T:Minkowski}.\hfill\qed
\end{proof}

Let us now discuss how to construct the \textit{outer} and \textit{inner} approximations of flexibility domains using \textit{prototypes}. In this paper, we consider the two types of flexibility domains: either 1) the flexibility region is a compact domain with a boundary defined by piece-wise polynomials, or 2) the flexibility domain is a collection of admissible points in the $(p,q)$-space. Note that, we allow non-convex representations of the flexibility domains.
In this paper, we consider flexibility domains that can be represented in the generic form of:
\begin{align}\label{E:flex_compact}
\mathcal{F}&=\bigcup_{k=1}^K\mathcal{F}^k\\
\text{where }~\mathcal{F}^k&=\left\lbrace (p,q)\left|\, g_1^k(p,q)\!\geq\! 0,\dots,\,g_{m^k}^k(p,q)\!\geq\! 0\right.\right\rbrace\!,\!
\end{align}
where $g_j^k(p,q)\,\forall k\in\lbrace 1,2,\dots,m^k\rbrace\,\forall i$ are polynomials. This representation can be used to represent the continuous and discrete flexibility domains  of the types depicted in Fig.\,\ref{F:domains}, as explained in the following examples.

\begin{example}
(\textsc{Batteries}) The flexibility domain of a battery, with a maximum charge/discharge rate of $p^{\max}$ and the apparent power rating of $s\!>\!p^{\max}$\,, is given by
\begin{align*}
\mathcal{F}\!=\!\left\lbrace (p,q)\left|p\in[-p^{\max},{p}^{\max}],\,|q|\leq\sqrt{s^2-p^2}\right.\right\rbrace,
\end{align*}
which could be expressed in the form of \eqref{E:flex_compact}, with $g_1(p,q)\!=\!s^2\!-\!p^2\!-\!q^2,$ and $g_2(p,q)\!=\!\left(p^{\max}\right)^2\!-\!p^2$. \hfill\qed\end{example}

\begin{example}
(\textsc{PV Inverters}) The flexibility domain of a battery unit, with a maximum active power generation of $p^{\max}$ and the apparent power rating of $s\!>\!p^{\max}$\,, is given by
\begin{align*}
\mathcal{F}\!=\!\left\lbrace (p,q)\left|\,p\!\in\![-p^{\max},0],\, |q|\!\leq\! \sqrt{s^2\!-\!p^2}\right.\right\rbrace,
\end{align*}
which could be expressed in the form of \eqref{E:flex_compact}, with $g_1(p,q)\!=\!s^2\!-\!p^2\!-\!q^2,$ and $g_2(p,q)\!=\!-\!p^{\max} p\!-\!p^2$. \hfill\qed\end{example}

\begin{example}
(\textsc{Wind Inverters}) The flexibility domain of a wind inverter, with a maximum active power generation of $p^{\max}$ and the apparent power ratings $s_1\!>\!\sqrt{\alpha}p^{\max}$ (due to rotor current limits) and $s_2\!>\!\sqrt{\alpha}p^{\max}$ (due to stator current limits)\,, for some $\alpha>0$ is given by \cite{Lund:2007,Tian:2013,Martin:2015}
\begin{align*}
\mathcal{F}&=\mathcal{F}^1\bigcup\mathcal{F}^2\bigcup\mathcal{F}^3\\
\mathcal{F}^1&=\left\lbrace (p,q)\left| \,p\in[-p^0,0]\,,\,q\in[-q^0,\,q^0]\right.\right\rbrace\\
\mathcal{F}^2&=\left\lbrace (p,q)\left|
p\in[-{p}^{\max},-p^0),\,0\leq q\leq\sqrt{s_2^2-\alpha p^2}\right.\right\rbrace\\
\mathcal{F}^2&=\left\lbrace (p,q)\left|
p\in[-{p}^{\max},-p^0),\,-\sqrt{s_1^2-\alpha p^2}\leq q\leq 0\right.\right\rbrace
\end{align*}
where $p^0$ and $q^0$ are much smaller than the rated capacities. The flexibility can be expressed in the form of \eqref{E:flex_compact}, with
\begin{align*}
g_1^1(p,q)&\!=\!-p^2\!-\!p\,p^0,~g_2^1(p,q)\!=\!(q^0)^2\!-\!q^2,\,\\
g_1^2(p,q)&\!=\!-p^2\!-\!p\,\left(p^0\!+\!p^{\max}\right)\!-\!p^0p^{\max},\,\\
g_2^2(p,q)&\!=\!q,\,g_3^2(p,q)\!=\!s_2^2\!-\!\alpha p^2\!-\!q^2,\,\\
g_1^3(p,q)&\!=\!g_1^2(p,q),\,g_2^3(p,q)\!=\!-q,\,g_3^3(p,q)\!=\!s_1^2\!-\!\alpha p^2\!-\!q^2.\qed
\end{align*}\end{example}

\begin{example}\label{Ex:hvac}
(\textsc{Air-Conditioners}) The flexibility domain of a residential air-conditioner with an active power consumption rating of $p^{\max}$ (equal to the power consumed in `on' state) is represented by
\begin{align*}
\mathcal{F}&=\mathcal{F}^1\bigcup\mathcal{F}^2\\
\mathcal{F}^1&=\left\lbrace (0,0)\right\rbrace,\,\mathcal{F}^2=\left\lbrace ({p}^{\max},\gamma {p}^{\max})\right\rbrace
\end{align*}
where $\gamma>0$ is related to the power factor. One possible way of representing the flexibility in the form of \eqref{E:flex_compact} is by choosing $g_1^1(p,q)\!=\!-p^2,\,g_2^1(p,q)\!=\!-q^2,\,g_1^2(p,q)\!=\!-\left(p-p^{\max}\right)^2$ and $g_2^2(p,q)\!=\!-\left(q-\gamma p^{\max}\right)^2$\,. \hfill\qed\end{example}

In the scope of this work, we will focus our attention to \textit{prototype} domains that are convex polygons, expressed as
\begin{align}\label{E:proto}
\!\!\mathcal{F}^0\!=\!\left\lbrace (p,q)\left|\, A\begin{bmatrix}
p\\q
\end{bmatrix}\!\leq\!b\,,\,A\!=\!\!\begin{bmatrix}
a_{1p}&a_{1q}\\\vdots\\a_{np}&a_{nq}
\end{bmatrix}\!,\,b\!=\!\!\begin{bmatrix}
b_1\\\vdots\\b_n
\end{bmatrix}\! \right.\right\rbrace\!.\!
\end{align}

\begin{example}
(\textsc{Unit Square}) A prototype domain of the shape of a unit-square centered around the origin, $\mathcal{F}^0\!=\!\left\lbrace (p,q)\left|\,|p|\!\leq\!1,\, |q|\!\leq\! 1\right.\right\rbrace$, can be expressed in the form of \eqref{E:proto} with $A\!=\!\!\begin{bmatrix}
1&-1&0&0\\0&0&1&-1
\end{bmatrix}^T\!$, $b\!=\!\!\begin{bmatrix}
1&1&1&1
\end{bmatrix}^T\!$.\hfill\qed\end{example}

