Present-moment-awareness: This is perhaps the most commonly used definition of Mindfulness. To quote the widely cited paper "Mindfulness: A proposed operational definition" by Bioshp et. al. from the journal "Clinical Psychology: Science and Practice, 2004"1 – Mindfulness involves two things (1) observing and attending to the changing field of thoughts, feelings and sensations from moment to moment and; (2) with an orientation that is characterized by curiosity, openness and acceptance. For example, as I type this, I hear honking of cars, chirping of birds, clicking of the keyboard, I feel the movement of the breath, movement of the abdomen; I observe thoughts about mindfulness etc. It is a Sunday morning, no hurry and that makes the environment conducive for being mindful. What about a Monday morning while stuck in traffic? That is what one should try and see. The key resource here is attention and it can be completely hijacked by thoughts and emotions to the extent that no attention is left to observe.
A variant of this flavour is "Mindfulness is attention to the movement of thought" or "Mindfulness is attention to the train of thought as it moves from one station to another." Just like we are aware of the movement of body parts like hands and legs as they move, we can be aware of the movement of thought which involves subtle material movement of chemicals, electrical signals through the neural network. This definition is advocated by Jiddu Krishnamurti2 and his collaborator David Bohm. Bohm called it proprioception3 of thought.
Seeing false as false: Mindfulness is being aware of the possibility of a cognitive illusion while thinking. Kahneman's "Thinking, fast and slow" shows us that a large part of our thinking is automatic. It is also subjected to cognitive biases especially when we navigate the uncertainty around us. The fast and automatic thinking mode creates what is called cognitive illusions4. For example, when we read the Google story, we feel that we know what caused the success of Google. Kahneman calls this "illusion of understanding". We are subjected to many such illusions – like "illusion of skill", "illusion of control", "illusion of time" etc. We are mindful when we are aware of the possibility of these illusions while we are thinking. It is similar to the awareness of being fooled while watching a magic show5. For example, as I write this blog, I might be under the impression that the three flavours of mindfulness will be useful to the reader. But I may be currently subjected to the "overconfidence bias". Who knows?
Notice wasteful thoughts: Mindfulness is noticing that the current thoughts (or train of thought) are wasteful or not serving any useful purpose. "Will readers like this blog?" Dwelling on this thought may lead to some changes that may improve the blog. However, an excessive and repetitious thinking like this is not going to serve any useful purpose. I might as well do my best in writing the blog and leave the rest to the readers. Moreover, if I get a specific comment about some sentence or a paragraph not being clear or even incorrect, it will be good to be open to modifying it. To quote Nobel Laureate John Nash who recovered from schizophrenia, "It is a matter of policing one's thoughts trying to recognize paranoid ideas and rejecting them, just the way somebody who wants to lose weight has to decide consciously to avoid fats or sweets."7 For Nash, the recognition started with ideas related to politics as wasteful.
In short, we looked at the three flavours of mindfulness: present-moment-awareness, seeing false as false and noticing wasteful thoughts. They are overlapping. And none of them involves a specific posture, closing of eyes, a quiet room etc. It is a state you can be in anytime, anywhere. Hope you find some of these flavours useful.
1. "Mindfulness: A proposed operational definition" by Bishop et. al., Clinical Psychology: Science and Practice, September 2004, Volume 11, Issue 3, pages 230-241.
3. David Bohm explains proprioception of thought in the book "Thought as a system". Check out a summary in my blog and also in dbohm.com site.
4. I have written about 3 cognitive illusions from Kahneman's "Thinking, fast and slow" in this blog: 3 powerful illusions created by thought.
5. Check out my blog: Learning mindfulness through "Penn and Teller: Fool us" magic show. The concept of illusion is prominently present in Hindu scriptures as Maya and in Buddhist Mahayana literature as Vipallasa.
6. "I am that" by Nisargadatta, chapter 66 (All search for happiness is misery), page 314.
7. For Johan Nash quote, see my blog: A beautiful mind and 3 acts of creativity, madness and awakening.
8. Eckhart Tolle's quote is from his interview by Oprah Winfrey on the third chapter of A New Earth. Check it out on youtube here.
It has been over five years since I first wrote about various elements of an organizational innovation ecosystem (see the picture above). In this half a decade I got opportunities to meet people from several dozen organizations – from various types such as for-profit, not-for-profit, Government, NGO etc. What did I find? Which elements seem to be in place? Which elements are hard to find? Which elements would I replace today? And which new ones might I add? Let's explore in this article.
Idea management process: Many organizations are making serious efforts in improving their idea management process. Some are also trying to bring various disjoint processes under one broad umbrella – e.g. kaizen, Quality circle, Idea portal, R&D, Internal VC process etc.
Rewards & Innovation day: HR department has been playing a role in putting rewards & recognition process in place. I got an opportunity to visit the stalls put up on the innovation day in organizations like Titan.
Training programs: L&D department has been playing a key role in rolling out training programs that raise awareness on innovation.
Laboratory & corporate venture fund: In terms of structures, I see investments in labs and even in putting a corporate venture fund together.
Challenge process: Taking ownership of top business challenges and keeping them alive in a challenge book is something that I don't see much. Managers who take up this role of owning one or more key business challenges are called champions in our book "8 steps to innovation". A live and prioritized challenge book can bring focus to innovation efforts. It might also contribute to the strategy.
Success stories: Like Master Shifu follows a bright spot to train Kung Fu Panda, there is an opportunity in digging deeper the success stories and finding scalable approaches. Unfortunately, managers are so busy with problems, that they don't have time for studying the bright spots – be it the people who give ideas regularly, prototyping etc.
Partnership network: This is perhaps the toughest asset to build and manage. It takes years and very few people have the patience to look that far. However, it is an extremely potent asset for building innovation capacity.
Any new element I would add today? Perhaps an element titled "innovation sandbox" – structures where experimentation capacity is massively increased in a specific area. Also I would replace the element "Immersive Research" with a more commonly used term "Design Thinking". And replace "Success stories" with "Bright spot focus". (See the updated picture below).
Overall, I still feel that the ecosystem view can provide a useful perspective while building innovation capacity systematically.


We spend a lot of time choosing the people and relationships in our lives. It just makes sense. The people we share our lives with have a huge impact on our happiness and satisfaction.
But when you think about how much time we spend at work, it's amazing that we don't invest more into making sure we are in a job that fits us. And the reverse is true as well- we all know the positive or negative impact an employee can have on a business. Yet surprisingly, recruiting is often under resourced or has the wrong people performing the task.
That is the beauty and the complexity of the recruitment business. Good recruiters are able to truly understand and match the needs of business with the needs of an individual.
And this is what sets FourQuarters apart. People are the heartbeat of our Business. We believe our business shouldn't be complex to be good. Simple things like "doing what we say" and delivering great outcomes through passion, integrity, reliability and expertise- these are the things we've built our business on.
As we continue to grow, we are optimistic about the future. We move forward, confident that the results we achieve and the experience of working with us will continue to build solid and enduring relationships.


Constructed from an ultra-durable fiberglass and metal design, the 2B1703 Kwik Flex® Soccer Goal is designed to be long-lasting through endless training sessions. The tension bars, vinyl posts and crossbar give this goal the look and feel of a traditional soccer goal with the ability to be set up and taken down in minutes without any tools. Due to its size, lightweight design and easy assembly, this goal is absolutely perfect for recreational practice, training and casual backyard use.


text:
\section{Introduction}
Multistationarity  (the existence of more than one  steady state under particular biological conditions)  in cellular systems can be seen  as a mechanism for cellular decision making.  How it arises is therefore fundamental to the understanding of cell signaling, that is, the communication of signals to regulate  cellular activities and responses. Generally, cell signaling  involves  post-translational modifications of proteins, such as phosphorylation, acetylation, or methylation. These modifications  change the state of a protein in a discrete manner, for example from an active to an inactive state.

In eukaryotes,  reverse phosphorylation is the most frequent  form  of protein modification affecting $\sim\!30\%$ of all  proteins in humans \cite{cohen}.
{\it Kinases} catalyze the transfer of phosphate groups to target proteins and {\it phosphatases} catalyze the reverse operation.
After the completion of the human genome project, genome analysis estimated the number of  kinases to $\sim\!500$ \cite{manning-kinome}, while the number of phosphatases is smaller by two thirds \cite{cohen}.
Two  protein phosphatases, PP-1 and PP-2A, account for the vast majority of all phosphatase activity
 \cite{xiao-li} with more than 50 PP-1 targets  being characterized  \cite{Cohen:2002p271}.

As a consequence, there is a substantial complexity in the interplay between enzymes (kinases and phosphatases) and substrates, exemplified by systems where protein substrates use the same catalyzing enzymes (enzyme sharing),  and systems where different enzymes catalyze  the same reaction (enzyme competition). Competition and sharing are general examples of cross-talk between motifs.

The aim of this work is to determine  characteristics that lead to multistationarity. Following different modeling strategies it has already been shown that feedback in signaling networks as well as multisite phosphorylation can both account for multistationarity \cite{Kapuy:2009p16,Markevich-mapk,TG-Nature}.

We present a mathematical approach for analyzing the steady states of small systems.  Our method leads to explicit conditions for when multistationarity occurs in terms of rate constants and conserved total amounts of substrates and enzymes. Further  the approach provides means to study the stability of steady states.

First we present the motifs that we analyze and then we develop the method  to determine  multistationarity and to study stability. The paper concludes with some perspectives and discussion.

\begin{table}[b!]
\begin{tabular}{lp{13cm}}
\hline
Motifs & Biological phenomena \\ \hline
(b) & A kinase acting also as phosphatase on the same substrate, e.g. HPrK/P kinase-phosphatase in Gram positive bacteria \cite{chaptal-Hpr}.  \\
(c),(d) & Several kinases and/or phosphatases acting on the same substrate, e.g.  (i) Several kinases  phosphorylate the alpha subunit eukaryotic initiation factor (eIF2$\alpha$) at Ser51 \cite{haro-santoyo}; (ii) The  phosphatases MPK-1 and  PTP-SL both modify ERK1 \cite{Shaul:2007p309}.
\\
 (e) & Multi-site phosphorylation  by different kinases and phosphatases at each site, e.g.  (i) Primed kinases, e.g.~GSK-3 \cite{Cohen:2000p313}; (ii) Akt1 is (de)activated through three-site sequential (de)phosphorylation by three  different kinases (phosphatases) \cite{xiao-li}.  \\
 (f),(g) & Multi-site phosphorylation with the same kinase and/or phosphatase responsible for all modifications, e.g. (i) Two-site phosphorylation of ERK catalyzed by MEK; (ii) Dephosphorylation of ERK2 catalyzed by DUSP6 \cite{Ferrell:1997p318}. \\
 (h),(i) & The same enzyme catalyzing the modification of two different substrates, e.g.  the kinases ERK1, ERK2 and the kinase products of the p38 pathway catalyze phosphorylation of two substrates (the mitogen- and stress-activated protein kinase (MSK) 1/2 and the MAP kinase signal-integrating kinase (MNK) 1/2) \cite{Keshet:2010p272}.  \\
 (j),(k),(l) & Cascades with several modification steps and substrates, e.g.
 (i) MAPK cascades; (ii) Protein kinase A (PKA) phosphorylates  phosphorylase kinase, which in turn phosphorylates glycogen phosphorylase (with dephosphorylation carried out by the same phosphatase, PP-1,  in the two different layers)  \cite[Fig. 7.17]{Fell-book},\cite{PCohen}.\\ \hline
\end{tabular}
\caption{Cellular systems represented by  Motifs (a)-(l) }\label{biotable}
\end{table}

\section{Motifs}
\subsection{Description}\label{motif-description}
We analyze the motifs shown in Fig.~\ref{motifs}. The motifs are referred to as Motif (a)-(l) and  provide simple abstract representations of  known cellular systems.  Some examples motivating our choice of motifs are given in Table \ref{biotable}.
A rich source of examples is  found in the well-studied MAPK cascades.

