Hurrah, vague rantings with many indeterminate objects and ambiguous sentence subjects!
The only way to guarantee something gets done is to take the initiative to make it happen yourself.
Note that this isn't "the only way to get something done" or saying that "you have to do it yourself."
My actions need to become much more binary (because they tend to backslide into a grayscale gradient). If you see an action that needs to be taken, either do something about it and commit to it fully, or get out of the way and leave it behind. I mean really leave it behind. Don't just put it in your "to-do-later" list. Don't even have a to-do-later list. Be here. Now. Act here. Now.
As long as I'm spitting out disjointed fragments of thought: I'm sorry if I've been giving off radio silence (via email or in person, mostly) and been oddly distant lately (on occasion; it's not a 100% of the time thing) and given no explanation. It's partially out of necessity; there's a lot of stuff going on in my general life-the-universe-and-everything domain right now (workdeath included), and I've withdrawn somewhat so as not to impose crap on other people. I'll be fully back as soon as possible, and I'll try to do better at making it clear to people when I'm unable to fully interact with them at some particular point in time (even if the intent of the interaction is to make me feel better - I really appreciate it, and it means a lot, but I can't always respond to it at that moment). I'm really bad at saying no, so what you usually end up with is half-assed interactivity. I'm trying to say no when it needs to be said.


text:
\section{Introduction}
Models of the cardiac action potential have been developed to study cardiac diseases such as arrhythmia \cite{luo_dynamic_1994,luo_dynamic_1994-1,faber_action_2000}, ischaemia \cite{terkildsen_balance_2007} and acidosis \cite{crampin_dynamic_2006}. Increasing model complexity has led to concerns over the occurrence of drift and non-unique steady states \cite{guan_discussion_1997,fraser_quantitative_2007,kneller_time-dependent_2002}, particularly for extensions of the DiFrancesco and Noble \cite{difrancesco_model_1985} and Luo-Rudy \cite{luo_dynamic_1994,faber_action_2000} models. While solutions to these issues have been proposed using conservation principles \cite{hund_ionic_2001,livshitz_uniqueness_2009}, they have not been universally applied for more recent models, many of which still use nonconservative stimulus currents that predispose them to drift \cite{aslanidi_mechanisms_2009,carro_human_2011,grandi_novel_2010}. More recently, the Food and Drug Administration (FDA) has initiated plans to use cardiac action potential models to assess potential drug side-effects on cardiac instability through the human \textit{ether-\`{a}-go-go}-related gene (hERG) K\textsuperscript{+} channel. Thus, with an increasing emphasis on model robustness and accuracy, there is a renewed incentive to resolve the issues of drift and non-unique steady states \cite{sager_rechanneling_2014,colatsky_comprehensive_2016}.

Drift is the failure of a model to reach a consistent limit cycle when simulated over long periods, and is often caused by a nonconservative stimulus containing current with no charge carrier \cite{guan_discussion_1997,hund_ionic_2001}. Hund \textit{et al.} \cite{hund_ionic_2001} derived a charge conservation law, and found that nonconservative stimulus currents violate this conservation law, hence they proposed K\textsuperscript{+} ions as the current charge carrier to resolve this. A related issue in many models where drift has been resolved is that steady state limit cycles under constant pacing depend upon the initial conditions and are therefore non-unique \cite{fraser_quantitative_2007,hund_ionic_2001,kneller_time-dependent_2002}. Thus, depending on the initial conditions, the same model may lead to different conclusions. Like drift, authors have suggested that charge conservation can constrain initial conditions such that they lead to the same steady state \cite{hund_ionic_2001,kneller_time-dependent_2002,livshitz_uniqueness_2009}.