\subsection{Constructing Outer Approximation}

An outer approximation of the compact flexibility domain in \eqref{E:flex_compact}, using a \textit{homothet} of the prototype in \eqref{E:proto} amounts to finding positive scalar $\overline{\alpha}$ and 2-dimensional vector $\overline{\beta}\!=\!\begin{bmatrix}
\overline{\beta_p} &\overline{\beta_q}
\end{bmatrix}^T$ such that the following set inclusion condition is satisfied,
\begin{align}
\mathcal{H}\!\left[\overline{\alpha},\overline{\beta};\mathcal{F}^0\right]&\!=\!\left\lbrace (p,q)\left|\,\begin{bmatrix}
p\\q
\end{bmatrix}\!=\!\overline{\alpha}\!\begin{bmatrix}
p^0\\q^0
\end{bmatrix}\!+\!\!\begin{bmatrix}
\overline{\beta_p}\\\overline{\beta_q}
\end{bmatrix}\!,\,(p^0\!,q^0)\!\in\!\mathcal{F}^0\! \right.\right\rbrace\notag\\
&\!=\!\left\lbrace (p,q)\left|\,A\begin{bmatrix}
p\\q
\end{bmatrix}\!\leq\!\overline{\alpha}\,b\!+\!A\!\begin{bmatrix}
\overline{\beta_p}\\\overline{\beta_q}
\end{bmatrix}\! \right.\right\rbrace\!\supseteq\mathcal{F}.
\end{align}
This condition translates into a set of semi-algebraic conditions as follows:
\begin{align*}
\forall i\!\in\!\lbrace 1,\dots,n\rbrace:~a_{ip}\,(\overline{\beta_p}\!-\!p)+a_{iq}\,(\overline{\beta_q}\!-\!q)\!+\!\overline{\alpha}\,b_i\!\geq\!0\text{ on }\mathcal{F}.
\end{align*}
After relaxing the inequality `$\geq$' to strictly inequality `$>$' (note that for convex domains, for any $\alpha$ satisfying the inequality condition, we can always find an infinitesimally larger $\alpha$ that satisfies the strict inequality), we can use Theorem\,\ref{T:Putinar} to construct the following SOS optimization problem
\begin{align}\label{E:outer}
&\text{minimize}~\overline{\alpha}\!>\!0,\,\\
&\text{s.t., }\notag\\
&\overline{\beta_p}\!\in\!\mathbb{R},\,\overline{\beta_q}\!\in\!\mathbb{R},\notag\\
&\sigma_{ij}^k\!\in\!\Sigma[p,q]\,~\forall i\!\in\!\lbrace 1,\dots,n\rbrace,\,j\!\in\!\lbrace 1,\dots,m^k\rbrace,\,k\!\in\!\lbrace 1,\dots,K\rbrace\notag\\
&\forall k\!:\left\lbrace\!\! \begin{array}{r}\begin{bmatrix}
a_{1p} & a_{1q}
\end{bmatrix}\begin{bmatrix}
\overline{\beta_p}\!-\!p\\
\overline{\beta_q}\!-\!q
\end{bmatrix}\!+\!\overline{\alpha}\,b_1\!-\!\sum_{j=1}^{m^k}\sigma_{1j}\,g_j^k\in\Sigma[p,q]\\
\vdots\qquad\qquad \qquad\qquad \\
\begin{bmatrix}
a_{np} & a_{nq}
\end{bmatrix}\begin{bmatrix}
\overline{\beta_p}\!-\!p\\
\overline{\beta_q}\!-\!q
\end{bmatrix}\!+\!\overline{\alpha}\,b_n\!-\!\sum_{j=1}^{m^k}\sigma_{nj}\,g_j^k\in\Sigma[p,q]\end{array}\!\!\right.\notag
\end{align}
Note that the SOS conditions in the above SOS problem are affine in the decision variables ($\overline{\alpha},\,\overline{\beta_p},\,\overline{\beta_q},\,\sigma_{ij}^k$) and hence can be solved directly. Note that the value of $\overline{\alpha}$ represents how \textit{large} the homothet is, and therefore by solving for the minimal $\overline{\alpha}$ we ensure that the \textit{outer approximation} is the tightest.

\begin{remark}
The problem formulated in \eqref{E:outer} can be used to compute the outer approximation for both the continuous flexibility domains as well as the discrete flexibility domains of the type shown in Fig.\ref{F:hvac} (and described in Example\,\ref{Ex:hvac}).
\end{remark}

\subsection{Constructing Inner Approximation}

Solving for the \textit{inner approximation} is not as straightforward. Given a scaling factor $\underline{\alpha}$ and a translational vector $\underline{\beta}$\,, checking whether the homothet  $\mathcal{H}\!\left[\underline{\alpha},\underline{\beta};\mathcal{F}^0\right]$ is included completely inside the flexibility domain $\mathcal{F}$ can be done by solving the following feasibility problem
\mysubeq{}{
&\text{given}~\underline{\alpha}\!>\!0,\,\underline{\beta_p}\!\in\!\mathbb{R},\,\underline{\beta_q}\!\in\!\mathbb{R},\\
&\text{check:}~\forall (k,i)\,g_i^k\geq 0\text{ on }\!\!\left\lbrace\! (p,q)\!\left|\,A\!\begin{bmatrix}
p\\q
\end{bmatrix}\!\leq\!\overline{\alpha}\,b\!+\!A\!\begin{bmatrix}
\overline{\beta_p}\\\overline{\beta_q}
\end{bmatrix}\! \right.\right\rbrace
}
which can be cast into an SOS feasibility problem (for some given $\underline{\alpha}\!>\!0\,,\,\underline{\beta_p}\!\in\!\mathbb{R}$ and $\underline{\beta_q}\!\in\!\mathbb{R}$):
\begin{align}\label{E:inner}
&\text{find}~\sigma_{ij}^k\!\in\!\Sigma[p,q]\,~\forall \left\lbrace\begin{array}{l}i\!\in\!\lbrace 1,\dots,m^k\rbrace,\,\\
j\!\in\!\lbrace 1,\dots,n\rbrace,\,\\
k\!\in\!\lbrace 1,\dots,K\rbrace\end{array}\right.\\
&\text{s.t. }\notag\\
&\forall k\!:\!\left\lbrace\!\!\begin{array}{r}g_1^k\!-\!\sum_{j=1}^n\sigma_{1j}^k(\begin{bmatrix}
a_{jp}~\, a_{jq}
\end{bmatrix}\begin{bmatrix}
\underline{\beta_p}\!-\!p\\
\underline{\beta_q}\!-\!q
\end{bmatrix}\!+\!\underline{\alpha}\,b_j)\in\Sigma[p,q]\\
\vdots\qquad\qquad \qquad\qquad\qquad\\
g_{m^k}^k\!-\!\sum_{j=1}^n\sigma_{m^kj}^k(\begin{bmatrix}
a_{jp}~\, a_{jq}
\end{bmatrix}\begin{bmatrix}
\underline{\beta_p}\!-\!p\\
\underline{\beta_q}\!-\!q
\end{bmatrix}\!+\!\underline{\alpha}\,b_j)\in\Sigma[p,q]\end{array}\right.\notag
\end{align}
Notice that the SOS constraints in \eqref{E:inner} are bilinear in the decision polynomial variables $\sigma_{ij}^k$ and the \textit{homothet} parameters $\underline{\alpha}$ and $\underline{\beta}$. Therefore this cannot be solved directly to find out the \textit{best} inner approximation, and can only be used to check whether a given homothet is an inner approximation or not. In this paper, we propose a heuristic to find the homothet parameters that define the best inner approximation. Note that given a $\underline{\beta}$ the best inner approximation is the largest \textit{homothet} that is contained inside the flexibility domain, which can be solved by running a bisection search for the maximum $\underline{\alpha}$ for which \eqref{E:inner} is feasible. The value of this largest $\underline{\alpha}$ can be further improved if we can identify a direction in which to \textit{translate} the \textit{homothet}, by detecting the edges of the polytope which touch the flexibility domain boundary (i.e. \textit{binding} edges). The \textit{best} inner approximation is computed in a two-stage iterative process as described below.

\subsubsection{Step 1}
Find $\underline{\alpha}$ given $\underline{\beta}$\,. Given a $\underline{\beta}$ we can
run a bisection search for the largest positive scalar $\underline{\alpha}$ that solves \eqref{E:inner}.

\subsubsection{Step 2}
Update $\underline{\beta}$\,. Once we have found the largest homothet $\mathcal{H}\!\left[\underline{\alpha},\underline{\beta};\mathcal{F}^0\right]$ of the \textit{prototype} polygon, that is contained wholly inside the flexibility domain, we can identify the edges of the \textit{homothet} which lie on the boundary of the flexibility domain. The edges represent the \textit{binding} constraints that limit the expansion of the inner \textit{homothet}. Thus we choose a direction $\hat{b}$ that is a vector sum of all the directions orthogonal to the \textit{binding} edges, and choose a new $\underline{b}\leftarrow \underline{b}+\varepsilon\hat{b}$\,, for some sufficiently small scalar $\varepsilon$\,. Checking which edges are binding can be done by solving appropriate sum-of-squares problems, which we have omitted for brevity.

These two steps are repeated until a convergence in the value of $\underline{\alpha}$ is achieved.
Let us denote by $\mathcal{H}\!\left[\underline{\alpha^*},\underline{\beta^*};\mathcal{F}^0\right]$ the \textit{largest} homothet contained inside the flexibility domain, such that there exists no $\underline{\alpha}>\underline{\alpha^*}$ and $\underline{\beta}$ for which $\mathcal{H}\!\left[\underline{\alpha},\underline{\beta};\mathcal{F}^0\right]$ is an inner approximation. Let us assume that $\mathcal{H}\!\left[\underline{\alpha^0},\underline{\beta^0};\mathcal{F}^0\right]$ is an inner approximation for some translational vector $\underline{\beta^0}$ and scaling factor $\underline{\alpha^0}$. Then the success (convergence) of the above two-stage algorithm depends on the following condition:
\begin{assumption}\label{AS:monotonic}
$\underline{\alpha}(\epsilon)$ increases monotonically with $\epsilon\in[0,1]$\,, where $\underline{\alpha}(\epsilon)$ is the largest scaling factor corresponding to the translational vector $\underline{\beta}(\epsilon)=\underline{\beta^0}+\epsilon\left(\underline{\beta^*}-\underline{\beta^0}\right)$\,.
\end{assumption}

Note that the inner approximations do not exist for DERs that have discrete flexibility domains. Hence the above method is only applicable to continuous flexibility domains.