To understand how multistationarity relates to enzyme usage we  base our investigation on a motif that does not show multistationarity itself. Therefore we build  the motifs from a one-site phosphorylation cycle which is mono\-stable  \cite{Gold-Kosh-81,Gold-Kosh-84,Bluthgen-sequestration,salazarN1} and shown in  Motif (a). A specific kinase (phosphatase) catalyzes phosphorylation (dephosphorylation) and all mo\-di\-fications can be reversed.    In general, protein phosphoforms are denoted by $S$ and $P$, Fig.~\ref{motifs}. If one phosphoform is converted into another, an arrow is drawn and  the enzyme ($E$ or $F$) catalyzing the reaction is indicated.
\begin{figure}[b!]
\centering
\includegraphics{figure1.pdf}
\caption{\small Motifs composed of one or two one-site cycles. Motifs with purple label, and only these, admit multiple biologically meaningful steady states. $S_i$ and $P_i$ are substrates with $i=0,1,2$  phosphorylated sites. $E, E_1, E_2$ denote kinases, and $F, F_1, F_2$  phosphatases. In Motif (b) the  kinase and the phosphatase are the same enzyme.
}\label{motifs}
\end{figure}

Motifs (a)-(d) cover different possibilities for a one-site modification process. In Motif (b), the same enzyme catalyzes  phosphorylation and dephosphorylation. Motifs (c) and (d) account for  competition between  kinases and/or phosphatases to catalyze the same modification(s).

In eukaryotes, phosphorylation of most proteins takes place in more than one site \cite{olsen-phosphoproteome}, potentially with different bio\-logical effects \cite{wu-selective}. Combination of two one-site cycles into a two-site sequential  cycle   yields three motifs: (e) all enzymes are different, (f)  only one kinase but two phosphatases, and (g)  one kinase and one phosphatase.  By symmetry, Motif (f)  represents as well a motif with one phosphatase but two kinases. We assume for simplicity that both phosphorylation and dephosphorylation proceed in a sequential and distributive manner \cite{salazar_review}; that is, one site is (de)phosphorylated at a time in a specific order.

Motif (h) represents one-site modification of two substrates that share the same kinase but  use different phosphatases. This motif represents  by symmetry also a system with shared phosphatase.  If  both the kinase and the phosphatase are shared, we obtain Motif (i).

Finally, two one-site modification cycles can be combined in a cascade motif, where the activated substrate of the first cycle acts as the kinase of the next. The interplay between enzymes is represented by three cascades: (j)  dephosphorylation at each layer uses different phosphatases, (k) the phosphatase is  not layer specific, and (l) the  kinase of the first layer ca\-ta\-lyzes the modification in the second layer as well.

\subsection{Mathematical modeling}

We assume that any modification $S \rightarrow S^*$  follows the classical \emph{Michaelis-Menten} mechanism  in which an intermediate complex $Z$ is formed reversibly but dissociates into product and enzyme  $G$  irreversibly:

\centerline{\xymatrix{
S + G \ar@<0.5ex>[r]^(0.6){a} & Z  \ar@<0.5ex>[l]^(0.4){b} \ar[r]^(0.4){c} & S^* + G
}}

The phosphate donor, generally ATP, is assumed to be in large constant concentration   and hence embedded into the rate constants. Imposing mass-action kinetics, the species concentrations over time  can be modeled by a system of polynomial differential equations. For example, in Motif (a) the  equations are (here $E$  also refers to the concentration of the kinase $E$, and similarly for the other species):
\begin{align*}
\dot{E} &= (b^E + c^E)X- a^E E S_{0} &\dot{X} &=  -(b^E + c^E)X + a^E E S_{0}  \\
\dot{F} &=(b^F + c^F)Y -a^F F S_{1} & \dot{Y} &= -(b^F + c^F)Y + a^F F S_1   \\
\dot{S_{0}} &=  b^{E} X +  c^F Y  - a^{E} E S_{0} & \dot{S_{1}} &=  c^E X +b^{F} Y - a^{F} F S_{1},
\end{align*}

\noindent where  $X$ $(Y)$ is the intermediate complex formed by the enzyme $E$ $(F)$ and the substrate $S_0$ $(S_1)$, and $\dot{x}$ denotes differentiation of $x=x(t)$ with respect to time.   For all motifs, there are conservation laws which define time-conserved quantities (total amounts), e.g. $\dot{E}+\dot{X}=0$ and so  $\overline{E}=E+X$ is conserved. The total amounts are fixed  by the initial  concentrations  and determine the state space of the dynamical system. Motif (a) has three conserved  total amounts, namely $\overline{F}=F+Y$ and $\overline{S}=S_0+S_1+X+Y$ in addition to that of $\overline{E}$.

The steady states of the system are  solutions (potentially negative) to the polynomial equations obtained by setting all derivatives  to zero with the constraints imposed by the conservation laws, once total amounts have been fixed. These laws imply that some steady state equations are redundant,
e.g. either $\dot{E}=0$ or $\dot{X}=0$ can be disregarded.
We focus on  the \emph{biologically meaningful steady states} (BMSSs), that is, the steady states for which all concentrations are non-negative (positive or zero). If at least two BMSSs exist for fixed total amounts, then  the system is said to be multistationary.

The specific form of the chemical reactions for  Motifs (a)-(l) together with the corresponding systems of differential equations are described in the Supplementary Material (SM), attached at the end of the main text.

\section{The Steady State Function $\varphi$}
In this section we outline the procedure used to analyze the  motifs. Details of the mathematical analysis are in the SM.

The system of equations describing the steady states can be reduced  substantially by elimination of variables \cite{TG-Nature,Feliu:2010p94}. For the  motifs considered here, elimination of variables implies that the steady states are characterized by a relation $\overline{S} = \varphi(Y)$ between the concentration of one of the species, typically an intermediate complex $Y$, and the total amount of a substrate $\overline{S}$. The concentrations   of the other species are given in terms of $Y$, usually as ratios of polynomials in $Y$.
By imposing all concentrations to be non-negative, $Y$ is restricted to a set $\Gamma$ of possible values.
Further, for any $\overline{S}\geq 0$, there is {\it at least one} BMSS, that is, $\overline{S}=\varphi(Y)$ for some $Y$ in $\Gamma$.
The function  $\varphi$ is continuous  and differentiable in $\Gamma$ and depends on the rate constants and the total amounts, except for $\overline{S}$.

The number of BMSSs can be found from the  ana\-ly\-sis of $\varphi$. If $\varphi$ is strictly increasing or decreasing in $\Gamma$,  $\varphi$ is one-to-one and hence, for a given total amount $\overline{S}$, there is a corresponding unique $Y$ at steady state. Consequently, multistationarity cannot occur (Fig. \ref{summary}a).

Figs. \ref{summary}b and \ref{summary}c show situations where multistationarity occurs. If $\varphi$ has increasing and decreasing parts, or if $\Gamma$ is not connected, then   $Y_1\not=Y_2$ with $\varphi(Y_1)=\varphi(Y_2)=\overline{S}$ might exist. Hence, there are at least two  BMSSs with the same  $\overline{S}$.

These two figures represent substantially different switch responses. In Fig. \ref{summary}c, there is only one BMSS for low $\overline{S}$. An increase of $\overline{S}$ to $\overline{S}_{max}$ causes the system to switch to  a `high' steady state (high $Y$)   under the assumption that the green steady states in the figure are stable. If $\overline{S}$ is decreased again to $\overline{S}_{min}$, then  the system switches back  to a `low' steady state. In Fig. \ref{summary}b,  there is  one BMSS for low $\overline{S}$. An increase of $\overline{S}$  keeps the system in the first branch of $\varphi$ and thus it will behave as a monostationary system.

\begin{figure}[b!]
\includegraphics{figure2.pdf}
\caption{\small  Possible shapes of $\varphi$ in $\Gamma$ (colored regions: magenta=unstable BMSSs; green=(possible) stable BMSSs).
(a) $\varphi$ is increasing and for any $s$, there is one BMSS ($y$) such that $\varphi(y)=s$. (b) $\Gamma$ consists of two disconnected regions. For $s<\overline{S}_{\rm min}$ there is one BMSS; for $s=\overline{S}_{\rm min}$ there are precisely two; and for $s>\overline{S}_{\rm min}$ there are three;  $\varphi$ is also defined  in the white region but some concentrations become negative. (c) $\varphi$ is in part decreasing, in part increasing. For $\overline{S}_{\rm min}<s<\overline{S}_{\rm max}$ there are three BMSSs; for $s=\overline{S}_{\rm min}$ or $s=\overline{S}_{\rm max}$, there are two; and for $s<\overline{S}_{\rm min}$ or $s>\overline{S}_{\rm max}$,  there is  one. }\label{summary}
\end{figure}

Interestingly,  the derivative $\varphi'(Y)$ of $\varphi(Y)$  provides means to determine whether some steady states are unstable. Unstable steady states are unattainable under biological conditions. Specifically, we find that either the regions in which $\varphi$ is increasing or those in which it is decreasing must correspond to unstable steady states, see Section \ref{stability}.

 In summary, the function $\varphi$ determines whether multiple BMSSs exist and encodes information about the stability of steady states.
In the next section we analyze  $\varphi$ for Motifs (e) and (f).  We show how enzyme sharing in a two-site cycle (f)  leads to multistationa\-ri\-ty, as opposed to a two-site cycle with different enzymes (e). A detailed analysis of all motifs is given in the SM.

\section{Mono- versus Multistationarity}

\subsection{Monostationarity}

Motifs (a)-(e), (h), and (j) have exactly one BMSS for any choice of rate constants and total amounts. In all cases, the function $\varphi$ is increasing in $\Gamma$. The procedure is very similar in all cases and  is thus only illustrated for Motif (e).  We take some effort in explaining the details as the procedure might have general applicability.