While the studies by Hund \textit{et al.} \cite{hund_ionic_2001} and Livshitz and Rudy \cite{livshitz_uniqueness_2009} suggest measures to eliminate drift and attain a unique steady state by using conservation laws, their analyses are limited in their scope and not a comprehensive solution for all models. Because existing studies \cite{hund_ionic_2001,livshitz_uniqueness_2009} explore charge conservation only in specific models, and the conservation laws were derived from physical intuition rather than a principled mathematical approach, it is difficult to generalise their findings to other models. Furthermore, because these studies focus only on conservation of charge, they may miss other conservation laws relevant for long-term behaviour, such as those corresponding to ions, ion channels and buffers. A general approach is, therefore, desirable to deal with the issues of drift and steady states in a more systematic manner and for a broader range of models.

To facilitate a general approach, we propose the use of bond graphs which explicitly model energy transfer across physical systems to ensure compliance with conservation principles. Bond graphs were initially invented to model hydroelectric systems \cite{paynter_analysis_1961} and they have subsequently been extended to model chemical \cite{borutzky_advances_1995}, biochemical \cite{oster_network_1973,gawthrop_energy-based_2014} and electrochemical systems \cite{gawthrop_bond_2017-1}. As with all physical systems, biological processes must obey the fundamental principles of physics and thermodynamics \cite{omholt_human_2016}, therefore bond graphs are well-suited for constraining models of biological systems to physically plausible solutions \cite{gawthrop_hierarchical_2015}, and also for inferring the energetic cost of biological processes \cite{gawthrop_bond_2017-1,gawthrop_bond_2017,gawthrop_hierarchical_2015,gawthrop_energy-based_2017}. Because the bond graph representation emphasises analogies between different physical domains, electrophysiological systems can be analysed as an analogous biochemical system with a stoichiometric matrix that describes the stoichiometry of each reaction within its columns \cite{beard_energy_2002,beard_thermodynamic_2004,gawthrop_energy-based_2014,van_der_schaft_mathematical_2013}. In this context, the ``conservation principle'' described in earlier studies is an example of the more general principle of a conserved moiety in metabolic and bond graph analysis \cite{haraldsdottir_identification_2016,gawthrop_hierarchical_2015}.

In this study, we develop a bond graph model of the cardiac action potential and outline a general approach to study the effects of conserved moieties on drift and steady-state behaviour. Our bond graph model simulates physiological action potentials, and because bond graphs are energy-based this easily provides an estimate of the energetic cost (in Joules) of the cardiac action potential. Our analysis reveals conservation of charge as one of the conserved moieties of our model, along with other conserved moieties corresponding to ions, channels, transporters and buffers. We observed that our model solution was subject to drift when the stimulus current violated any conservation laws corresponding to the conserved moieties, and that changes to the initial conditions led to different steady states if the value of any conserved moiety was changed. To demonstrate that our approach is general, we analyse variants of our bond graph model where different ions have been fixed at a constant concentration (corresponding to ``chemostats''). It should be noted that fixing an ion concentration can change the conserved moieties of a system, therefore influencing a model's susceptibility to drift and non-unique steady states. The bond graph approach is a useful and general method to identify and interpret conservation principles, and it can link conserved moieties to individual steady states. We build upon existing reports \cite{hund_ionic_2001,livshitz_uniqueness_2009} to propose solutions for drift and non-unique steady states which work for all cardiac action potential models that can be represented using bond graphs.