\section{Quality of Approximation}\label{S:metric}

In order for the approximation of the flexibility domains to be used in network-level resource optimization, it is important that the approximations are \textit{close} to the actual flexibility domains. In this section, we propose metric(s) to quantify the \textit{closeness} of the approximation. Such metrics could be useful to choose from a set of \textit{prototypes} to approximate the flexibility domain of a given DER. Furthermore, such metrics could be passed up to the network optimizer, along with the approximating \textit{homothets}, to facilitate better resource allocation. In this paper, we discuss two such possible metrics. First one is related to the worst case error in a dispatched point (from network operator) and a feasible solution:
\begin{definition}\label{D:distance}
The distance metric $\pi^d(\overline{\mathcal{F}},\mathcal{F})$ for two sets $\overline{\mathcal{F}}\supset\mathcal{F}$ is defined as the maximal distance between any point in $\overline{\mathcal{F}}\backslash\mathcal{F}$ and its nearest feasible point in $\mathcal{F}$\,.
\end{definition}
\begin{proposition}\label{P:distance}
The distance metric for the outer and inner approximations of the type $\overline{\mathcal{H}}=\mathcal{H}\!\left[\overline{\alpha},\overline{\beta};\mathcal{F}^0\right]$ and $\underline{\mathcal{H}}=\mathcal{H}\!\left[\underline{\alpha},\underline{\beta};\mathcal{F}^0\right]$\,, where $\mathcal{F}^0$ is a polygon, is given by
\begin{align*}
\pi^d(\overline{\mathcal{H}},\underline{\mathcal{H}})=\max_i \left\lVert (\overline{\alpha}-\underline{\alpha})\,v_i + \overline{\beta}-\underline{\beta}\right\rVert_2
\end{align*}
where $v_i\,\forall i$ is the vector representing the vertices of $\mathcal{F}^0$.
\end{proposition}
\begin{proof}
Since homothetic transformation include only scaling and translation, the edges in both the inner and outer homothets are parallel to each other. Therefore the maximal distance between the two polygons occur at the respective vertices.\hfill\qed
\end{proof}
The second metric is related to the likelihood of a dispatched point lying inside the actual flexibility domain:
\begin{definition}\label{D:area}
The area metric $\pi^a(\overline{\mathcal{F}},\mathcal{F})$ for the outer approximated and actual flexibility domains, $\overline{\mathcal{F}}\supset\mathcal{F}$\,, is defined as the likelihood that an optimally dispatched point in $\overline{\mathcal{F}}$ also lies inside $\mathcal{F}$\,.
\end{definition}

To compute this metric one needs to assign a probability of each point in the approximated domains being dispatched by the network operator. In absence of any prior knowledge of the probability, one can start by assuming that each point in the approximated domain is \textit{equally likely} to be dispatched. Under such an assumption, we can compute the area metric as follows:
\begin{proposition}\label{P:area}
The area metric for the outer and inner approximations of the type $\overline{\mathcal{H}}=\mathcal{H}\!\left[\overline{\alpha},\overline{\beta};\mathcal{F}^0\right]$ and $\underline{\mathcal{H}}=\mathcal{H}\!\left[\underline{\alpha},\underline{\beta};\mathcal{F}^0\right]$\,, is given by $\pi^a(\overline{\mathcal{H}},\underline{\mathcal{H}})=\left({\underline{\alpha}}/{\overline{\alpha}}\right)^2$\,.
\end{proposition}
\begin{proof}
Note that the area under a homothet $\mathcal{H}\!\left[{\alpha},{\beta};\mathcal{F}^0\right]$ is equal to $\alpha^2$ times the area under the prototype $\mathcal{F}^0$\,. The rest follows directly.\hfill\qed
\end{proof}
Note that the larger the value of the area metric, the better are the domain approximations, while for the distance metric the smaller value implies better approximation. These metrics are applicable directly to continuous flexibility domains. For discrete domains, alternative methods need to be devised to compute the metrics (not covered in this article).

\section{Numerical Results}\label{S:result}

\begin{figure*}[thpb]
\centering
\captionsetup{justification=centering}
\subfigure[battery (DER 1)]{
\includegraphics[scale=0.27]{box_1.eps}\label{F:box_1}
}
\hspace{0.1in}
\subfigure[solar PV inverter (DER 2)]{
\includegraphics[scale=0.27]{box_2.eps}\label{F:box_2}
}
\hspace{0.1in}
\subfigure[wind inverter (DER 3)]{
\includegraphics[scale=0.27]{box_3.eps}\label{F:box_3}
}
\hspace{0.1in}
\subfigure[battery (DER 4)]{
\includegraphics[scale=0.27]{box_4.eps}\label{F:box_4}
}
\hspace{0.1in}
\subfigure[wind inverter (DER 5)]{
\includegraphics[scale=0.27]{box_5.eps}\label{F:box_5}
}
\hspace{0.1in}
\subfigure[aggregated flexibility]{
\includegraphics[scale=0.27]{box_aggr.eps}\label{F:box_aggr}
}
\caption[Optional caption for list of figures]{Outer and inner approximations of a collection of PV inverters, wind inverters and batteries, using unit square as a prototype.}
\label{F:box}
\end{figure*}
In this section, we present some numerical results to demonstrate the aggregation of flexibility domains of different types of DERs. Fig.\,\ref{F:box} shows the plots of outer and inner approximations of a collection of five DERs (consisting of PV inverters, wind inverters and batteries), using unit square as a prototype, including the approximation of their Minkowski sum. The values of the distance metric and the area metric for all these approximations are also computed and shown on the plots.
\begin{figure*}[thpb]
\centering
\captionsetup{justification=centering}
\subfigure[solar PV inverter (DER 2)]{
\includegraphics[scale=0.27]{hex_2.eps}\label{F:hex_2}
}
\hspace{0.1in}
\subfigure[wind inverter (DER 5)]{
\includegraphics[scale=0.27]{hex_5.eps}\label{F:hex_5}
}
\hspace{0.1in}
\subfigure[aggregated flexibility]{
\includegraphics[scale=0.27]{hex_aggr.eps}\label{F:hex_aggr}
}
\caption[Optional caption for list of figures]{Outer and inner approximations of the same set of DERs, using regular unit hexagon as a prototype.}
\label{F:hex}
\end{figure*}
Fig.\,\ref{F:hex} shows the approximations using a regular unit hexagon as the prototype, for the same set of devices (only a couple of them shown on the figure). In this particular example, the approximations using a regular hexagon as the prototype turns out to be better than the approximations using unit square as the prototype, according to both the area metric and the distance metric. For example, the value of the area metric of the approximation of the aggregated flexibility turns out to be higher for the regular hexagon prototype ($\pi^a=0.30$) than for the square prototype ($\pi^a=0.26$), while the value of the distance metric is lower with regular hexagon as the prototype ($\pi^d \approx 21.4$) than with a square prototype ($\pi^d \approx 23.7$).

\begin{figure*}[thpb]
\centering
\captionsetup{justification=centering}
\subfigure[individual air-conditioner]{
\includegraphics[scale=0.27]{tri_1.eps}\label{F:tri_1}
}
\hspace{0.1in}
\subfigure[collection of air-conditioners]{
\includegraphics[scale=0.27]{tri_aggr.eps}\label{F:tri_aggr}
}
\caption[Optional caption for list of figures]{Outer approximations of a collection of ten residential air-conditioners with discrete flexibility domains, using a triangle as a prototype.}
\label{F:tri}
\end{figure*}

Finally Fig.\,\ref{F:tri} shows the results from approximating the aggregated flexibility of a collection of discrete loads (residential air-conditioners) via a triangle as a prototype. While the approximation of an individual DER results in a very sparse approximated flexibility domain, the approximation of the aggregated flexibility domain tends to be much denser. While a specific quantification of the accuracy (or, quality) of the approximation for discrete DERs is not provided in this article, Fig.\,\ref{F:tri} shows qualitatively how the larger population size of an ensemble of switching loads can lead to better approximation of the aggregated flexibility.

\section{Conclusions}\label{S:concl}
We envision a distribution system optimization framework in which thousands of these DERs are scheduled to operate the system efficiently. Heterogeneity of the DERs, manifested in the different forms of their flexibility domains, pose a serious challenge to the scalability of such an optimization problem. Furthermore, any such optimization framework needs to be able to accommodate a plug-and-play approach whereby any new DER can be easily integrated into the system. In this work, we presented a geometric approach to \textit{homogenizing} the flexibility domains of different types of DERs via \textit{homothets} of some \textit{prototype} domain. We further looked into the choice of the prototype domain, and the choice of the parameters of the homothets, such that the outer (and inner, when applicable) approximations of the flexibility domains are \textit{good}. Simulation results are provided to illustrate the approach. Future efforts will concentrate on extending this framework to model the dynamic evolution of the flexibility, as well as modeling the uncertainties in the flexibility of DERs.