Motif (e) consists of three phosphoforms of the substrate, $S_0,S_1,S_2$, with subscript indicating the number of phosphorylated sites.  The chemical reactions of the system are:

\noindent
\centerline{\small
\xymatrix@R=11pt@C=16pt{
S_{0} + E_1 \ar@<0.4ex>[r]^(0.6){a_{1,E}} & X_1  \ar@<0.4ex>[l]^(0.4){b_{1,E}} \ar[r]^(0.4){c_{1,E}} & S_{1} + E_1 &
S_{1} + E_2 \ar@<0.4ex>[r]^(0.6){a_{2,E}} & X_2  \ar@<0.4ex>[l]^(0.4){b_{2,E}} \ar[r]^(0.4){c_{2,E}} & S_{2} + E_2 \\
S_{1} + F_1 \ar@<0.4ex>[r]^(0.6){a_{1,F}} & Y_1  \ar@<0.4ex>[l]^(0.4){b_{1,F}} \ar[r]^(0.4){c_{1,F}} & S_{0} + F_1 &
S_{2} + F_2 \ar@<0.4ex>[r]^(0.6){a_{2,F}} & Y_2  \ar@<0.4ex>[l]^(0.4){b_{2,F}} \ar[r]^(0.4){c_{2,F}} & S_{1} + F_2
}}
We denote the inverse of the Michaelis-Menten constants of $E_i$  by $\kappa_{i,E}=a_{i,E}/(b_{i,E}+ c_{i,E})$ and of $F_i$ by $\kappa_{i,F}=a_{i,F}/(b_{i,F}+ c_{i,F})$.  The ratio of the catalytic constants of phosphatase and kinase is denoted by $\mu_i=c_{i,F}/c_{i,E}$.

The system has five conserved total amounts, which are assumed to be positive: Four for enzymes, $\overline{E}_i = E_{i} + X_{i}$ and $\overline{F}_i = F_{i} + Y_i$ ($i=1,2$),  and one for substrate, $ \overline{S}  =   S_{0}+S_1+S_2 + X_{1}+X_2+Y_1+Y_2$.  The steady state equations can be rewritten as
\begin{align}\label{twocycle_dif}
X_1 &= \kappa_{1,E} E_1 S_{0} &\quad Y_1&=\kappa_{1,F} F_1 S_1 &\quad X_1 &= \mu_1 Y_1 \\
X_2 &= \kappa_{2,E} E_2 S_{1} &\quad Y_2&=\kappa_{2,F} F_2 S_2 &\quad X_2 &= \mu_2 Y_2. \nonumber
\end{align}
The last column gives $X_i$ in terms of $Y_i$. The total amounts $\overline{E}_i,\overline{F}_i$ give $E_i,F_i$ in terms of $Y_i$ as well: $E_i=\overline{E}_i-\mu_iY_i$, $F_i=\overline{F}_i-Y_i$.
Further, if $\overline{E}_i,\overline{F}_i>0$ then $E_i=0$ or $F_i=0$ cannot be solutions to Eq.~\eqref{twocycle_dif}.
It follows that  the concentrations $E_i,F_i$ are positive if and only if $Y_i$ is in $\Gamma_i=[0,\xi_i)$ with
$\xi_i=\min(\overline{F}_i,\overline{E}_i/\mu_i)$.

We further isolate $S_0,S_1$ from the first row in Eq.~\eqref{twocycle_dif} and $S_2$ from the second and obtain
\begin{equation}\label{sy}
S_0 = \frac{\mu_1 Y_1}{\kappa_{1,E}(\overline{E}_1-\mu_1Y_1) }, \quad S_i= \frac{Y_i}{\kappa_{i,F}(\overline{F}_i-Y_i) }
\end{equation}
for $i=1,2$. Then, $S_0,S_1$ (resp. $S_2$) are non-negative  increasing  continuous functions of $Y_1$ in $\Gamma_1$ (resp. $Y_2$ in $\Gamma_2$).
The remaining equation, $X_2=\kappa_{2,E} E_2 S_{1}$, gives $Y_2$ in terms of $Y_1$:
\begin{equation}\label{f1}
Y_2 =f(Y_1)=\frac{\kappa_{2,E} \overline{E}_2 Y_1}{\mu_2(\kappa_{1,F}(\overline{F}_1 - Y_1) + \kappa_{2,E} Y_1)}. \end{equation}
The function $f$ is non-negative increasing and continuous in $\Gamma_1$. Further, for $Y_2$ to be in $\Gamma_2$,
it is required that $Y_1$ is  in $\Gamma=[0,\xi)\subseteq\Gamma_1$ with $\xi=\min(\xi_1, f^{-1}(\xi_2))$.

Finally, using Eq.~\eqref{f1}, we find that  $X_2$ and $S_2$ are increasing functions of $Y_1$  in $\Gamma$. Therefore, using the formulas above,  all  concentrations at steady state  are non-negative if and only if  $Y_1$ is in $\Gamma$.  We conclude that  the BMSSs of the system satisfy
$$\overline{S} =S_{0}+S_1+S_2 + X_{1}+X_2+Y_1+Y_2 = \varphi(Y_1)$$
for $Y_1$ in $\Gamma$. Since $\varphi$ is a sum of  increasing  continuous functions in $Y_1$, then so is $\varphi$. Additionally, $\varphi(0)=0$ and $\varphi(Y_1)$ tends to infinity as $Y_1$ tends to $\xi$. Thus, $\varphi$ has  the form in Fig. \ref{summary}a with a unique $Y_1$ for any given $\overline{S}$, that is, there is one BMSS.

\subsection{Multistationarity}
We consider a two-site phosphorylation system with one kinase but different phosphatases for each phosphoform, as shown in Motif (f). Multistationarity has been observed numerically in this system  \cite{Markevich-mapk}. The system reduces to Motif (e)  by setting $E_1=E_2$ and  we use the notation introduced previously. The conservation laws are the same with the exception that  there is only one kinase law, $\overline{E}=E+X_1+X_2$. Define $\xi_i=\min(\overline{F}_i,\overline{E}/\mu_i)$ and $\Gamma_i=[0,\xi_i)$.

The system of equations to be solved is similar to  Eq.~\eqref{twocycle_dif} with $E=E_i$. Thus, we start by writing $X_i,E,F_i$ as  functions of $Y_1,Y_2$. Since $E,F_i$ must be positive at any BMSS, we require $0\leq Y_i<\overline{F}_i$ and $\mu_1Y_1+\mu_2Y_2<\overline{E}$.
For these values we obtain
$$ S_0 = \frac{\mu_1 Y_1}{\kappa_{1,E}(\overline{E}-\mu_1Y_1-\mu_2Y_2) }, \quad S_i= \frac{Y_i}{\kappa_{i,F}(\overline{F}_i-Y_i) }$$
for $i=1,2$, which are non-negative increasing continuous functions of $Y_i$. Using $X_2 = \kappa_{2,E} E S_{1}$, we obtain  $Y_2$ as a non-negative continuous function of $Y_1$ in $\Gamma_1$:
$$Y_2=f(Y_1)=\frac{\kappa_{2,E}(\overline{E} -\mu_1 Y_1) Y_1}{\mu_2(\kappa_{1,F}( \overline{F}_1 -Y_1) + \kappa_{2,E} Y_1)}. $$
This function resembles that in Eq.~\eqref{f1} except for the quadratic term in the numerator, which is a consequence of the conservation law for $\overline{E}$ involving both $Y_1$ and $Y_2$.  Further, $f$  might not be increasing for all $Y_1$.

Let  $\Gamma=\{Y_1\in \Gamma_1, \textrm{ such that } f(Y_1)\in \Gamma_2 \}.$ Using the formulas derived above,  all concentrations at steady state  are non-negative if and only if  $Y_1$ is  in $\Gamma$. Hence, for any BMSS,
$$\overline{S} =S_{0}+S_1+S_2 + X_{1}+X_2+Y_1+Y_2 = \varphi(Y_1)$$
with $Y_1$ in $\Gamma$. The function $\varphi$ is continuous with $\varphi(0)=0$ but $\Gamma$ might not be a connected interval.

Define $\Lambda =(1+\kappa_{2,E}/\kappa_{1,F})\mu_1 \overline{F}_1 - \overline{E} $. If $\Lambda \leq 0$,
then $f$ is an increasing function in $\Gamma$ and we conclude that there is exactly one BMSS.
If  $\Lambda> 0$,  then  $f$ has a unique local maximum for some  $\alpha$ in $\Gamma_1$ and all cases  in Fig. \ref{summary} can occur.   By varying the value of $\overline{F}_2$ while keeping the other constants fixed, we obtain (Fig. \ref{motiff}):
\begin{itemize}
\item[(i)]  $\overline{F}_2\leq (\overline{E}-\mu_1\overline{F}_1)/\mu_2$ (orange): $\Gamma=[0,\alpha_1)$ with $f(\alpha_1)=\overline{F}_2$. The function $f$, and thus $\varphi$, are increasing
and  there is  one BMSS  (Fig.~\ref{summary}a).
\item[(ii)] $ (\overline{E}-\mu_1\overline{F}_1)/\mu_2 < \overline{F}_2\leq f(\alpha)$ (green): $\Gamma= [0,\alpha_1)\cup (\alpha_2,\xi_1)$ with $\alpha_1\leq \alpha\leq\alpha_2$ and $f(\alpha_1)=f(\alpha_2)=\overline{F}_2$. Hence,  $f$ is increasing in $[0,\alpha_1)$, decreasing in $(\alpha_2,\xi_1)$ and multistationarity occurs (Fig. \ref{summary}b).
\end{itemize}
When $f(\alpha)< \overline{F}_2$ there is an $M$ such that:
\begin{itemize}
\item[(iii)] $f(\alpha)<\overline{F}_2< M$ (purple): $\Gamma=[0,\xi_1)$. The function $\varphi$ has a decreasing part and multistationarity occurs (Fig.~\ref{summary}c).
\item[(iv)] $M\leq \overline{F}_2$ (blue):  $\Gamma=[0,\xi_1)$. The function $\varphi$ is  increasing  and there is  one BMSS  (Fig.~\ref{summary}a).
\end{itemize}

\begin{figure}[t!]
\centering
\includegraphics[scale=1]{figure3.pdf}
\caption{\small The function $\varphi$ for Motif (f)  for different values of $\overline{F}_2$ and fixed $\overline{E}>\mu_1\overline{F}_1$ and $\Lambda>0$. Let $N=(\overline{E}-\mu_1\overline{F}_1)/\mu_2$. The values $M$ and $\alpha$ depend on $\overline{E}$, $\overline{F}_1$ and the rate constants (see text). The set $\Gamma$ is disconnected only when $N<\overline{F}_2\leq f(\alpha)$. For large $\overline{F}_2$, $\varphi$ approaches the black line. The vertical bars mark the boundary of $\Gamma$.}\label{motiff}
\end{figure}

\begin{figure}[b!]
\begin{center}
\includegraphics[scale=1]{figure4.pdf}
\end{center}
\caption{\small Conditions for multistationarity are given. The shared enzyme is marked with a colored square; the link is marked with a colored circle; predominant modifications are marked in bold.  The symbol $\gg$ is short for `much larger'. }\label{multitable}
\end{figure}

\subsection{Understanding Multistationarity}
Motifs (f), (g), (i), (k) and (l) exhibit multistationarity for some choices of total amounts and  rate constants  (Fig.~\ref{multitable}).
The regions for which multistationarity occurs are detailed in the SM.
In Motifs (i), (k) and (l) it appears only as in Fig.~\ref{summary}c, while in Motifs (f) and (g) both the forms in Fig.~\ref{summary}b and Fig.~\ref{summary}c occur.