\section{Methods}
\label{sec:methods}
\subsection{Model components}
To study the issues of drift and non-unique steady-states, we built a bond graph model of the cardiac action potential, with the minimal number of channels and pumps required to simulate a physiological action potential, and maintain ionic concentrations over long periods of simulation. Accordingly, our model was based on the Luo-Rudy 1994 dynamic model \cite{luo_dynamic_1994}, although it is possible to use other models and/or model more sub-cellular processes. Model components are shown in \autoref{fig:cardiac_AP_model}A, together with the overall bond graph structure (\autoref{fig:cardiac_AP_model}B). Ion channels and Ca\textsuperscript{2+} buffering components were based upon their representations in Luo and Rudy \cite{luo_dynamic_1994}. The L-type Ca\textsuperscript{+} channel in the Luo-Rudy model is permeable to calcium, sodium and potassium, but we neglected its sodium conductance as this has a relatively small contribution to the action potential. The Na$^+$/K$^+$ ATPase model was based on the model by Terkildsen \textit{et al.} \cite{terkildsen_balance_2007}, with modifications suggested by Pan \textit{et al.} \cite{pan_cardiac_2017} to allow conversion into a bond graph model. The equation for the Na\textsuperscript{+}-Ca\textsuperscript{2+} exchanger (NCX) current in Luo and Rudy did not have an obvious correspondence to a bond graph structure, thus we modelled this component using a simple bond graph module that was fitted to experimental data \cite{kimura_identification_1987,beuckelmann_sodium-calcium_1989}. Further detail on the modelling of each component is given in the Supporting Material.

\begin{figure}
	\centering
	\includegraphics[width=0.9\linewidth]{Cardiac_AP_fig}
	\caption{Action potential model. \textbf{(A)} Cell schematic; \textbf{(B)} Overall bond graph structure. The bond graph modules Na{\_}channel, NaK, K{\_}channels, LCC, NCX and Ca{\_}buffer contain more detailed aspects of the bond graph structure which are described further in the Supporting Material. Coloured bonds link bond graph modules to the appropriate chemical species. Definitions: $I_\mathrm{Na}$, sodium current; $I_\mathrm{K1}$, time-independent K\textsuperscript{+} current; $I_\mathrm{K}$, time-dependent K\textsuperscript{+} current; $I_\mathrm{Kp}$, plateau K\textsuperscript{+} current; $I_\mathrm{LCC}$, L-type Ca\textsuperscript{2+} current; NCX, Na\textsuperscript{+}-Ca\textsuperscript{2+} exchanger; Na/K, Na$^+$/K$^+$ ATPase; TRPN, troponin; CMDN, calmodulin.}
	\label{fig:cardiac_AP_model}
\end{figure}

\subsection{Bond graph modelling}
Here we briefly outline bond graph components as used in electrophysiological modelling. For a more comprehensive introduction, the texts by Gawthrop and Smith \cite{gawthrop_metamodelling:_1996} and Borutzky \cite{borutzky_bond_2010} provide detailed descriptions of bond graph theory, and Gawthrop and Bevan \cite{gawthrop_bond-graph_2007} provide a short tutorial for engineers. Theory for bond graph modelling of biochemical systems can be found in \cite{oster_network_1973,gawthrop_energy-based_2014,gawthrop_hierarchical_2015,gawthrop_bond-graph_2017}.

Bond graphs consist of components (representing physical objects and processes), bonds (representing the transfer of energy), and junctions (representing network structure). Each bond carries two variables: an effort $e$ and a flow $f$, such that their product determines the power of the bond (i.e.~$p=ef$). Thus bond graphs explicitly account for energy transfer, and are thermodynamically consistent. Because effort and flow are generalised variables, they can represent quantities from a variety of physical systems, including mechanical ($e=\text{force}$ [N], $f=\text{velocity}$ [m/s]), electrical ($e=\text{voltage}$ [V], $f=\text{current}$ [A]) and hydraulic systems ($e=\text{pressure}$ [Pa], $f=\text{volumetric flow rate}$ [$\si{m^3/s}$]) \cite{borutzky_bond_2010}.