\section*{Acknowledgment}

The authors would like to thank Dr. Andrey Bernstein of National Renewable Energy Laboratory, USA, for his helpful remarks and discussions on this work.

\IEEEtriggeratref{8}

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


I'm using the hardware PWM output with wiringpi. It provides the function pwmSetClock that should make it possible to change the frequency. (https://projects.drogon.net/raspberry-pi/wiringpi/functions/). I believe since the default is 200 Mhz setting the divisor to 200000000 should make an LED hooked up to the output flash visibly, but that is not the case.
The rest of the answer assumes we're in mark-space mode.
I also did some experimenting with the allowable range of values for pwmSetClock() and pwmSetRange(). As noted in one of the other answers, the valid range for pwmSetClock() seems to go from 2 to 4095, while the valid range for pwmSetRange() is up to 4096 (I didn't attempt to find a lower-limit).
The range and clock (a better name is probably divisor) both affect the frequency. The range also affects resolution, so while it may be possible to use very low values, there is a practical limit to how low you will probably want to go. For example, if you used a range of 4, you could achieve higher frequencies, but you will only be able to set the duty cycle to 0/4, 1/4, 2/4, 3/4 or 4/4.
The Raspberry Pi PWM clock has a base frequency of 19.2 MHz. This frequency, divided by the argument to pwmSetClock(), is the frequency at which the PWM counter is incremented. When the counter reaches a value equal to the specified range, it resets to zero. While the counter is less than the specified duty cycle, the output is high, otherwise the output is low.
pwmFrequency in Hz = 19.2e6 Hz / pwmClock / pwmRange.
If you use the maximum permissible values for pwmSetClock() and pwmSetRange(), you will end up with the minimum achievable hardware PWM frequency of ~1.14 Hz. This will certainly give a visible flicker (more of a flash, really) to an LED. I did confirm the above equation with an oscilloscope, and it seems to hold. The upper frequency limit will be affected by the resolution you need, as described above.
Note: My servo expects a 50Hz signal.
This is the code I'm using. I'm trying to see what will change as i change the settings.
From what i've tested, it seems the divisor goes from 2 to some number less than 5000. I would guess it has something to do with the binary representation of those numbers which are being directlly set in the register. Once the numbers binary representation has more bits than the register can take it just takes the first bits and interpretes the numbers that way. Thats why the strange behaviour comes when going from 4000 to 5000.
Not the answer you're looking for? Browse other questions tagged gpio hardware pwm wiringpi or ask your own question.
How to set a fixed Frequency and change duty cycle from 0 to 100 in Raspberry Pi hardware PWM?
What is the maximum frequency of a pulse width modulation signal for the raspberry pi 3?
PWM - What does pwmSetClock() and pwmSetRange() mean?


We talked to top florists to get tips on how to keep your summer wedding flowers fresh.
Opt for flowers that will stay fresh throughout the entire day. Look for ones with a waxy texture to ensure staying power. Hawaiian blooms, such as orchids, are a great option (check out cymbidium and dendrobium orchids). Ginger halcyons, birds-of-paradise, tiger lilies, and even roses will champion high temperatures too. Buying local flowers is another way to go; blooms that are in season in your area will more likely survive a long day in a bouquet. Check with your florist to see which ones will work for your venue.
When it comes to wedding flowers, the higher the temperature, the more upkeep they'll require. Have them delivered the day of the wedding and make sure there's a refrigerator on-site to store them before the ceremony starts. Also, be mindful of your flowers during photography sessions. When your photographer isn't snapping away, have a friend or bridesmaid hold your bouquet in a shady spot, or place it in a vase of cool water. If your blooms will be exposed to the summer heat for an extended amount of time, keep a spray water bottle on hand and give your flowers a light misting every hour or so.
For the color of your flowers, check out which flowers will be in bloom around your ceremony and reception site, and consider bold versions of those hues. For an outdoor or semiformal wedding, think violet, hot fuchsia, mango, magenta, and green. Wine colors and deeper shades are appropriate for formal weddings, like dark red roses or deep purple lilies. When it comes to casual weddings, sunflowers are a great option since you only need a few to create a vibrant pop of color.
You have plenty of summer centerpiece arrangements to choose from. If you're having a formal ballroom wedding, go for tall vases overflowing with a mix of bold and deep-hued flowers accented with feathers or gems. To create a modern vibe, display monochromatic green, orange, or even yellow blooms in clear Lucite containers. For an outdoor wedding, consider wooden containers filled with colorful, locally grown flowers. During the cocktail hour, daisies in simple Mason jars will perk up the space. Or look into potted centerpieces so guests can take them home as favors.


We build digital advertising campaigns that are everywhere your customers are, highly targeted, and effective.
Connecting your company with potential customers is our mission and step one is to make sure your brand is in the right place at the right time, in front of the right people. Whether it's through display ads, social media ads, retargeting, or pay per click in Houston, we have the knowledge, skills, and experience to get your brand noticed online.
Earning and maintaining top placement in search results is a long and complicated process. If you're new to an industry, market, or launching a new product, you can't afford to wait until you rank near the top in organic rankings.
We combine keyword research and content strategies to execute Pay Per Click campaigns, like Google AdWords, that effectively generate search engine traffic from targeted keywords in a relatively short period of time. As a result, Houston PPC campaigns are a great way to supplement organic search results for new SEO campaigns or for highly competitive search terms.
Digital display advertising is a cost effective way to reach thousands potential customers in your target market.
We design and develop display ad campaigns to fulfill specific needs, whether it's to increase brand awareness, or to find and convert customers as part of a larger marketing campaign. Our designers and online marketing specialists create effective and memorable display campaigns that are true to your brand.
Retargeting works by tracking who has visited your site and displaying your ads to them as they visit other sites online. The good branding and repeated exposure often result in higher click-through rates and increased conversions than traditional display ads.
Our retargeting campaigns allow you to devote more marketing horsepower to your brand awareness and product marketing allowing you to convert previous website visitors into customers.
Advertising on popular social media platforms offers boundless approaches to who, when, and why an individual may be served an ad and requires nuanced targeting and measurement.
Our online marketing specialists and Houston pay per click experts work to incorporate your social media advertising into your current social media strategy and determine the right demographics, geographical regions, and interests to target the right people, in the right place, and at the right time.


Veterans Day is an annual reminder to give thanks to the men and women who have protected the American way of life through their service in our Armed Forces.
For Cottman Transmission and Total Auto Care, a nationwide auto repair and transmission company for almost any make or model vehicle, foreign or domestic, the holiday has a special meaning. Roughly 25 percent of Cottman shops nationwide are owned and run by veterans.
Typical of that commitment to service is what one Cottman franchisee, Fred Bowen who has four highly successful shops in North Carolina, says has been a major factor in his success. Bowen, 57, credits his success 100 percent to his sixteen years as an officer in the Marine Corps, where he served throughout the U.S., in South and Central America, Asia and the Pacific.
Cottman's veteran-owned locations include shops in Denver, CO; Wheat Ridge, CO; Maple Shade, NJ; Woodbury Heights, NJ; Cornelius, NC; Durham, NC; Greensboro, NC; Winston-Salem, NC; Cincinnati, OH; Lansdale, PA; Philadelphia, PA; Mauldin, SC; Austin, TX; Cedar Park, TX; Round Rock, TX, Richmond, VA and The Woodlands, TX.
With locations across the U.S., Cottman Transmission and Total Auto Care is a transmission and auto repair company for almost any make or model vehicle, foreign or domestic. Cottman Transmission and Total Auto Care specializes in complete transmission service, brakes, suspension, air conditioning service and much more. Cottman is based in Horsham, Pa. For more information, please visit www.cottman.com.