 It is remarkable  that  in Motifs (f), (k) and (l) multistationarity occurs for any set of rate constants and depends only on the initial conditions (that is,  the total amounts). Thus, multistationarity can occur in these systems independently of the specific kinetics. In contrast,  multistationarity in Motif (i) depends on the rate constants and hence not all  kinetics exhibit multistationarity. The same  appears to be  the case for Motif (g)  \cite{conradi-mapk,WangSontag}.

The common characteristic of these motifs is that a single enzyme is responsible for catalyzing two different substrate modifications, which  at the same time are \emph{linked} (Fig.~\ref{multitable}). Indeed, in Motifs (f) and (g) the substrates are linked through $S_1$, which is a modified as well as an unmodified substrate for the shared enzyme $E$. For the Motifs (k) and (l), the link is given by $S_1$ which is a modified substrate and a kinase, and the common enzymes are $F$ and $E$, respectively. In Motif (i) the kinase $E$ is common and the phosphatase $F$ provides the link (or {\it vice versa}). In contrast, in Motif (h)  an enzyme is responsible for two different modifications, but there is no link between the two substrates. Consequently,  multistationarity cannot be observed.

Multistationarity  can arise from two opposing dynamics acting on the same substrate (Fig.~\ref{multitable}). For example,  in Motif (f), if $\overline{F}_1$ is much bigger than $\overline{E}$ and $\overline{F}_2<M$, then there are multiple BMSSs. Thus, since the amount of phosphatase in the first cycle is much larger than the amount of kinase, $S_1$ is pushed towards the unmodified form $S_0$, while in the second cycle  $S_1$ is driven towards the fully modified form $S_2$ (because $\overline{F}_2<M$).

In Motif (i), provided the conditions on the parameters are fulfilled  (Fig.~\ref{multitable}), multistationarity occurs if either $\mu_1\overline{F}>\overline{E}  >\mu_2 \overline{F}$ or  $\mu_2\overline{F}<\overline{E}<\mu_1 \overline{F}$. It implies that in one cycle the phosphatase `wins', while in the other the kinase does.

\section{Stability Analysis}\label{stability}

BMSSs are defined as steady states for which all concentrations are non-negative. However, a steady state is biologically attainable only if it is (asymptotically) stable, that is, nearby trajectories are attracted to it. We show here for our motifs that if  $\varphi'(Y)<0$ for some steady state $\varphi(Y)=\overline{S}$, then it is unstable.

\subsection{The Jacobian and variable elimination}
For a system of ordinary differential equations in $\mathbb{R}^m$, a steady state $z$ is asymptotically stable if all eigenvalues of the Jacobian evaluated at $z$ have negative real parts \cite[Thm.~1.1.1]{Wiggins}.
Since the Jacobian is a real matrix,   the complex eigenvalues come in pairs of conjugates  and their product is a positive number. If $m$ is odd and all eigenvalues have negative real parts, their product, and hence the determinant of the Jacobian, must be negative. If $m$ is even and $z$ stable, then the product of the eigenvalues must be positive.  Thus,  the sign of the determinant of the Jacobian  provides a necessary condition for a steady state to be stable and a sufficient condition for it to be unstable.

For $x=(x_1,\dots,x_n)$ let $x^{(j)}=(x_1,\dots,\widehat{x_{j}},\dots,x_n)$ ($x$ with $x_j$ removed).
We make the following observation (see SM for a proof): Let $f=(f_1,\dots,f_n)\colon\Omega\subseteq \mathbb{R}^n\rightarrow \mathbb{R}^n$ be a differentiable function defined on an open set $\Omega$ and $z$ such that $f(z)=0$. Assume that $x_j$ can be eliminated from the equation $f_i=0$ in a neighborhood around $z$; that is, there exists a differentiable function $\psi\colon\Omega^{(j)}\subseteq \mathbb{R}^{n-1}\rightarrow \mathbb{R}$, $z^{(j)}$ in  $\Omega^{(j)}=\{x^{(j)}|x\in\Omega\}$, such that $x_j=\psi(x^{(j)})$ if $f_i(x)=0$.
Define $\bar{f} \colon \Omega^{(j)} \rightarrow \mathbb{R}^{n-1}$ by
$\bar{f}_k(x)=f_k(x_1,\dots,x_{j-1},\psi(x),x_j,\dots,x_{n-1})$ for all $k\neq i$ and let $\bar{J}$ denote the associated Jacobian. Then, the determinant of the Jacobian of $f$ at $z$ satisfies
\begin{equation}\label{jacobian}
 (-1)^{i+j}\frac{\partial f_i}{\partial x_j}(z)\ \det(\bar{J}(z^{(j)})) = \det(J(z)).
 \end{equation}

\subsection{Unstable steady states}
The relation between the sign of the determinant of the Jacobian and stability, together with Eq. \eqref{jacobian},  lead to a criterion to detect unstable steady states. For each motif, let $x=(x_1,\dots,x_n)$ be the species concentrations, $\dot{x}_i=h_i(x)$ the differential equations and   $\overline{A}_1=g_1(x),\dots,\overline{A}_c=g_c(x)$  the equations for the total amounts. We choose the order of the species such that $x_i$, $i=1,\dots,c$,  can be isolated from $\overline{A}_i=g_i(x)$ and the steady state equation $\dot{x}_i=0$ becomes redundant.  For fixed total amounts, $\overline{A}_1,\dots,\overline{A}_c$, the steady states are the solutions to the system  $f(x)=0$ of $n$ equations in $n$ variables with $f_i(x)=g_i(x)-\overline{A}_i$ for $i=1,\dots,c$ and $f_i(x)=h_i(x)$ for $i=c+1,\dots,n$.

Let $J(z)$ denote the Jacobian of $f$ at $z$. In the SM we prove: If $z$ is a steady state, that is, $f(z)=0$, and either (i) $n-c$ is even and $\det(J(z))<0$ or (ii) $n-c$ is odd and $\det(J(z)) > 0$, then $z$ is unstable. The proof relies on the observation made about the eigenvalues and Eq.~\eqref{jacobian}.

The function $\varphi$ of our motifs is derived through successive elimination of variables precisely from the system of equations $f(x)=0$. Using Eq.~\eqref{jacobian},  the sign of $\det(J(z))$ at a steady state $z$ can be traced back from the sign of the derivative of $\varphi$ (the Jacobian of a system with one equation) by considering  the equation number ($i$), the equation variable ($j$), and the sign of $\partial f_i/\partial x_j$ after each elimination.

To exemplify the  procedure, consider Motif (f), where $n=10$ and $c=4$. The  system is (see SM for details):
\begin{align*}
f_1(x)  &= E + X_1+X_2 - \overline{E}  & f_6(x) & =  X_2 - \kappa_{2,E} E S_{1}  \\
f_2(x)  &= F_1 + Y_1 -\overline{F}_1  & f_7(x) &= X_1-\mu_1 Y_1 \\
f_3(x) &= F_2 + Y_2 -\overline{F}_2  &   f_8(x) &=X_2- \mu_2 Y_2 \\
f_4(x) &=  S_0 + S_1 + S_2+X_1+X_2 + Y_1+Y_2 - \overline{S}  & f_9(x) &=  Y_2- \kappa_{2,F} F_2 S_2   \\
f_5(x) &=  X_1 - \kappa_{1,E} E S_{0}  & f_{10}(x) &=Y_1- \kappa_{1,F} F_1 S_1
\end{align*}
with species $x=(E,F_1,F_2,S_0,X_1,X_2,S_1,S_2,Y_2,Y_1).$
The function $\varphi$ is  $f_4$ in terms of $Y_2$ after successive eliminations. Let $\epsilon_k=\pm 1$ depending on whether the sign of the determinant of the Jacobian changes ($-$) or not ($+$) after the $k$-th elimination. Then, $\sign(\varphi'(Y_2)) = \left(\prod_k \epsilon_k\right) \sign(\det(J(z)))$, where $z$ is the steady state with $z_9= Y_2$.

The order and sign of the eliminations are shown in Table~\ref{elimination_table}. We find that  $\prod_k \epsilon_k=1$, implying   that the sign of $\varphi'(Y_2)$ agrees with the sign of  the determinant of the Jacobian of $f$ evaluated at the corresponding steady state.
Since $n-c=6$ is even, we conclude that the values of $Y_2$ for which $\varphi$ is decreasing, that is, $\varphi'(Y_2)<0$, correspond to unstable steady states. Further, it follows that unstable points come between other steady states that  presumably are stable.

\begin{table}[t!]
\renewcommand{\arraystretch}{1.3}
\setlength{\tabcolsep}{3pt}
\centering
\begin{tabular}{cccc||cccc}
\hline
$k$ & Elimination &  Behavior$^{\rm a}$ & $\epsilon_k$$^{\rm b}$ & $k$ & Elimination &  Behavior & $\epsilon_k$\\ \hline
1 & $(f_1,E)$  &  $(1,1,+)$ & +  &6 & $(f_5,S_0)$ & $(2,1,-)$ & +  \\
2 & $(f_2,F_1)$  & $(1,1,+)$ & +  & 7 & $(f_6,S_1)$ &  $(2,1,-)$ & +  \\
3 & $(f_3,F_2)$ &  $(1,1,+)$ & +  & 8 & $(f_9,S_2)$ & $(2,1,-)$ & +  \\
4 & $(f_7,X_1)$  &  $(4,2,+)$ & +  & 9 & $(f_{10},Y_1)$ & $(2,1, -)$ & + \\
5 & $(f_8,X_2)$  & $(4,2,+)$ & + \\ \hline
\end{tabular}
\begin{flushleft}
{\small $^{\rm a}$ $(i,j,\sigma)$  indicates that $i,j$ are the indices of the equation and variable iteratively being eliminated and $\sigma$ corresponds to whether $\bar{f}_i$ ($f_i$ after substitution of the previous eliminations) is increasing ($\sigma=+$) or decreasing ($\sigma=-$) as a function of $x_j$.
  \\
$^{\rm b}$ obtained as obtained as $\sigma(-1)^{i+j}$.
}
\end{flushleft}
\caption{Elimination of variables for Motif (f). After each elimination  the system $\bar{f}$ is rewritten  to correctly determine the sign  of $\partial\bar{f}_i/\partial x_j$ before the next elimination}

\label{elimination_table}
\end{table}

\subsection{Stability in monostationarity motifs}
The Routh-Hurwicz criterion \cite{Hurwitz} gives sufficient and necessary conditions for the Jacobian to have all eigenvalues with negative real parts. Thus, the (asymptotic) stability of a steady state can be determined by this criterion.
For the Motifs (a)-(e) and (h) the criterion is fulfilled and the unique BMSS is asymptotically stable. We have not been able to determine this for Motif (j).