The network structure of a bond graph is specified by 0 and 1 junctions. The 0 (or effort) junctions specify that efforts of all connected bonds are equal, and thus to ensure conservation of energy through this junction, the flows of the bonds must sum to zero. In the electrical and hydraulic domains, 0 junctions represent parallel connections, whereas they represent series connections in the mechanical domain. By a similar principle, 1 (or flow) junctions specify that the flows of all connected bonds are equal, ensuring that their efforts sum to zero. Thus, 1 junctions correspond to series connections in the electrical and hydraulic domains, and parallel connections in the mechanical domain.

\begin{figure}
\centering
\begin{turn}{90}
\begin{minipage}{0.7\paperheight}
\includegraphics[width=\linewidth]{analogies}
\caption{Conceptual representations of physical systems. \textbf{(A)} A bond graph for the illustrated simple electric circuit with two capacitors and a resistor in series. \textbf{(B)} A bond graph analogous to the electric circuit in (A) can also represent the chemical reaction $A \rlh B$. \textbf{(C)} Bond graphs can also model interaction of components in both the chemical and physical domains, such as the transport of an ion across a membrane. \textbf{(D)} Transport of an ion across a membrane through an ion channel involves gating which modulates the rate of reaction. Thus the ion channel is analogous to a potentiometer.}
\label{fig:representations}
\end{minipage}
\end{turn}
\end{figure}

To illustrate the use of a bond graph for electric circuit analysis, we consider the electric circuit where two capacitors are connected to a resistor in series (\autoref{fig:representations}A). All components are linear, described by the equations:
\begin{align}
	V_A &= \frac{q_A}{C_A} \qquad \text{(capacitor)} \\
	V_B &= \frac{q_B}{C_B} \qquad \text{(capacitor)} \\
	I &= \frac{V_R}{R} \qquad \text{(resistor)}
\end{align}
The 1 junction enforces Kirchhoff's voltage law, such that:
\begin{align}
	V_R = V_A - V_B
\end{align}
Combining these equations gives rise to a system of first-order differential equations:
\begin{align}
	\frac{dq_A}{dt} &= -I = \frac{V_B - V_A}{R} = \frac{q_B}{RC_B} - \frac{q_A}{RC_A} \\
	\frac{dq_B}{dt} &= I = \frac{V_A - V_B}{R} = \frac{q_A}{RC_A} - \frac{q_B}{RC_B}
\end{align}

More recently, bond graphs have been extended to model biochemical systems \cite{oster_network_1973,gawthrop_energy-based_2014} where the chemical potential $\mu$ [$\si{J/mol}$] is the effort variable, and molar flow rate $v$ [$\si{mol/s}$] is the flow variable. Each chemical species is represented as a capacitor. However, in contrast to the electrical domain, the constitutive equation for the capacitor representing each species is nonlinear:
\begin{align}
	\mu = RT\ln(Kx)
	\label{eq:cp}
\end{align}
where $x$ [mol] is the molar amount of the species, $K$ [$\si{mol^{-1}}$] is a species thermodynamic constant, $R=8.314\ \si{J\cdot  mol^{-1} \cdot K^{-1}}$ is the gas constant and $T$ is the absolute temperature of the system. Reactions are modelled as two-port resistors using the Marcelin-de Donder equation as the constitutive equation:
\begin{align}
	v = \kappa (e^{A^f/RT} - e^{A^r/RT})
	\label{eq:MdD}
\end{align}
where $\kappa$ [$\si{mol/s}$] is a reaction rate constant and $A^f$ [$\si{J/mol}$] and $A^r$ [$\si{J/mol}$] are the forward and reverse affinities, respectively. The two affinities represent the potential energies present in the reactants and products, and the reaction proceeds in the direction of decreasing potential. As illustrated by the example in \autoref{fig:representations}B, the reaction $A \rlh B$ has a physical analogy to \autoref{fig:representations}A, with the same equivalent electric circuit. By using the constitutive equations in Eqs. \ref{eq:cp} and \ref{eq:MdD}, the reaction velocity for the bond graph model follows mass-action kinetics:
\begin{align}
	v = \kappa_1 (e^{A^f/RT} - e^{A^r/RT})
	= \kappa_1 (e^{\mu_a/RT} - e^{\mu_b/RT})
	= \kappa_1 (K_a x_a - K_b x_b)
	= k^+ x_a - k^- x_b
\end{align}
where the forward and reverse rate constants are $k^+ = \kappa_1 K_a$ and $k^- = \kappa_1 K_b$. For more general chemical reaction networks, 1 junctions describe the presence of multiple reactants or products in a single reaction, whereas 0 junctions describe the involvement of a single species in multiple reactions \cite{gawthrop_energy-based_2014}. For some models, we may wish to keep the amount $x$ of a species constant and this is achieved by defining the species as a ``chemostat'' \cite{polettini_irreversible_2014}. Because chemostats can be interpreted as an external flow that balances internal flows, they require energy to be pumped into (or out of) the system \cite{gawthrop_hierarchical_2015}.