As the year-long conflict polarises Syrian society, Omar Abdel-Razek from BBC Arabic finds an Orthodox Christian community worried it could face trouble from both the government and opposition.
"The university has become a battlefield between the supporters and the opposition of the regime."
That was what Lena (not her real name), a medical student at the University of Aleppo, had said in her email informing me that she will not be able to meet me at campus as agreed.
She continued: "As a Christian, both sides are suspicious of me. In fact I'm not with or against the regime."
Lena said she never cared about politics until she and her family found themselves talking about it everyday when the crisis in Syria began over a year ago.
"We followed the simple rule 'don't talk politics', and then you can do anything else," she said.
In the past, when I was going to my exams, my mother's main concern for me was to do an 'excellent' job. Now her main concern is for me not to take a taxi because of the kidnappings," Lena said.
While some Christian intellectuals have openly opposed President Bashar al-Assad and were imprisoned by his regime, it seems that the majority fear the unknown if the regime were to collapse.
They cite the situation of Christians in Iraq and recently Egypt as the basis for their fear.
The Syriac Orthodox Church was once one of the major Christian churches in the Eastern Roman Empire; Syriacs translated Greek documents into Arabic.
Their number has decreased now to 140,000 according to Father Gregorious Yohanna Ibrahim, the Metropolitan of Aleppo.
When I met him in his monastery I asked how the Christian minority is dealing with the crisis which has engulfed the country.
"Do not call us a minority, we are a unique community with deep roots in the country," he said angrily.
"The opposition and the regime committed mistakes, [they] did not return to wisdom, and blood brought more blood," he continued.
"We call for dialogue that should include everybody who represents the opposition, not just those the government calls the opposition."
I asked Father Gregorious Yohanna if some Christians side with the regime because of fear.
"Look, we have concerns, we have great concerns, we can't wish the Iraqi model for anyone and the Christians of the region also feel uneasy with what happened in Egypt recently," he said.
"Our concerns are not related to who will come to power, we are afraid that whoever will come may close their eyes and ears, or will not like to deal with us," he continued.
"We don't fear the Islamists, we fear the violent extremists who will not accept the other," he said.
When I visited, few people were out in the streets around the Greek Orthodox Patriarchate in the old city of Damascus. Names of the streets, buildings and bazaars in this tourist area, still carry much of its Christian past, but the church where I met Bishop Louka al-Khoury was nearly empty.
Bishop Louka prides himself in belonging to the oldest Arab church.
"Can you name one single Syrian party or political movement that did not have a Greek Orthodox among its leaders?"
I noticed the nostalgic tone in his words.
"Christian Syrians were accused of siding with the regime, but this is not true," he insisted.
"Syrians belong only to their homeland not to regimes, it's that patriotism Christians have that made them the first to sacrifice for their country.
"We have some fears no doubt, because we have never witnessed violence like that which we see on the ground now.
"But we don't side with a regime; we side with our country and with anybody who serves our homeland and our interests," Bishop Louka al-Khoury said.


text:
Leadership from Zero to 30,000 Feet
September 9, 2021 September 8, 2021 Timothy I. Thomas and Rip Tilden
You've likely seen news stories of violence in the skies as passengers become unruly, enraged, and abusive. Well, I (Tim) was on a flight at the end of August that had all the makings of major passenger disgruntlement, to put it mildly. But because of the great leadership of our captain, the flight didn't make it into the headlines.
Our flight was heading into Chicago when the captain announced that a front was moving in and he had been instructed to go into a holding pattern above the O'Hare International Airport. We could see thunderheads darkening the sky and coming closer by the minute.
After circling for a while, the captain came on again. He explained that he was going to fly west and then north to try coming in behind the front. At this point, my "leadership" antennae went up as I noticed that the captain was being fully transparent with the passengers. So often, the opposite happens on flights. You know something is wrong or suspect that you are going to be delayed, but the crew keeps you in the dark. You ask questions and get no answers and become more and more frustrated. (I should know … I have logged more miles in the air than I can count.)
We felt the plane come out of the holding pattern and accelerate as the captain punched it to try to beat the strengthening winds. Some fifteen minutes later, he brought us the bad news: O'Hare had completely shut down. No planes could land, including ours. With our fuel level dropping, we had to go to another airport – located in Rockford, Illinois – to refuel. The captain went on to say that Rockford is a tiny airport and that when we arrived, we would park the plane. Other planes were also being diverted to Rockford to refuel. The airport did not have the staff or equipment to permit passengers to deplane, so we would simply be sitting on the tarmac for the duration.
We landed at Rockford and I observed that people were not angry. Certainly, the disappointment was palpable because we would not get to Chicago on time, but there was no yelling, no cursing, no irate demands. People were calm. Why? Because they knew exactly what was happening.
Eventually, the captain informed us that we were second in line to be refueled. When the fuel truck came up to our plane, he let us know how long it would take. All the details people were wondering about were answered.
There was a sigh of relief when the captain announced that O'Hare had re-opened. He explained that we would get in the queue of planes to take off, and that he would keep us apprised. Which he did. As soon as he knew that we would arrive in Chicago at a certain time, we knew it. And we arrived exactly when he said we would.
Now, bear in mind that we arrived three hours late at O'Hare. Yet nobody was upset. Nobody was throwing a fit. Nobody was asking for compensation. Not a single voice had been raised the entire time.
As the icing on the cake, the captain spoke with every single passenger as we deplaned to apologize for the delay and thank us for our patience. I admit, I held up the line when I reached him. I told him how absolutely extraordinary the experience had been. That I have been traveling for business for 23 years and have never had such full transparency and timely updates. I congratulated him on his leadership and told him he would be the focus of a future blog. He laughed and said, "I owed it to you as passengers to keep you updated. I owed it to you to stand here and greet each of you and offer my apologies for the delay. That is my responsibility."
And that is what great leadership looks like in a difficult situation. Openness and honesty. Transparency and communication. Responsibility and ownership.
No, our flight didn't make the headlines. In a way, I wish it had. More people need to hear about people like that captain – people who make a difference because they know what it is to be a great leader.
Tags: communication leadership
Two Pilots. Two Delays. Two Very Different Outcomes.
People Know
What's holding you back? (HeadTrash 2, Part 1 of 7)
The toughest of elephants — change at the top


Boar in the City: Is this the place for a fat-tired e-bike?
When you look on the website for the Boar electric fat bike you see all the images of young people going up and down hills in Whistler, BC. When the people at Surface 604 offered to send me one for a test drive, I was a bit dubious at first, being a boomer in the city instead of a kid on a mountain. However, Sam Atakhanov, their VP of product development, told me that it wasn't just for trails, and could replace cars for a lot of people living in cities; they say so right there in their story.
Our vision was to create the "Sport Utility" of bikes. One bike that could take you anywhere, in any season. A bike that let you bring what you want. A bike that was so fun to ride and so versatile that the second car would just sit in the driveway collecting dust. Or, even better, a bike that would replace the car altogether.
After a few days riding this everywhere, I have concluded that Sam just might be right about there being a place for this Pig in the City.
The first thing one has to get over is the whole idea of the fat bike, with these massive four inch wide Kenda Juggernaut 26" tires. My first thought is that they might be great on the beach (and probably fabulous in snow when winter comes) but that they will be terrible in the city. I thought the rolling resistance from them would make it impossible to move this bike under pedal power. In fact, this turned out not to be true; the bike comes with ten speed gearing and the bike actually was easier to move than I thought it would be.
And in fact, they just eat up streetcar tracks and potholes and the terrible road conditions that you often find in Toronto bike lanes. Manhole covers, sewer grates, even this stretch of bike lane, all the usual obstructions that I go around, I just rode right over. It may not be a dirt trail in Whistler, but city riding has its own share of obstacles that just disappear under the tires of a fat bike.
Power delivery to the motor is regulated by a torque sensor in the dropout hanger that senses how much torque you apply to the pedals; the harder you pedal, the more power the electric motor provides. The result is smooth power delivery and a natural ride much like a regular bike. The torque sensor has the added benefit of acting like a Battery Management System (BMS). The power going to the motor is instantly reduced when you reduce the torque and turns off completely when you stop pedalling. The effect is greatly reduced power consumption, longer range and longer battery life.
You can control how much of a boost by cranking up the assist mode with the + and - buttons on the control pad; I was most comfortable at 2 and 3, which got me up to about 22 kmph. My daughter, who used the bike for her very long ride to work, maxed it out at 32 kmph, which is faster than I ever went on it. She writes that it "felt like it was too fast to feel comfortable in the bike lane, but not fast enough to feel comfortable in a regular lane," a problem I didn't share.
But just because you can go that fast doesn't mean that you have to or you should, any more than the guy owning the BMW has to drive twice as fast as the speed limit. In some ways I think that this kind of e-bike could actually be safer in the city, given the way that those tires grip the road. I also found that I was stopping at a lot more stop signs than I usually do; the power boost makes it a lot easier to get back up to speed. (Because remember, it's physics.) On the other hand, my daughter noted that "the power came in handy when I wanted to catch a light before it changed - the burst of speed was very helpful." Perhaps these should be restricted to aging boomers.
Toronto is mostly pretty flat, with the downtown on a slight tilt down toward Lake Ontario. But there are a few hills in Midtown, through ravines and up the old shoreline of post ice age Lake Iroquois. I took the Boar up Mount Pleasant Road, which goes up and down through a ravine and is probably the hardest hill in Toronto. I have avoided it for years. I still had to pedal a bit and there was some heavy breathing along the way, but the bike really just ate it up.
As an e-bike n00b, I do not miss it; I think it would have confused things, another control to mess up with. I found the pedal assist to be totally natural.
I found the biggest con to the bike to be its size and weight; you are not going to be dragging this up stairs, and I had trouble finding room for it on a few bike racks. It also is a big attention getter; my daughter notes that she had to talk about it to a crowd of ten guys at the local bar when she rode up on it. Also, get the sizing right; I tested the large bike and both my daughter and I, who are small, found the seating position uncomfortable as we were leaning forward to reach the handlebars.
But especially if one gets the optional carriers, this could be a great grocery hauler as well. Before this test drive I would have flat out dismissed a fat-tired e-bike for city use. But as we age and those hills seem to get longer and higher, and as our cities get more congested with cars while every parking lot sprouts a condo, I can see this being a viable option for a lot of people, young and old. And even Mikael at Copenhagenize sees a role for e-bikes among older users, noting that in the Netherlands, the average age of an e-bike rider is over sixty.
In summary, the Boar takes the sting out of hills and laughs at potholes and sewer grates. Its big tires are glued to the road. It's totally intuitive and easy to use. I can see this being really useful for boomers who want to keep riding, and yes, it might even replace a car for some. There is a real role to play for a boar in the city.
Should you buy an electric bike? Your questions answered!