\section{Discussion}
We have investigated small motifs without feedback that account for cross-talk, enzyme competition, sharing and specificity in post-translational modification systems and  determined some features that lead to multistationarity in signaling pathways.

Bistability, and generally multistability, in biological systems is seen as a mechanism of cellular decision making. Compared to systems with a single steady state, the presence of multiple stable steady states provides a possible switch between different responses and increased robustness with respect to environmental noise.  Our study has been driven by the observation that biological systems deviate from a one-to-one correspondence between enzymes and the modifications they catalyze. This phenomenon, known as cross-talk and enzyme sharing, can  cause  multistationarity and hence be essential for regulating  signaling systems.

Our work extends the view of multistationarity as arising from multisite phosphorylation \cite{TG-Nature}  to the view that  multistationarity is driven by a single enzyme that  catalyzes linked substrates.  Two opposing dynamics acting on the same substrate is a recurrent characteristic of multistationarity. These observations await a precise mathematical formulation and an investigation of its generality.

Our approach is conceptually simple and reduces to the study of analytical properties of a function $\varphi$ that relates a conserved total amount and the concentration of a species at steady state. The graph $(\varphi(Y),Y)$ can be seen as a bifurcation diagram with one parameter, $\overline{S}$.
When monostationarity occurs,  analysis of $\varphi$ is quite straightforward, while a more in-depth analysis is required when  multistationarity occurs. An advantage of this approach is that unstable steady states are readily detected from the  form of  $\varphi$.

The existence of $\varphi$ is not guaranteed  in general. For larger systems, a detailed study independently of the rate constants  cannot be pursued. However, we have shown that for cascades of arbitrary length (extentions of Motif (j)), the function $\varphi$ exists and  properties of the full cascade can be derived from properties of the building block, the one-site cycle  \cite{Feliu:2010p94}. We are currently working on extending this approach to other systems.

There are some mathematical characterizations of mono\-stationarity in chemical reaction networks that relate to our work.
The theory of monotone systems \cite{smith-monotone} characterizes systems in which there is only one BMSS and at the same time gives conditions for global stability of the BMSS.  However, a condition for the theory to be applicable here is that  no species take part in more than two reactions \cite{angelisontag2}. This condition is only fulfilled for Motif (a) and hence the theory cannot be applied here.

The only general theory of applicability is that of injective systems \cite{craciun-feinbergI,craciun-feinbergII,craciun-feinberg-pnas}. The motifs that do not allow multiple steady states are in fact  injective in the sense of \cite{craciun-feinbergI} when modeled as a {\it continuous flow stirred tank reactor}. This fact  implies that {\it at most one} steady state  exists \cite{craciun-feinberg}. The advantage of this theory is that monostationarity is derived for more general kinetics than mass-action \cite{Banaji-donnell}.
However, when restricted to mass-action, our approach is as simple as checking for injectivity and provides in addition simple  rational functions that enable further comprehensive studies of variation in species concentrations, such as stimulus-response curves and signal amplification \cite{Feliu:2010p94,Feliu-proc}.

\bigskip
\emph{Acknowledgements.}
EF is supported by a postdoctoral grant from the ``Ministerio de Educaci\'on'' of Spain and the project  MTM2009-14163-C02-01 from the ``Ministerio de Ciencia e Innovaci\'on''.  CW is supported by the Lundbeck Foundation, Denmark. Neil Bristow, Freddy Bugge Christiansen and Michael Knudsen are thanked for commenting on the manuscript.

redpajama_set_name: RedPajamaArXiv


text:
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redpajama_set_name: RedPajamaCommonCrawl


text:
  Bonneval-sur-Arc est
       un village
       situé dans le département de Savoie en Rhône-Alpes. On dénombrait 239 habitants en 2008.

La ville propose de nombreux  équipements, elle propose entre autres un terrain de tennis, un domaine skiable, une patinoire et un équipement de roller/skate.

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redpajama_set_name: RedPajamaGithub


Our task for the weekend was to put the final touchings to the road to the backpump station from Scotland Road Bridge.
.. for Bob to Spread it - nice to see Bob back on a dig.
Alison wishes that her Morris would go as fast as this machine !
Lesley was worried that the back pumps will overfill the canal.


text:
Bernard Scholtz
M • 9th March 1990 • Namibia • All-Rounder • Right-Hand Batsman • Left-Arm Orthodox
Teams (1): Namibia (115)
115 37 20 134 25* 160 83.75 7.88 0 0 0 3 6 3 108 2129 123 2189 17.31 17.80 6.17 1.14 0 4 4/11 17 6
Overall Rankings — June 2021
Batsman ranking
No current ranking
Bowler ranking
25th 3
Rating24.81
Fielder ranking
1012th 1
Rating6.97
All-rounder ranking
Rating0.99 0.15 (5 Nov 2021)
International Rankings — June 2021
7th —
Rating26
0.3 —
2021 ICC Men's T20 World Cup
8/11 T20I NAM @ IND - - did not bat - - - - - - 0 2 3 1 0 11 0 11 - - -1.1 - - - 0
5/11 T20I NAM v NZ - - did not bat - - - - - - 0 1 1 3 0 15 1 5 - - 57.54 - - - 0
31/10 T20I NAM @ AFG 2 11 not out 6 13 11 0 0 54.54 11.64 1 6 1 0 8 0 8 - - -0.35 1 - - 40.5
27/10 T20I NAM v SCO - - did not bat - - - - - - 0 1 5 2 0 16 0 8 - - -3.57 - - - 0
22/10 T20I NAM @ IRE - - did not bat - - - - - - 0 1 4 3 0 25 1 8.33 - - 40.53 - - - 0
20/10 T20I NAM v NED - - did not bat - - - - - - 0 1 1 4 0 31 0 7.75 1 - -16.61 1 - - 51.56
18/10 T20I NAM v SL 1 11 run out (P Nissanka) 0 4 2 0 0 0 -13.5 2 3 3 0 16 1 5.33 1 - 33.87 - - - 0
2021 Namibia v Papua New Guinea T20I Match 2021/22
10/10 T20I NAM v PNG - - did not bat - - - - - - 0 2 1 2 0 14 1 7 - - 31.4 - - - 0
2021 Namibia v Scotland T20I Match 2021/22
9/10 T20I NAM v SCO - - did not bat - - - - - - 0 1 5 3 0 16 1 5.33 - - 66.23 - - - 0
2021 Namibia in United Arab Emirates T20I Match 2021/22
5/10 T20I NAM @ UAE - - did not bat - - - - - - 0 2 5 2 0 19 0 9.5 - - -8.62 - - - 0
2021 Uganda in Namibia T20I Series 2021
5/4 T20I NAM v UGA - - did not bat - - - - - - 0 2 5 3 0 23 2 7.66 1 - 103.72 - - - 0
5/4 T20I NAM v UGA - - did not bat - - - - - - 0 2 5 2.4 0 14 1 5.25 - - 36.44 - - - 0
3/4 T20I NAM v UGA - - did not bat - - - - - - 0 1 4 4 0 20 1 5 - - 106.37 - - - 0
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23/2 NAM @ IrelA - - did not bat - - - - - - 0 2 1 3 0 36 0 12 - - -21.1 - - - 0
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21/2 NAM @ IrelA 2 9 c. S Doheny b. G Delany 5 13 7 0 0 71.42 6.9 1 5 3 0 26 0 8.66 - - -8.72 - - - 0
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Are You At the End of Your Rope?
Sometimes it can be frustrating to have unanswered prayers. Even the message behind praying for stuff is convoluted somewhat. Some Christians believe that you shouldn't pray for "stuff" and that if you do, that it's a form of idolization -- for instance, you'd rather "things" more than a relationship with God. But biblically speaking, that's just not true at all. A lot of pastors will try and say that you should ask for deeper things and to only use prayer to praise God. Well, yes---praising God and being grateful for what we have now is important. But God wants us to go to Him for everything else too. It's up to Him whether or not those 'orders' get fulfilled. If our own earthly loved ones can provide "stuff" for us, then what makes us think that God can't? In Luke 11:9-13, it clearly states: "And so I tell you, keep on asking, and you will be given what you ask for. Keep on looking, and you will find. Keep on kn
Even the Strongest People Cry Throughout my entire life, I was always told, "Don't cry, baby, don't cry," by both my parents. They wanted to see me happy---they wanted to see me OK and they certainly did not want to see me fall apart. Maybe in a way, they'd take the blame and say it was all their fault somehow. Or maybe, they didn't want to cry themselves. Most of me believes that they loved me so much, that it hurt them to see me in some kind of pain, whether emotional or physical. I remember many years ago, I had to go for lasik eye surgery. I was legally blind and the surgery was risky. They made me sign all of these forms saying that it was an 80/20 chance of me going completely blind, with the exception of a cornea replacement---not in my favor of course. I said, "I'm blind anyway, just do it." When I came out of surgery, it was more intense than most would go through, because my cornea was too thin, and needed much more time to heal. I
How I Stopped Making Pain, Trauma & Grief My Identity
Years ago, I suffered from chronic pain. Some doctors called it "degenerative disc disease" while other physicians referred it to "fibromyalgia." They couldn't quite pinpoint what was wrong with me and why I was experiencing such excruciating pain. They admitted me to the hospital for a week to do some testing for autoimmune diseases and other possible diagnoses, to only come up with "myalgia." I guess it's another word for, "We don't know, but we're gonna slap a label on it." During that time, I also developed an ulcer due to all of the NSAIDS (ibuprofen) I was taking to relieve some of the pain. They also gave me Percocet, but it didn't work quite as well as the anti-inflammatories. I had no choice because my stomach would suffer. When I realized I was developing a dependency on the pills, I weaned off and tried smoking weed, which did nothing except make me high and hungry. I never understood why people used it for pain.