The bond graph framework for biochemistry can be extended to electrochemical systems \cite{gawthrop_bond_2017-1} as demonstrated in \autoref{fig:representations}C, which models the transport of a positively charged species $X$ across a membrane. It should be noted that chemical species are described with C components that have a logarithmic association, whereas the C component corresponding to the (electric) membrane potential has a linear constitutive relationship. A transformer (TF) is used to convert the membrane voltage into an equivalent chemical potential through Faraday's constant ${F = 96485\ \si{C/mol}}$, such that:
\begin{align}
	\mu_P &= FV \\
	I &= Fv
\end{align}
Thus, the reaction velocity is:
\begin{align}
	v = \kappa_1 (e^{A^f/RT} - e^{A^r/RT})
	= \kappa_1 (e^{(\mu_i + \mu_P)/RT} - e^{\mu_e/RT})
	= \kappa_1 (K_i x_i e^{zFV/RT} - K_e x_e)
\end{align}
By setting $v=0$ the familiar Nernst equation can be derived \cite{gawthrop_bond_2017-1}. However, where electrical circuit representations of the membrane Nernst potential use voltage sources, the bond graph approach necessarily accounts for possible changes in ionic concentrations, and thus this ``voltage source'' is split into two capacitors that provide an equivalent voltage difference.

We chose to represent ion channels such that conductance was modulated by membrane voltage, both directly and indirectly through gating processes. A bond graph representation for this relationship is given in \autoref{fig:representations}D. As shown, this model has the same electrical representation as \autoref{fig:representations}C however it uses a variable resistor. The bond graph representation contains the same states, with C:xi, C:xe, and C:mem (with a transformer) connected through 0 junctions. In this case however, the Re components that describe the constitutive relation have been changed, such that Re{\_}GHK:r1 is connected to an additional effort that modulates its velocity, and the gating affinity $A^g$ is added to both the forward and reverse affinities to describe changes in permeability due to gating. Further detail on modelling ion channels using bond graphs is given in the Supporting Material.

\subsection{Modelling approach}
\label{sec:modelling_approach}

Because bond graphs constrain the equations of a model to ensure thermodynamic consistency, many existing models do not have a direct bond graph representation \cite{gawthrop_hierarchical_2015}. For the example here, equations representing ion channels in the Luo-Rudy model could not be directly translated into a bond graph model due to difficulties with simultaneously modelling open-channel currents and channel gating, and due to thermodynamic inconsistencies in the time-dependent K\textsuperscript{+} and L-type Ca\textsuperscript{2+} channels (see Supporting Material). Therefore rather than attempting to reproduce the Luo-Rudy equations exactly, we built a bond graph structure as implied by the equations in Luo and Rudy model, and chose parameters of our bond graph model to fit aspects of the Luo-Rudy model as closely as possible, specifically the current-voltage (I-V) curves and gating parameters. For all other components conversion into a bond graph model was more straightforward, and we used the methods of Gawthrop \textit{et al.} \cite{gawthrop_hierarchical_2015}. Further information on the bond graph model, and parameter identification is given in the Supporting Material.