text:
Home » Living in Singapore » Schools » A principal with principles
A principal with principles
19th June 2019 by Expat Living 4 Min Read
With 25 years of teaching under her belt and experience building a London school from the ground up, Sir Manasseh Meyer International School (SMMIS) is excited to have Principal ELAINE ROBINSON at the helm. She sat down to talk to us about why this position was one she couldn't pass up.
I was born and raised in Liverpool, but lived in Israel, Hong Kong and, most recently, London.
Your undergraduate degree is in Theology. How did you end up in education?
I graduated from Birmingham University with joint honours in Theology and Cultural Studies. It was there that I was inspired by the cultural theories of Michel Foucault. Later I received an MA in Philosophy of Education from The Institute of Education at the University of London. This introduced me to the writings of John Dewey and the concepts of democratic and moral education and the wellbeing of the child as the centre of education. It was during this time that I was inspired to become a school leader. I always wanted to work in education, and religion is my passion. My two degrees are the foundation of all that I do.
How long have you been teaching?
I've been in education for over 25 years. My career began as a youth leader in the UK and Hong Kong. In 2002, I started formally teaching. I've taught Religious Education and, in London, I mostly taught A level and GCSEs.
You won a prestigious award while working in London. Why were you given this honour?
I helped to set up the first pluralist Jewish Day School in the UK. It's a school that caters to all denominations in the Jewish community. The Jewish Community Secondary School (JCoSS) is a trailblazing school. As Deputy Head, I was involved in defining the direction of the school, creating ethos documents, developing curriculum and, of course, teaching. It was my dream job. I was incredibly excited to be involved in building a school from scratch. Seeing our first cohort graduate was an inspiring and emotional moment.
What attracted you to Singapore?
My family and I moved here in July 2017 so I could take on the role of Principal at SMMIS. I had been in a leadership role at JCoSS for over eight years, and I was ready to take on a Headship role. This job felt like the right job at the right time. It was interesting and exciting enough that I was prepared to leave my alma mater. It offered an adventure for me and my family. It's thrilling to be in Singapore, a country that is committed to religious harmony, which is something I feel very passionate about. The microcosm of the SMMIS community is fascinating too, in that it's just as varied and dynamic as the society in which it exists.
Is it difficult to go from teaching students to leading a school?
Leading a school is the natural pathway from classroom teaching. All teachers have a vision of how they would like to see children educated. Being the Principal of the school means you can influence and direct every aspect of the child's educational experience – from the physical to the spiritual. It's the ultimate opportunity to a see your educational vision become a reality and impact on the lives of so many.
Tell us three things that sets SMMIS apart from others.
Ours is a not-for-profit, boutique school that offers individualised learning for our students. We have a strong commitment to values education, and social activism pervades all that we do. SMMIS is committed to interfaith education and interfaith dialogue with real grassroots interactions with young people in Singapore. We teach Jewish Education as well as World Religions, and celebrate all religious festivals. There's a strong community feel here – we're one big family.
Does the school offer Hebrew?
Yes, though it isn't the only language on offer. We have a diverse student body that includes both Jewish and non-Jewish students. Students can choose between Hebrew and Mandarin, just as they can follow a Jewish Education track or one that covers Jewish culture as part of the study of world religions. Hebrew is taught either as a mother tongue for native speakers or as a second language for non-native speakers. Language lessons begin in our pre-school classes, when the children are around 18 months old.
Your school moved locations not long ago. What does the new campus offer?
We moved to our purpose-built Sembawang campus in May 2016. It has a rooftop swimming pool, basketball court, soccer pitch and state-of-the-art auditorium that houses our beautiful Steinway grand piano and has seating for up to 400 people.
Fun Facts about Elaine:
First job you ever had: Waiter
Book you never tire of reading: Wuthering Heights
Number of kids: Two of my own, hundreds of students
Favourite sports team: Liverpool FC, of course!
Favourite travel spots: Somewhere quiet with a book and a hammock
SMMIS at a Glance:
Ages accepted: 18 months to Grade 10 (growing into Grade 12 over the next couple of years)
Cost per year: $14,000-$24,000
Sir Manasseh Meyer International School
3 Jalan Ulu Sembawang
6331 4633 | smmis.edu.sg
Read more in our Schools section:
Which school's student-teacher ratio has got tongues wagging?
Top international schools in Singapore
Categories: Kids Living in Singapore Schools Schools Tags: International Schools in Singapore Sir Manasseh Meyer International School
About Expat Living
Expat Living is your trusted guide if you are moving to or living in Singapore! Our team will help you find out about shopping, dining, entertainment, schools, travel, fashion, finance, health and beauty.
National Day Parade – watch it!


Bedoom Furniture Sales Modern Home Decoration – Bedroom is one of the most important spaces of the house, where you take complete rest with extra comfort, so it is most important to have best quality bedroom furniture to furnish your bedroom well. When you are renovating the old house or building a new house, it is most important to add the sight bedroom furniture that can give you extra comfort and space. When it comes to the furniture, always try to keep suggestive furniture in your bedroom; never overcrowd your bedroom because it makes your bedroom look like odd. It is most important to select the right one furniture that should be installed in the bedrooms. Basically your bedroom furniture should include a bed, a pair of chairs, a mirror, a dressing table, a reading table and bookshelves, and you want to invest more money, you can install a couch of sofa in your bedroom. During installing the furniture it is most important to take the right measurement and find the right furniture that can go with your bedroom. Having the right furniture with proper measurement will help you to save a lot of space in your bedroom.
If you are looking to have bedroom furniture then you should search a best bedroom furniture shop that can offer best quality bedroom furniture to you. Bedroom furniture shop or store is one of the best options to get the right one that have different kinds of bedroom furniture with different shapes, sizes and colors. If you are searching for kid's bedroom furniture then you also have an option to install bunk beds. There are so many bunk bed models available in the market area with bright colors and extra comfort. But it is most important to have quality furniture either it is bedroom furniture or dining room furniture.
If you are looking to have dining room furniture then it is better to go for dining room furniture sales that organized from different furniture shop's owners. Dining room furniture sales are better to get quality dining room furniture with enough amount of discount.
This is about the Bedroom Furniture Sales Modern Home Decoration you can find many pictures related to the article which all the pictures are the best pictures. Click the picture Bedroom Furniture Sales Modern Home Decoration to find the original size and you can download it for free. We have collected many pictures of the Bedroom Furniture Sales Modern Home Decoration so you can get informations you are searching for, we have specified the category in Bedroom Furniture Sales Modern Home Decoration Information. to make you easier in searching the informations.


Whilst we have never been that impressed by this estate?s white wines, their Pinot Noir has been a real eye opener. This is not a jammy Pinot as it has an appealing freshness and vivacity that raises it to a serious class. It is quite remarkable value. Vibrant dark ruby colour, the palate is bursting with strawberry and blackberry fruit with a hint of woodiness against a rich earthy backdrop. Good acidity and length. For drinking now. Serve slightly cool.
generations (since 1495). The Manor is located on the southern fringe of the C"tes de Thongue, near the village of Montblanc about ten kilometers east of Beziers on the last group of hills overlooking the Mediterranean sea. The majority of the vineyards lie on the hillsides running down to the coastal plain and are cooled by the maritime breezes coming off the Mediterranean.
The Chateau de Coussergues Winery has over 600 hectares of which 210 have been set aside for vines. It is run by Arnaud de Bertier who, together with his wine-maker Natalie Arnaud (who trained at St. Halletts in the Barossa Valley), understand the importance of low yields for Pinot Noir and have kept production to around 50hl/ha.
They plant an impressive array of different grape varieties here including Chardonnay, Sauvignon and Viognier for white wines and Pinot Noir, MourvŠdre, Syrah, Grenache, Cabernet-Sauvignon, Merlot and Cinsault for the reds.