The memory of Saint John the Dermokaitis ("the Branded") is preserved in the Synaxarion of Delahaye, noting that he was an ascetic on Mount Olympos in Bithynia. He may be the same individual as John the Monk, who was known for the sanctity of his life, under Emperor Romanos I Lekapenos (919-944). Emperor Romanos sent a sealed epistle to this John the Monk, containing a confession of his sins.
Theophanes Continuatus reports that when Emperor Romanos was in exile on the Prince's Islands, having been deposed by his own sons, he had a dream in which he was dragged naked by two eunuchs to an enormous fire tended by a great number of demons, which occupied the entire Tzykanisterion, the imperial polo court at the palace. Two other people - one of Romanos' sons and the Bishop of Herakleia - were thrown in and burned, and the next day the emperor learned that they had both been put to death at the very time of his dream. Romanos was saved at the last moment in his dream by the Mother of God who appeared suddenly, stopped the eunuchs, asking them to be merciful, and clothed the terrified naked emperor.
This dream had a tremendous effect on the emperor. It led him to the staging of an exuberant performance of self-humiliation, involving a public confession of his sins. Stripped of his clothes, in front of 300 weeping monks, he prostrated himself and asked for forgiveness from each and every one of them. All this culminated in an extensive whipping session, provided by a neophyte.
After this he is reported to have written down a list of his sins, and then spared no trouble or expense in having large numbers of monks and holy men in various locations pray and shed tears on his behalf. Among these holy men was John the Monk. When this was done, the document was miraculously found to be wiped clean. The old emperor finally acquired an official letter of absolution, and he was buried with this precious document when he died shortly afterwards.


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Archive: Chinese troops fire on protesters in Tiananmen Square – BBC News
Subscribe to BBC News www.youtube.com/bbcnews First broadcast 4 June 1989. Chinese troops opened fire on pro-democracy protesters in Beijing's Tiananmen Square on Saturday evening. The collection of students and labourers had been occupying the site for several weeks. Despite the outbreak of "unremitting gunfire", the protesters refused to leave. The BBC's Kate Adie reports from


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Dunedin, NZ
Posted on March 28, 2010 | by Sue
Our first stop on the 226 mile drive from Christchurch to Dunedin is Oamaru. An historic seaport town nestled on the South Island's east coast. While Oamaru's early wealth was founded on gold, it was agriculture that provided the driving force for a thriving commercial port and harbor area. Although commercial usage has steadily declined over time, the original structures remain intact and the area is undergoing a revival. The Woolstore Cafe is in a restored building and there we enjoyed the day's special – lamb burgers with fries. Once again I was delighted to find gluten-free "slices" – wonderfully moist, cake-like treats: chocolate hazelnut and a pear honey (my waistline is not in decline!).
Oamaru Bay
During our stay in Christchurch we were advised to stop and see the Moeraki Boulders on our trip south. The boulders are situated some 40km south of Oamaru at Moeraki on State Highway One. It is a five minute walk along the beach to the boulders. From a distance they are not impressive in size, but up close the details become apparent. A little research revealed there incredible history… the boulders were embedded in the soft mudstone cliff at the beach and the forces of the sea have eroded the cliff away, exposing the round formation of the boulders. The boulders were formed by the crystallization of calcium and carbonates around charged particles, as one website described it – "a process similar to the way pearls are formed". Although this process took four million years.
Originally we had planned to end our journey in Christchurch, but our friends, Sally & Bruce, encouraged us to continue south to Dunedin and the Otago peninsula. Dunedin is home to the University of Otago, New Zealand's first university and the Otago Polytechnic. The University accounts for about 20 percent of the city's population and this weekend was the start of the semester so lodging was booked downtown. Online we found a room at the newly opened St. Clair Beach Resort and after driving through the city found ourselves at the oceanfront where surfers were rallying and practicing for the next day's Asia Pacific Long Board Championship. An excited Jay was soon talking to his buddy, Mark (surfer dude), via Skype – holding up the MacBook (see Jay's review of the Ultimate Travel Computer) so Mark could see the surfers. Enjoying the sound of the surf and tired from a long day of driving, that night we dined nearby at Salt – a great little restaurant about two blocks from the hotel.
Surfers at St Clair Beach in Dunedin
Waking the next morning to the sounds of loud speakers announcing the surfers we check it out for awhile from our balcony, then jump in the car and head out to the Otago Peninsula. Our destination is the Royal Albatross Colony at Taiaroa Head, on the tip of the Otago Peninsula. We drive out on Portobello Road along the edge of the harbor, then return on Highcliff Road along the top of the Peninsula enjoying the spectacular views of both routes.
Taiaroa Head is unique for the diversity of wildlife which abounds on this small headland. The albatross is one of eleven bird species which breed in the area and this is the only mainland breeding colony for any albatross species found in the southern hemisphere. The first Taiaroa-reared albatross chick flew in 1938 and this now protected nature reserve has grown into an established colony with a population of around 140 birds.
The breeding birds arrive at Taiaroa Head in September. The nest, built during early November, is formed by a bird sitting down and pulling vegetation and earth around itself with its bill. The white egg, weighing up to 500 grams, is laid during the first three weeks of November. The parents share incubation duty in spells of two to eight days over a period of 11 weeks – one of the longest incubation periods of any bird. The incubating bird sleeps much of the time its mate is away
Albatross with chick
When the chick has hatched, the parents take turns at guarding it for the first 30 to 40 days, and the feeding of the chick is also shared by both parents. Nearly 12 months after their arrival at Taiaroa Head, having cared for egg and chick over a period of some 300 days, the parents will leave the colony to spend a year at sea before returning to breed again. The chicks hatch during late January and early February; it takes about three to six days to finally emerge from the egg after making a hole in the shell. Albatross Breading Cycle For the first 20 days the chick is fed on demand, then meals decrease to three or four times a week. At 100 days the chick's down reaches a maximum length of 12 centimetres. At this age the chick is fed larger meals, up to two kilograms at a time, of more solid substance. From early August the chick is fed lighter meals and in September, when fully fledged, it wanders from the nest testing its outstretched wings and eventually takes off with the aid of a strong wind. The young albatross will spend the next three to six years at sea; many then return to this unique headland to start another generation of Royals of Taiaroa.
Stomach contents of a deceased albatross
While away at sea the albatross swallows plastic debris – in the North Pacific debris is concentrated in two huge eddies – in these areas the surface water contains six times more plastic than plankton by weight. Adult albatrosses breeding on Hawaiian atolls ingest the plastic, probably mistaking it for food, and then feed it to their chicks. As a result, thousands of chicks die yearly in Hawaii because their stomachs fill with plastic leaving no room for real food.
Rare Stewart Island Shag mud nests
From the nature reserve viewing area we saw the rare Stewart Island Shag mud nests.
Lighthouse on the Otago Peninsula
The lighthouse is a short walk from the reserve with views of the ocean and seals camouflaged among the dark stones.
Shade loving sheep along the roadside
Driving back on the Highcliff Road we came upon these wool laden sheep enjoying the shade; below is a view of the lush Otago Peninsula.
View of the Otaga Peninsula
After a full day out on the Otago Peninsula we make reservations to dine in downtown Dunedin at Bacchus. Set in the heart of Dunedin in one of Dunedin's historic buildings, Bacchus overlooks the Octagon (city center of Dunedin), and is known for it's quality lamb and beef dishes and a first rate wine selection. We enjoyed a first class meal and good wine recommendations.
The following morning we check out at 10am (the standard time in NZ), return our rental car, check our luggage at train station and head to Plato for brunch. Plato is a relaxed eatery located on the harborfront of Dunedin and was recommended by our waitress at Bacchus last night. Hands down one of the best brunch dishes ever – Basque Eggs – free-range eggs broken over pan-fried potatoes, mushrooms, chorizo, tomatoes, feta and spinach, grilled with grated parmesan.
Walking into town we make a visit to the Dunedin Public Art Gallery. As we made our way through the galleries the exhibit that stood out was Taryn Simon: An American Index of the Hidden and Unfamiliar. Described as "A collection of photographs that document the inaccessible places that exit below the surface of American identity." The two images that stood out for me and contrasted each other were both in Washington State – a nuclear waste shot and the Olympic National Temperate Rainforest. The museum is worth checking out and this exhibit is there until May 9, 2010.
We eventually make it back to the Octogon to check out the South Island Bagpipe competition… here are Jay's photos…
Bagpipers practicing for the South Island Competition
Bagpipers present themselves to the Competition Official
The tradition continues with these young bagpipers
Bagpipe Competition Judges chat with an onlooker
Our train leaves mid-afternoon… we are taking The Taieri Gorge Limited train, Dunedin's prestige tourist train operating from the historic Railway Station. This scenic train & bus tour will eventually land us in Queenstown, NZ. This historic train travels through the rugged and spectacular Taieri River Gorge, across wrought iron viaducts and through tunnels carved by hand more than 100 years ago.
Dunedin Train Station
Platform at the Dunedin Train Station
Interior of the historic Taieri Gorge train
Gramma's traveling bears on Taieri Gorge Train
At one of our stops along the way, a grandma sets her bears out and photographs them. She tells Jay she will email the pictures to her grandchildren later as a fun way for them to follow her travels.
Posted in Art, Cities, Countries, Dining, Dunedin, Lodging, Music, New Zealand, Sightseeing | Tagged art, dining, museum, sightseeing
Akaroa, NZ
Queenstown, NZ


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Tag Archives: Quanzhou
26 December, 2013 · 12:27
The 44m high West Pagoda, one of two at Quanzhou's Kaiyuan Temple complex, a Buddhist temple first constructed in the year 686 AD. The temple stands at the west end of Xi Jie (West Street), a bustling thoroughfare recalling the China of the past, of tiny ramshackle businesses, chaotic congested streets, honking buses and outdoor food stalls.
A monk trains a young boy in the yard at Kaiyuan Temple in Quanzhou.
Door handles on the East Pagoda at Kaiyuan Temple in Quanzhou.
A doorway on Quanzhou's Xi Jie. The city seems to be awakening from a tourist slumber, cleaning up the old parts of the town and erecting plaques in English and Chinese explaining the history of the area.
An egret on Xiamen's Yundang Inner Lake.
A family walking along the western edge of Xiamen's Yundang Inner Lake.
The food markets near Xiamen's pedestrian shopping street, Zhongshan Lu.
Seafood cooked in its shell in the streets around Zhongshan Lu. Xiamen is famous in the rest of China for its seafood.
Xiamen's south-west shore in the distance, as seen from the highest point on the nearby island of Gu Lang Yu. Gu Lang Yu has historically been the preserve of foreigners, working in embassies and living in ostentatious villas, giving the island a colonial European atmosphere that helps make it a top-3 destination for Chinese domestic tourism.
Workers unloading construction materials from boats on Gu Lang Yu, an island that is practically free of vehicles.
This means that bricks and sand and cement and everything else gets pulled by men using handcarts like these.
A dapper man in a suit jacket on a sampan sorts his catch for the day on the eastern shore of Gu Lang Yu.
Because of its quaint architecture and scenic locations, the island is hugely popular with local newlyweds, who often eschew the black-and-white traditions we're used to and go for colourful dresses and hipster vests.
Back on Xiamen itself, a tour group prepares for a photo in front of the 280mm German-built cannon at Huli Shan Fortress on the island's southern shore.
The fortress occupies 13,000 square metres and has a collection of cannons, of which the 280mm, with its 7km accurate range, is the largest. It claimed a Japanese destroyer in 1941 and has a large feature about that event. More recent hostilities have been with the nationalist-controlled Taiwanese island of Jinmen, to the east of Xiamen. Whether those events are less important, or just that they don't fit neatly into the Chinese national myth perhaps time will tell.
Tagged as China, Quanzhou, travel, Xiamen
The Guandi Temple in Quanzhou, Fujian province in China. Quanzhou, about 45 minutes on the train from Xiamen, was once a bustling traders' town at the end of the maritime silk road. The temple stands next to what is left of a 1000 year old mosque, built by the Arab, Persian and Indian traders.
Reminders of another significant part of the region's history, opium pipes for sale in Quanzhou's markets.
Ornaments for sale in the markets near Quanzhou's 1000-year old mosque.
Ornaments for sale at the markets near Quanzhou's 1000-year old mosque.
A bridge over the Yundang Inner Lake in Xiamen, Fujian province, China
Sunset view of the south shore of Xiamen's Yundang Inner Lake.
A girl and her father fishing on Xiamen's Yundang Inner Lake.
Three egrets on the rapids of the inlet to Xiamen's Yundang Inner Lake.
An egret on the rapids at the inlet to Xiamen's Yundang Inner Lake.
Egrets lined up to swoop for fish in the rapids at the inlet to Xiamen's Yundang Inner Lake.
Flowers in Xiamen's Huweishan Park.
A rock carving at Xiamen's Nanputuo Temple.
Kids at sunset at Xiamen's Nanputuo Temple.
21 October, 2013 · 21:09