\subsection{Finding conserved moieties}
Within a biochemical model, conserved moieties are chemical structures that are neither created, removed nor broken down. A common example in energy-dependent metabolic networks is the adenosine moiety found in AMP, ADP and ATP \cite{haraldsdottir_identification_2016,gawthrop_hierarchical_2015}. Mass balance specifies that the total amount of each conserved moiety remains constant, and if information on the molecular structure of each species of a reaction network is available, these conservation laws can be derived by counting the number of moieties across all species \cite{haraldsdottir_identification_2016}. In practice, many models do not contain this structural information and this approach cannot be used, however the conservation laws still hold. Here we outline a method to find conserved moieties using stoichiometric information rather than chemical structures.

Models of cardiac electrophysiology can be represented by the differential equation
\begin{align}
	\dot{X} = NV
\end{align}
where $X(t)$ is a vector of each state (such as species, or charge difference across a membrane), $N$ is the stoichiometric matrix \cite{beard_energy_2002,beard_thermodynamic_2004,gawthrop_energy-based_2014,van_der_schaft_mathematical_2013}, and $V$ is a vector of fluxes (such as reaction velocities, or ion channel currents) \cite{gawthrop_energy-based_2014,liebermeister_modular_2010,beard_energy_2002}. If the model contains chemostats, the entries of $X$, and rows of $N$ corresponding to the chemostats are deleted prior to performing the above analysis \cite{polettini_irreversible_2014}. Using results from biochemical systems \cite{gawthrop_energy-based_2014}, if $g$ is a row vector in the left nullspace of $N$, i.e.~$gN=0$, then
\begin{align}
	g\dot{X} = gNV = 0
\end{align}
Therefore the linear combination $gX$ is constant for the duration of the simulation. We call the linear combination of species represented by $g$ a conserved moiety. The space of all conserved moieties can be described by a left nullspace matrix $G$, whereby linear combinations of the rows of $G$ give all possible conserved moieties $g$ \cite{palsson_systems_2006,klipp_systems_2009}. Advantages of using the left nullspace are that it does not require information on chemical structures and it accounts for all conservation laws. The left nullspace matrix for any given system is generally not unique, however there are many well-established techniques for calculating nullspace matrices \cite{anton_elementary_2014}, specialised approaches for finding meaningful conserved moieties in biochemical networks \cite{schuster_what_1995,schuster_determining_1991,haraldsdottir_identification_2016} as well as methods for finding conserved moieties from the junction structure of a bond graph \cite{gawthrop_bond-graph_2017}. In this study, we chose conserved moieties with clear physical interpretations \cite{schuster_determining_1991}, but our conclusions hold regardless of our choice of the left nullspace matrix.

\subsection{Stimulus currents}
The cardiac action potential model was stimulated using a constant current stimulus that contained enough charge to raise the membrane potential by 30 mV over 0.1 ms. As recommended by Kneller \textit{et al.} \cite{kneller_time-dependent_2002}, conservative stimulus currents contained K\textsuperscript{+} ions as the charge carrier.

\begin{figure}
	\centering
	\includegraphics[width=0.9\linewidth]{single_AP}
	\caption{A simulation of the cardiac action potential using a bond graph model. \textbf{(A)} Membrane voltage, following stimulation with a conservative stimulus current (arrow); \textbf{(B)} Ion channel currents; \textbf{(C)} Transporter and gating currents; \textbf{(D)} Membrane voltage over three cycles, for comparison with (E) and (F); \textbf{(E)} Power consumption; \textbf{(F)} Energy dissipated, with the variable $E$ representing the energy consumption over the duration of the action potential. The model was run initially for 300 ms to allow the membrane potential and channel gates to stabilise. The intracellular ion concentrations were dynamic variables with initial concentrations $\mathrm{[Na_i^+]} = 10\ \si{mM}$, $\mathrm{[K_i^+]} = 145\ \si{mM}$ and $\mathrm{[Ca_i^+]} = 0.12\ \si{\micro M}$. Constant concentrations were $\mathrm{[Na_e^+]} = 140\ \si{mM}$, $\mathrm{[K_e^+]} = 5.4\ \si{mM}$, $\mathrm{[Ca_e^+]} = 1.8\ \si{mM}$,  $\mathrm{[MgATP] = 6.95\ \si{mM} }$, $\mathrm{[MgADP] = 0.035\ \si{mM} }$, $\mathrm{[P_i] = 0.3971\ \si{mM} }$ and $\mathrm{pH = 7.095 }$. $T = 310\ \si{K}$.}
	\label{fig:single_AP}
\end{figure}