text:
Loughrie History, Family Crest & Coats of Arms
This Loughrie surname is an Anglicized form of the Gaelic "Luachra," derived from the word "luachair," which means "rushes" or "sedges."
Early Origins of the Loughrie family
The surname Loughrie was first found in Armagh (Irish: Ard Mhacha) located in the province of Ulster in present day Northern Ireland, where they held a family seat as ecclesiastics in west Armagh and Antrim. Irish history was greatly influenced by the Norman invasion of 1172, and thereafter, the surnames of Irish Gaelic clanns and septs and many of the Norman families became almost indistinguishable. This family name was found later in Tyrone about 1430.
Early History of the Loughrie family
This web page shows only a small excerpt of our Loughrie research. Another 95 words (7 lines of text) covering the years 1416, 1576, 1612, and 1652 are included under the topic Early Loughrie History in all our PDF Extended History products and printed products wherever possible.
Loughrie Spelling Variations
Spelling variations of this family name include: Loughran, Lochrane, Lochraine, Lutheran, Lochran, Laugheran, Loughrey, O'Loughran, O'Lochrane, O'Lochran, O'Loughraine and many more.
Early Notables of the Loughrie family (pre 1700)
More information is included under the topic Early Loughrie Notables in all our PDF Extended History products and printed products wherever possible.
Migration of the Loughrie family
Some of the first settlers of this family name or some of its variants were: Owen Loughran, who was an 'enforced emigrant' from Ireland to America in 1738; Peter Loughran, who was recorded in Philadelphia in 1826; Jeremiah Loughry, who arrived in New York in 1740.
Norman invasion
Family seat
Loughrie (Irish)


text:
Home » International Day of the World's Indigenous Peoples
International Day of the World's Indigenous Peoples
There are an estimated 370 million indigenous people in the world, living across 90 countries. They make up less than 5 per cent of the world's population, but account for 15 per cent of the poorest. They speak an overwhelming majority of the world's estimated 7,000 languages and represent 5,000 different cultures.
Indigenous peoples are inheritors and practitioners of unique cultures and ways of relating to people and the environment. They have retained social, cultural, economic and political characteristics that are distinct from those of the dominant societies in which they live. Despite their cultural differences, indigenous peoples from around the world share common problems related to the protection of their rights as distinct peoples.
Indigenous peoples have sought recognition of their identities, way of life and their right to traditional lands, territories and natural resources for years, yet throughout history their rights have always been violated. Indigenous peoples today, are arguably among the most disadvantaged and vulnerable groups of people in the world. The international community now recognizes that special measures are required to protect their rights and maintain their distinct cultures and way of life.
As a result of loss of their lands, territories and resources due to development and other pressures, many indigenous peoples migrate to urban areas in search of better prospects of life, education and employment. They also migrate between countries to escape conflict, persecution and climate change impacts. Despite the widespread assumption that indigenous peoples live overwhelmingly in rural territories, urban areas are now home to a significant proportion of indigenous populations. In Latin America, around 40 per cent of all indigenous peoples live in urban areas — even 80 per cent in some countries of the region. In most cases, indigenous peoples who migrate find better employment opportunities and improve their economic situation but alienate themselves from their traditional lands and customs. Additionally, indigenous migrants face a myriad of challenges, including lack of access to public services and additional layers of discrimination.
The 2018 theme will focus on the current situation of indigenous territories, the root causes of migration, trans-border movement and displacement, with a specific focus on indigenous peoples living in urban areas and across international borders. The observance will explore the challenges and ways forward to revitalize indigenous peoples' identities and encourage the protection of their rights in or outside their traditional territories.
The observance of the International Day will take place on Thursday 9 August 2018 from 3:00 pm to 6:00 pm in the ECOSOC Chamber at the United Nations Headquarters in New York. The programme can be found in Events. More information in the Department of Economic and Social Affairs (DESA) page.
Languages play a crucially important role in the daily lives of all peoples, are pivotal in the areas of human rights protection, peace building and sustainable development, through ensuring cultural diversity and intercultural dialogue. However, despite their immense value, languages around the world continue to disappear at an alarming rate due to a variety of factors. Many of them are indigenous languages.
Indigenous languages in particular are a significant factor in a wide range of other indigenous issues, notably education, scientific and technological development, biosphere and the environment, freedom of expression, employment and social inclusion.
In response to these threats, the United Nations General Assembly (UNGA) adopted a Resolution (A/RES/71/178) on 'Rights of Indigenous Peoples', proclaiming 2019 as the International Year of Indigenous Languages.


A cluster munition is a type of air-dropped or ground-launched explosive weapon that ejects smaller submunitions. Commonly, this is a cluster bomb that releases many small bomblets over a wide area, posing risks to civilians both during attacks and afterwards. Vast numbers of these unexploded munitions inevitably remain behind long after a conflict has ended, often hidden in vegetation and are prone to go off if accidentally disturbed.
Formed in 1998, the Geneva International Centre for Humanitarian Demining (GICHD) works to eliminate these cluster munitions, mines and other explosive remnants of war.
When the Convention on Cluster Munitions (CCM) – an international treaty that addresses the humanitarian consequences and unacceptable harm to civilians caused by cluster munitions – came into effect on 1st August 2010 it gave a categorical prohibition on types of munitions and a framework for action. The Convention prohibits all use, production, transfer and stockpiling of cluster munitions. However, a problem in implementing it was that managers of stockpiles simply didn't know which of their munitions were in breach of the CCM.
Armed forces often accumulate varied stocks of munitions from different nations and manufacturers. These are frequently difficult to identify because at first sight they can be indistinguishable from other weapons, and information to decipher their markings was unavailable or hard to understand.
In response to this problem, GICHD contacted Fenix Insight, an Explosive Ordnance Disposal consultancy involved in the disassembly of landmines and cluster bombs throughout the world.
Having worked together previously on similar projects, Fenix Insight turned to Ballard Chalmers to build Cluster Munition Identification Tool (CMID).
The CMID shows stockpile managers and administrators where to look for the markings and codes, enabling them to identify the contents of the munitions, and if they are banned by the Convention. Such information is otherwise spread between old handbooks, manuals, or even lost.
The easily accessible and searchable database includes graphic navigation and identification of cluster munitions based on weapon category. The sofware was developed to be simple and intuitive enough to be used in real world conditions and an additional overview shows types and combinations of explosive submunitions that can be carried by such cluster munitions.
The CMID tool is available on the GICHD website and is in use by nations around the world in support of the Convention on Cluster Munitions.


Discovering tomorrow's energy on a global scale relies on pushing fundamental science at the micro-level, and new technologies are constantly improving that search for true understanding.
To help achieve that new fundamental knowledge, ExxonMobil has partnered with IBM to access its quantum computing capabilities, a partnership announced at this year's Consumer Electronics Show (CES) in Las Vegas.
But, what does this mean today and how does this technology help find new solutions for tomorrow's world — a world that needs more energy with fewer emissions?
With quantum computing, engineers and researchers can leverage quantum physics and simulate nature and chemistry in ways never before imagined.
Specifically, quantum computing may one day solve impossibly large, complex equations at rapid speeds. The potential applications for a company powering the daily needs of an energy-hungry world range from optimising a country's power grid to using highly accurate chemistry calculations to discover new materials for more efficient carbon capture.
On hand at CES to talk about this partnership, Vijay Swarup, vice president of research and development for ExxonMobil Research and Engineering Company told the audience that Quantum will help ExxonMobil in its dual challenge of providing the world with the affordable, scalable energy it needs while also mitigating the risks of climate change.
In its mission to expand these computing capabilities "out of the lab and into the world," IBM has created its Q Network, a worldwide community of Fortune 500 companies, startups, academic institutions and national research laboratories to explore applications across industrial sectors and science.
ExxonMobil is the first energy company to join that network and working in partnership with IBM is not a new endeavour for the company, as Swarup told the audience.