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The FDA Wants To Lower Nicotine in All Cigarettes, Which Will Make Smokers Smoke More
This is the same agency that cost thousands of lives with its botched vaccine rollout.
Veronique de Rugy | 4.29.2021 12:45 PM
(Photo by NeONBRAND on Unsplash )
If it doesn't look like avocado toast, you can't have it. That's the message I get loud and clear from Uncle Sam when I read story after story about the Food and Drug Administration's latest foray into stopping ordinary Americans from doing what ordinary Americans like to do.
Take the latest news that the FDA is thinking about requiring tobacco companies to lower the nicotine in all cigarettes sold in the United States. Its goal is to fight nicotine addiction. The paternalists at the FDA are also considering whether this proposal should be paired with a ban on menthol products.
This comes from the agency that has badly botched the COVID-19 response by delaying test and vaccine authorizations that could have saved countless lives. Now it has the nerve to tell Americans, most of whom are stressed out of their minds after a year of the pandemic and lockdowns, what they can or can't inhale.
While it may sound old-fashioned, I don't believe that it's the role of the government to tell fully consenting adults what they can and cannot do with their own bodies, even if their choice is something that most people disapprove of. And if you tell me that socialized medicine should give Uncle Sam the right to boss us around, I'll tell you that two wrongs don't make a right.
Besides, these measures are nonsensical. According to The Wall Street Journal, the idea behind the nicotine reduction measure is that it "would lower the chemical in cigarettes to nonaddictive or minimally addictive levels, aiming to push millions of smokers to either quit or switch to less harmful alternatives such as nicotine gums, lozenges, or e-cigarettes." Note that this same FDA has waged a war on these same e-cigarettes by banning the most popular flavors to ensure that these new and less harmful products were as unappealing as a plate of raw broccoli for breakfast.
Ask yourself this question: Do the geniuses at the FDA not realize that many people will simply smoke a greater number of cigarettes per day in order to get their nicotine fix?
Why would the FDA expect smokers to respond in a radically different way than all the people the government has tried to nudge with failed nanny state interventions to get to stop smoking or drinking sugary drinks in the past? I understand the superficial belief that raising the price of an item with taxes or other means as this proposal effectively suggests could discourage its consumption. But studies show that this isn't what happens in practice.
In fact, consumers have a knack for finding ways to consume the same amount of stuff that the government is trying to diminish the consumption of, especially when it comes to drugs, alcohol, or sugar. Sometimes they switch to substitutes that are even more dangerous.
For instance, studies find that smokers in high-tax states tend to consume cigarettes that are longer and higher in tar and nicotine than the ones consumed by smokers in low-tax states. This effect is especially pronounced among 18- to 24-year-olds because they have less money and insist on getting more bang for their buck. The same is true of harder drug prohibition. As the Cato Institute's Trevor Burrus tells me, "Prohibition makes drugs stronger for the same reason people smuggle flasks and not 12 packs at sporting events."
The same will happen with this latest nanny state gambit by the FDA. At the margin, a few, mostly light, smokers will give up the habit, but longtime and heavy smokers will likely start smoking more cigarettes to get their desired amount of nicotine. As with drugs and other prohibitions, this move is not neutral health-wise because, while nicotine doesn't lead to cancer or real harm, according to the FDA, the tar in each cigarette does. According to Cato Institute Senior Fellow Jeff Singer, who is also a fellow of the American College of Surgeons, "While nicotine is addictive, the tars in tobacco smoke are what do all of the damage to health. Reducing nicotine content might paradoxically make smoking more dangerous."
So, there you go: With its latest headline-grabbing proposal, the FDA would make smokers poorer and less healthy. We should also expect the black market to expand and offer smokers the stuff they've been wanting all along, including menthol cigarettes.
Why not, in this self-proclaimed land of the free, simply let adults choose as they wish.
COPYRIGHT 2021 CREATORS.COM
NEXT: Biden Is Using the Pandemic as an Excuse for Permanent Expansions of Government Power
Veronique de Rugy is a contributing editor at Reason. She is a senior research fellow at the Mercatus Center at George Mason University.
FDACoronavirusCigarettesRegulationWar on DrugsBlack Markets


"Malta welcomed the entry into force last Friday of the EU-Japan Economic Partnership Agreement - an ambitious milestone for bilateral relations," Malta's non-resident ambassador to Japan, André Spiteri told this paper.
"This is a great opportunity for Malta to explore more trade opportunities with the world's third largest economy. Malta stands to gain from such an agreement and government is committed to support enterprises that wish to explore the various benefits and opportunities of doing business with Japan."
Anthony Micallef, president of the Malta-Japan Chamber of Commerce said that "around 1,300 jobs in Malts are supported by trade with Japan. The EPA is a state-of-the-art trade deal, with great benefits for the Maltese economy. MJCC is working on this effect especially now that many Japanese companies are being encouraged to open an office here in Malta - not only to do business here but also to have one foot in the EU for expanding their trade. We encourage local businesses to join forces to maximise trade flows".
Japan is Malta's sixth largest trade partner outside the EU with exports by 44 Maltese companies to Japan currently reaching €106m as against imports of €60m. The Maltese government has identified sectors, which thanks to the EPA, might attract future Japanese investment. These include precision engineering, pharmaceuticals, machinery and mechanical appliances, plastic and plastic products, chemicals, aircraft parts, software development, toys and games.
Hailing the EPA entry into force, Jean-Claude Juncker, President of the European Commission said that: "Europe and Japan are sending a message to the world about the future of open and fair trade. We are opening a new marketplace, home to 635 million people and almost a third of the world's Gross Domestic Product, bringing the people of Europe and Japan closer together than ever before. It will give small businesses on both sides the chance to branch out to a completely new market."
"More than anything, our agreement shows that trade is about more than quotas and tariffs or millions and billions. It is about values, principles and fairness. It makes sure that our principles in areas such as labour, safety, climate and consumer protection are the global gold-standard. This only happens when you work with the most natural of partners, separated by thousands of kilometres but united in friendship and values."
Annual trade between the EU and Japan could increase by nearly €36bn once the EPA agreement is implemented in full since the pact is set to ultimately remove 97% of the tariffs applied by Japan to European goods and 99% of those applied by the EU. This will translate into an estimated saving of €1bn a year in duties paid by EU companies currently exporting to Japan.
EU's exports to Japan currently amount to €58bn in goods and €28bn in services. The EPA is seen as a major boon to EU agricultural exports in particular cheese, pork and wines, while ensuring trade mark protection to over 200 high-quality Geographical Indications products as well as to a selection of Japanese GIs. Other sectors expected to derive major benefits include financial services, e-commerce, telecommunications and transport. Moreover, the EPA gives EU companies access to the procurement markets of 54 large Japanese cities, while obstacles to procurement in Japan's economically important railway sector at national level are also removed.
Japan's main interest in a trade deal with Europe was reported to increase car exports, currently attracting a 10% EU tariff - to be lowered to zero over the next eight years. Although cars and their components account for about a fifth of Japan's exports to Europe, Japanese carmakers' share of the European market is only about 10% - much lower than in the US or Asia.
The EPA also reaffirms the shared commitment to sustainable development as well as a specific commitment to fully implement the Paris Agreement on Climate Change (2015). It reaffirms the shared values and common principles that form the basis of EU-Japan relations, including human rights, democracy and the rule of law. In addition the EU and Japan adopted decisions on 23 January to allow the free and safe flow of personal data between them, recognising each other's data protection systems as "equivalent", thus creating the world's largest area of safe data flows.
The companion Strategic Partnership, to be applied on a provisional basis pending ratification by all member states, commits to security cooperation on issues like nuclear proliferation, regional security, international terrorism and organised crime, cyber-security and energy and climate security. It provides an overarching framework for enhanced political and sectoral cooperation and joint actions on issues of common interest, including on regional and global challenges.
To take stock of the initial months of implementation, the first EU-Japan committee meeting will be held in Brussels in April. On the parallel issue of investment protection, negotiations with Japan will continue on standards and on dispute resolution, with a meeting of chief negotiators scheduled for March. The firm commitment on both sides is to reach convergence in the investment protection negotiations as soon as possible, in light of their shared commitment to a stable and secure investment environment in Europe and Japan.


The hierarchy for choosing European representatives from Belgium for European bodies is the works council, the health and safety committee and the union delegations.
Trade unions in Belgium are divided between competing confederations, which have clear political traditions. The two largest CSC/ACV and the FGTB/ABVV are linked to the christian and socialist movements respectively, while the smaller CGSLB/ACLVB is linked to the liberals. Despite this the unions are able to co-operate and around half the workforce is unionised – with union membership growing.
Workplace representation in Hungary is provided by both local trade unions and elected works councils with the balance between the two varying over time. Under the new labour code, unions have negotiating rights but have lost their monitoring powers and their right to be informed and consulted. Works councils have information and consultation rights but in practice often find it difficult to influence company decisions.
Unions are central to workplace representation in Denmark. Local union representatives take up employees' concerns with management and are often also members of the main information and consultation body – the cooperation committee.
European representatives from Luxembourg are chosen by the employee delegations. In most cases they must be employees, but this is not the case for the members of an SNB for a European Company, where union officials can also be chosen.
Workers' health and safety representatives represent Maltese employees in the area of health and safety. However, the legislation does not specify how many should be appointed or define their precise powers. They should be chosen by the employees in the first instance but, if the employees do not make a choice, the representatives are appointed by the employer.
In most companies with at least 50 employees and in some with fewer, employees have the right to elect representatives with health and safety responsibilities to a joint employee/employer health and safety committee. Many of the details of how they work – such as the precise number to be elected or their time-off rights – are left to be agreed between employees and employer in the company or collective agreements.


Whether it's about personal leadership, providing leadership to a team or leading an entire organization, we design and deliver tailor-made training courses and workshops for companies aiming to enhance the individual, team or organisation's capabilities to deal with change, as effective as possible. In fact, improving by transition!
We guide these transitions with our programs and tools, from organization-wide to individual and everything in between.
How can we service your organization?
How do I really connect with others?
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What skills do I have to learn before I am ready for a promotion?
How do I shift my focus from my own results to team results?
How did I become who I am today and how does that help others?
How do I turn a bunch of individuals into a successful team?
How do I shift my focus from 'doing it yourself' to 'helping others doing it successfully'?
How do I increase my impact being a role model, leading by example?
How do I know what my key drivers are and those of others?
How do I get more out of my team?
We facilitate this by providing insights, holding up a mirror and putting our finger (gently but firmly) on the sore spot.
One of our clients was developing a leadership curriculum for her organization. Their question was in the field of Personal Leadership. They asked us to develop something custom made for the target group of employees with 2 to 5 years of work experience and an academic background.
We designed and delivered "The Personal Leadership experience", a three-day training course in which personal and authentic leadership played a central role.
We started off with learning to recognize and acknowledge personal preference styles in yourself and others. The in-depth learning experience focused on "the game" that is played within organizations, how you enable yourself to make your own choices and oversee the consequences of those choices.
"Instead of only 'one-way teaching', there was a lot of variation between theory, practice, films and cases".
For an organization without a formal hierarchy in place but with a clear choice for coaching leadership, we developed "The Coaching Experience".
For a group of twelve seniors and partners we have designed a three-day training course in which we have provided in-depth professionalization in coaching techniques and skills.
During the training the group developed a way of working going forward in order to safeguard this professionalization within the organization.
"The practical training and the models used fit in well with our situation. We now work from one clear vision on coaching and the methodologies are well secured going forward".
For a FMCG client we developed a unique Young Potential Development program their future leaders.
In this eighteen months program the Young Potentials have to carry out an improvement project and an innovation project, sponsored by the management, based on nine core competencies in a pressure cooker situation.
At the end of the program, the participants themselves become coaches of the new generation Young Potentials. This creates the "double loop learning" effect.
"I don't know exactly what you guys do, but you ask one question and all of a sudden we are one day ahead and I have gained a lot of insights which really help me to move on in my personal development".
We believe that our knowledge should be made available to everyone. That is why we regularly organize workshops for interested parties. If you don't see the workshop you are looking for announced here, please ask for the possibilities.


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Op-ed: What's The Future Of Afghanistan After Trump?
Russian Special Presidential Representative for Afghanistan Zamir Kabulov is fairly certain that President-Elect Biden won't do much to turn the tide on outgoing President Trump's drawdown from Afghanistan despite newly promulgated legislation hindering the prospect of further cuts, but he's also concerned that US troops might be replaced by private military contractors in a scenario that he warned would be a mistake.
Helicopters carrying U.S. Army soldiers from the 1-320 Field Artillery Regiment, 101st Airborne Division, take off from Combat Outpost Terra Nova as the soldiers head home following a 10-month deployment in the Arghandab Valley north of Kandahar April 23, 2011. REUTERS/Bob Strong (AFGHANISTAN - Tags: MILITARY POLITICS IMAGES OF THE DAY)
Russia's Prediction For Afghanistan
Many questions are swirling about President-Elect Biden's foreign policy upon his impending inauguration next week, but one of the most relevant for all of Eurasia is what his stance will be towards the US' seemingly never-ending War on Afghanistan.
Russian Special Presidential Representative for Afghanistan Zamir Kabulov is fairly certain that President-Elect Biden won't do much to turn the tide on outgoing President Trump's drawdown from Afghanistan despite newly promulgated legislation hindering the prospect of further cuts, but he's also concerned that US troops might be replaced by private military contractors in a scenario that he warned would be a mistake. This is a pretty sound prediction which deserves to be elaborated upon more at length in order to better understand the logic behind it.
The US' New Central Asian Strategy
The author explained last year how "The US' Central Asian Strategy Isn't Sinister, But That Doesn't Mean That It'll Succeed". It was pointed out that Trump's official vision for the region as articulated by his administration's "Strategy For Central Asia 2019-2025" sharply contrasts the unstated one pursued by his predecessors.
Read more: India will be a roadblock in Russia-Pakistan relations
Instead of focusing on terrorist-driven divide-and-rule Hybrid Warfare, it concentrates mostly on peaceful regional connectivity in order to calmly expand American influence into the geostrategic Eurasian Heartland. The non-violent means that are to be relied upon to this soft power end should be commended, though one shouldn't also preclude the possibility of some elements of the former informal strategies remaining in place, especially following Biden's inauguration.
The Argument Against Another "Surge"
The former Vice President is bringing a bunch of Obama-era and -influenced officials (back) to the White House, hence why many feared that he might even seriously countenance repeating that administration's infamous but ultimately failed "surge". The geopolitical times have greatly changed since then, however, and there doesn't seem to be any real interest in doing so under the current conditions.
Not only is the planet reeling from what the author described as World War C — which refers to the full-spectrum paradigm-changing processes unleashed by the international community's uncoordinated efforts to contain COVID-19 — but America is on the brink of launching a domestic version of its "War on Terror" in response to Capitol Hill's storming last week and the US must also adapt to China's growing leadership role in the world. These take precedence over the Taliban.
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Improved US-Pakistani Ties Augur Well For Afghanistan
The author touched upon those last developments as well as the Biden Administration's lack of trust in the Modi one in his analysis earlier this week for Pakistan's Tribune Express about "The Three Factors That Will Shape The Future Of US-Pakistani Relations". It was concluded that bilateral relations will improve as a result of these pressures, which in turn will further reduce the possibility of the US doubling down on its failed War on Afghanistan.
The Taliban peace process, for as imperfect as it is, has veritably led to some noticeable results over the past year. Not only would it be a waste for Biden to scrap all of that just for the sake of spiting his predecessor, but it wouldn't serve much of a grand strategic purpose anyhow considering the progress that's being made on implementing the Trump Administration's Central Asian strategy.
Trump & Biden: Different Visions, Shared Interests
In fact, it's in Central Asia where Trump and Biden have a unique confluence of interests. The former's economic-driven policy of engagement dovetails well with the latter's plans to assemble a so-called "Alliance of Democracies". Both are non-military means for expanding influence and perfectly complement one another.
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While Biden will probably retain the US' troop presence in Afghanistan or even slightly increase it for domestic political reasons should he find it convenient to do so, he's unlikely to devote as much military time and effort to the conflict as Obama did for the earlier mentioned reasons. While the Central Asian Republics don't practice Western forms of democracy, the US nevertheless subjectively regards them as being different in substance from Russia and China's governing models, and thus comparatively more "legitimate" to partner with.
The Military-Industrial Complex's Pernicious Influence
Even so, the US' powerful military-industrial complex won't take too kindly to its most direct interests being threatened in the region through the civilian government's decision to keep troop levels at an all-time low. Bearing this in mind, it makes sense for Biden for execute the Trump Administration's reported proposal to privatize the conflict through private military contractors (PMCs) as the latter are an important cutting-edge part of the military-industrial complex, albeit one which enables Washington to retain a degree of "plausible deniability".
Many former servicemen transition from the Armed Forces to PMCs upon their honorable discharge because it pays much better, thus making these entities practically one and the same except in the legal sense, with both fulfilling the important task of guarding Afghanistan's $1 trillion in rare earth minerals.
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Looking forward, Biden (or rather, the power structure behind him) might not make much political progress on resolving America's War on Afghanistan, but he probably won't make things much worse either. Rather, this "endless war" might continue to persist, but simply become more and more "forgettable" so to speak.
Should he feel that it would be politically convenient to do so in the domestic sense, then he might either slightly raise the troop levels or publicly announce that some of the existing ones will be switch out for PMCs. His intelligence agencies will probably continue to foment low-intensity destabilization scenarios across the region, but likely won't concentrate too much effort on this as the US' grand strategic focus shifts elsewhere in light of the new domestic and international conditions in which the fading unipolar hegemon is forced to adapt.
Andrew Korybko is a political analyst, radio host, and regular contributor to several online outlets. He specializes in Russian affairs and geopolitics, specifically the US strategy in Eurasia. The views expressed in this article are the authors own and do not necessarily reflect the editorial policy of Global Village Space.
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You might remember BOCES from your own school days as a place for special education students and kids who couldn't succeed or didn't fit in at your "real high school." But today's BOCES is a whole different ballgame.
We still prepare students for the workforce, but we also provide students with important 21st century skills - such as critical thinking, teamwork, data analysis, resume writing - that will help them succeed in college, the military and their chosen career path. In fact, 95 percent of our Career and Technical Education students graduate high school - far exceeding the statewide graduation average - and many of them graduate with honors, earn college scholarships and carry technical endorsements on their Regents diplomas.
Don't you still offer the same courses you did several decades ago?
Yes, we offer a variety of programs in both traditional and new fields because they are viable career options. But, we no longer simply teach a trade. All CTE programs integrate curriculum based on New York State Learning Standards in core academic areas - math, English, social studies and science. Our Carpentry students, for example, need to learn math, geometry and physics in order to successfully build structures, but they learn these things in a way that is applicable to their lives. This helps make learning relevant and interesting for our students.
We offer a number of special education and alternative education programs and settings. Some students are in our programs because their districts do not have the appropriate staff for certain students - such as teachers of autism or deaf students. Some students are here because their learning styles are not suited to a traditional classroom and school structure, but they are able to find success here.
My child needs to attend the Alternative School, but I don't want him/her to be stuck there forever.
Many students do not feel "stuck" here - they enjoy it. Nevertheless, our goal is to work with the student, family and any relevant outside agencies to help transition students back to their home school whenever possible.
What kinds of services and extracurriculars can students participate in at BOCES?
For CTE students, Madison-Oneida BOCES hosts a chapter of the National Technical Honor Society and a chapter of SkillsUSA. Our Alternative Education students have leadership teams, mentoring groups, a school store and other options. Students from BOCES also have the option to participate in activities and clubs at their home school.
Why do you offer non-instructional services?
Administrative, business and management services can be costly for districts to support on their own. Many times, districts do not need someone to work in these types of positions full-time, but it is challenging to find a qualified person to work part-time. BOCES helps provide a solution. When two or more districts have similar needs - two districts each need a part-time payroll clerk, for example - BOCES can search for and hire someone who will then split his/her time between the two districts, and the districts will then share the cost of that employee. This allows districts to save money by paying only for the level of service they need; to have an appropriate, qualified person serving their needs; and to refocus their attention on students and programming.