(CBS News) When most people think about how the food they eat affects their appearance, bulging waistlines or greasy skin blemishes might come to mind. But did you know what you eat can go a long way to help your hair?
Or more importantly, missing out on these foods might leave your hair brittle and thinning. Dieters especially may be depriving themselves of essential nutrients their hair needs to stay healthy. "When you are on a crash diet, your hair crashes too," Dr. Alan J. Bauman, board-certified hair restoration physician in Boca Raton, Fla., told HealthPop.
Fad diets are typically very calorie-restrictive. This wreaks havoc with hair growth as the body defers nutrients to the more critical body functions. If someone is already at risk for hereditary hair loss, a crash diet might speed up his or her hair loss.
When it comes to foods that pack a beauty punch, it's hard to beat salmon, Dr. Bauman says. Loaded with omega-3 fatty acids, this high-quality protein source is also filled with vitamin B-12 and iron. Vegetarian? Include one or two tablespoons of ground flaxseed in your daily diet for some plant-based omega-3 fats to keep your hair strong.
"Popeye the Sailor Man" didn't eat all that spinach for healthy hair, but he could have. Spinach, like broccoli and Swiss chard, is an excellent source of vitamins A and C, which the body needs to produce sebum. Sebum is an oily substance that's secreted by hair follicles, sort of like the body's natural hair conditioner. Dark green vegetables also provide iron and calcium which boost hair health.
Legumes such as kidney beans and lentils should be an important part of your hair-care diet, says Dr. Bauman. Not only do they provide plentiful protein to promote hair growth, but ample iron, zinc, and biotin. While rare, biotin deficiencies can result in brittle hair.
Do you go nuts for thick, shiny hair? You should. Brazil nuts are one of nature's best sources of selenium, an important mineral for scalp health. Walnuts contain alpha-linolenic acid, an omega-3 fatty acid that may help condition hair. They are also a terrific source of zinc, as are cashews, pecans, and almonds. A zinc deficiency can lead to hair shedding, so make sure nuts are a regular on your healthy hair menu.
"Chickens and turkeys contain high-quality proteins that will help give you the healthy hair," Dr. Bauman says. Protein deficiencies can cause weak brittle hair and extreme deficiency can lead to a loss of hair color. Poultry also provides iron with a high degree of bioavailability, meaning the hair and body can easily reap its benefits.
Sink your teeth into hearty whole grains, including whole-wheat bread and fortified whole-grain breakfast cereals, for a hair-healthy dose of zinc, iron, and B vitamins.
The key to oysters' hair-boosting abilities is zinc - a powerful antioxidant that improves hair health. If oysters don't make a regular appearance on your dinner plate, don't despair. In addition to getting it from whole grains and nuts, you can also get zinc from beef and lamb.
Skim milk and yogurt are great sources of calcium, an important mineral for hair-growth. They also contain whey and casein, two high-quality protein sources. For some healthy hair foods "to-go," try bringing along a yogurt or cottage cheese cup. People can boost their hair benefits even more by stirring in a couple of tablespoons of ground flaxseeds or walnuts for omega-3 fatty acids and zinc.


0 Comments Published by KL Ocs Kid on Wednesday, May 2, 2007 at 11:28 PM.
NOW that's what people call history. Another memorable Anfield night, another semi-final win over Chelsea, and another Champions League final for Liverpool.
Like in 2005, the Stamford Bridge outfit felt the power of the famous old stadium as Rafael Benitez continued to cast his spell over Jose Mourinho in Europe. The Portuguese had belittled Liverpool during the build-up to the tie. Bad move. Fired up by those comments, the Liverpool players – backed by a raucous Anfield crowd – made Mourinho regret his outburst with a courageous performance to secure a seventh European Cup final appearance. But while the magnificent support from the stands played its part, this was a victory earned on the pitch. Liverpool levelled the tie through Daniel Agger's well-worked 22nd-minute strike before defending resolutely to keep Chelsea scoreless for 120 minutes to force a penalty shoot-out. Indeed, they had the chances to win the game before the penalties with an erroneous offside decision denying Dirk Kuyt a possible winner during extra time. Mourinho thought otherwise, but he was fooling only himself. Liverpool thoroughly deserve a second Champions League final in three seasons, where AC Milan or Manchester United lie in wait in Athens on May 23. Chelsea could well have been out of sight after a first leg last week in which only a fine performance from goalkeeper Pepe Reina kept Liverpool in with a chance. So it was apt the goalkeeper should assume the mantle of hero last night, saving from both Arjen Robben and Geremi in front of the Anfield Road End to allow Kuyt the poetic justice of stroking home the winning penalty and send the Liverpool players racing towards the Kop. Now Reina is poised to follow in the footsteps of his father, who appeared for Atletico Madrid in their European Cup final against Bayern Munich in 1974. For Liverpool's American owners George Gillett and Tom Hicks, this was the kind of evening for which they'd paid their millions. Both were in attendance, Gillett even coming down to the front of the directors' box before kick-off to shake hands with fans, sign autographs and have pictures taken. He ended the evening by being drenched with champagne after joining Liverpool's jubilant players in the dressing room. Gillett, like Hicks, has been well and truly bitten by the Anfield bug. Mourinho reckoned he was worthy of a round of applause from the Anfield crowd for his belatedly flattering comments on Liverpool. There was, however, about as much chance of that happening as the street vendor outside the ground shifting many of his puzzling Liverpool/Chelsea scarf combinations. Not for the first time, Benitez's tactics and line-up were spot on while Chelsea floundered with depressing long-ball tactics towards the increasingly ineffective Didier Drogba. While the Premiership remains Mourinho's domain, the Portuguese has been continually outsmarted by Benitez in Europe. The Liverpool manager had raised eyebrows by naming Bolo Zenden in midfield at the expense of Alonso who, having missed the corresponding fixture in 2005 through suspension, began on the bench. Zenden will have won a whole army of new admirers after a fine display against his former team. Alonso emerged in the second half to complement a midfield in which Steven Gerrard and Javier Mascherano dominated Frank Lampard, Claude Makelele and John Obi Mikel. Steve Finnan returned at right-back after missing the last four games with a neck injury, while Peter Crouch partnered Kuyt in attack – the same pairing that tormented Chelsea during Liverpool's 2-0 Premiership win here in January. Like the rest of Benitez's men, the pair ran themselves into the ground with a heroic effort. The Kop was in full voice long before kick-off, and the teams were greeted with a deafening wall of noise akin to that of 2005. While Luis Garcia netted in the fifth minute that evening, the home team had to wait until the 22nd minute to go ahead on the night and level the tie. At least there was no debate about whether it had crossed the line this time. Joe Cole netted the only goal last Wednesday to capitalise on Liverpool's sluggish start, but he was partially responsible for his team going behind after upending Steven Gerrard on the left for a free-kick. In a move straight from the training ground, Gerrard rolled the ball across for the approaching Agger to sidefoot through a group of players from the edge of the area into the bottom corner. Given Agger was heavily criticised being given the runaround by Drogba last week, it was small wonder the Danish centre-back celebrated with such gusto. It was a lead Liverpool merited for a vibrant, high-tempo opening as Chelsea stuck men behind the ball and booted long for Drogba, a defensive tactic Mourinho persisted with all night. Drogba then demonstrated both sides to his game as Chelsea finally began to build some momentum. First, the Ivorian embarrassingly writhed on the turf after being breathed on by Agger, and then solicited a fine block from Reina after Mascherano had given the ball away to Mikel. Chelsea came close again five minutes before half-time when Essien couldn't turn the ball home at the far post after Drogba had headed on a Frank Lampard corner, the effort striking the shoulder of the makeshift centre-back. Liverpool had the next opening on 56 minutes when neat trickery by Jermaine Pennant – the winger an outstanding performer before succumbing to injury – created space for a cross to the far post for Crouch, whose header was blocked by Petr Cech's legs before the ball was hacked away by John Terry. And they were closer moments later when John Arne Riise's left-wing cross was headed on to the crossbar by Kuyt with the Czech international keeper beaten. Drogba then succeeded in earning Agger a caution with some more simulation shenanigans before Liverpool carved out another opening, Terry misjudging a long pass but the ball wouldn't come down quick enough for Pennant, allowing Essien to race over and block his shot. The tension was tangible, especially when, on a rare Chelsea sortie, Ashley Cole found space behind the Liverpool defence and his low cross was turned over by Jamie Carragher inside the six-yard box with Drogba loitering. Zenden struck a 20-yard drive Cech clutched at the second attempt, but no more scoring meant Liverpool chartered new territory at Anfield in this competition with an extra-time period. If Chelsea were tiring from their efforts chasing the quadruple, it didn't show. Liverpool were then deprived of a perfectly good goal on 100 minutes when Alonso's piledriver was parried out to Kuyt, who rattled home. The assistant referee ruled the Dutchman was in an offside position when the initial shot came in; television replays showed otherwise. Benitez's side almost won it with two minutes remaining when Robbie Fowler, on for the exhausted Javier Mascherano, laid the ball off for Kuyt only for Cech to beat out the Dutchman's shot. The finale was so nerve-wracking that Benitez's wife Montse was praying in her seat in the directors' box and looking at the Kop instead of the spot-kicks as the players prepared for the decisive shoot-out. Then came the penalties. Athens need now prepare for a Scouse invasion. LIVERPOOL (4-4-2): Reina; Finnan, Carragher, Agger, Riise; Pennant (Alonso 78), Gerrard, Mascherano (Fowler 118), Zenden; Crouch (Bellamy 106), Kuyt. Subs: Padelli, Arbeloa, Hyypia, Gonzalez. BOOKINGS: Agger and Zenden (both fouls). CHELSEA (4-1-4-1): Cech; Ferreira, Essien, Terry, A Cole; Makelele (Geremi 118); J Cole (Robben 98), Obi Mikel, Lampard, Kalou; Drogba (Wright-Phillips 107). Subs: Cudicini, Bridge, Boulahrouz, Diarra. BOOKING: A Cole (foul). REFEREE: Manuel Mejuto Gonzalez (Spain). ATT: 42,554. This story has been reproduced from today's media. It does not necessarily represent the views or position of Liverpool Football Club.