\section{Results}
\label{sec:results}
\subsection{Simulation of a single action potential}
To verify that our bond graph model reproduced a typical action potential we simulated the model over a single beat (\autoref{fig:single_AP}A-C). The membrane potential (\autoref{fig:single_AP}A, with stimulation indicated by the arrow) resembled a typical cardiac action potential, with a distinct peak and plateau phase. The contributions of ion channel currents reproduce some common features of cardiac action potentials (\autoref{fig:single_AP}B). Once the action potential is initiated by a stimulus current, the sodium current $I_\mathrm{Na}$ briefly activates to give rise to a voltage spike. Following this, the plateau phase occurs where depolarising L-type Ca\textsuperscript{2+} currents oppose the repolarising K\textsuperscript{+} currents $I_\mathrm{K}$ and $I_\mathrm{Kp}$. Towards the end of the action potential, $I_\mathrm{K1}$ activates to restore the resting potential \cite{noble_models_2001}. Our model also simulates the reversal of NCX current across the action potential, and the consistent outward current of the Na$^+$/K$^+$ ATPase to maintain ionic gradients (\autoref{fig:single_AP}C). A consequence of modelling ion channels using bond graphs is that transitions between channel states are associated with a gating current resulting from charged residues moving in an electric field \cite{hodgkin_quantitative_1952}. Our model reveals that the total gating current across all channels $I_\mathrm{gate}$ has minimal contribution to total current (\autoref{fig:single_AP}C).

\autoref{fig:single_AP}E shows the power consumption of the membrane model over three cardiac cycles which was integrated to estimate the energetic cost of the cardiac action potential (\autoref{fig:single_AP}F). Note that energy continues to be consumed even during the resting state due the presence of currents associated with ion transporters. Thus while energy is predominantly consumed during the action potential, there is a rising gradient between action potentials (\autoref{fig:single_AP}F). By setting the energy consumption at the start of the second action potential to zero (\autoref{fig:single_AP}F, dotted blue line), we calculated the energetic cost over the duration of the action potential to be $46.8\ \si{pJ}$. Since the capacitive area of membrane for this model is $1.534 \times 10^{-4}\ \si{cm^2}$, the energy consumed per unit membrane area is $305\ \si{nJ/cm^{2}}$. When compared to Gawthrop et al.'s \cite{gawthrop_bond_2017-1} estimate of $173\ \si{nJ/cm^{2}}$ for the energetic cost of an action potential in the giant axon of a squid, the cardiac action potential uses 76\% more energy. The main reason for this difference is that in contrast to a neuron, the cardiac action potential contains a plateau phase with opposing currents. Despite the relatively slow rate of change in voltage, the Ca\textsuperscript{2+} and K\textsuperscript{+} currents remain relatively high, therefore a large amount of energy is dissipated during the plateau phase.

\begin{table}
	\caption{Conserved moieties associated with chemostat selection. Across some biochemical subgroups (``Moiety''), there are constraints (``Conserved quantity'') on a corresponding sum of species representing the total of the moiety. The conserved quantities remain constant over the course of a simulation. Q represents contributions of other species to charge imbalance across the membrane. The symbol $\Sigma$ represents charge contributions from Markov states of channels and transporters. The definition of $\Sigma$, and all species can be found in the Supporting Material and code.}
	\centering
	\bgroup
	\def1.3{1.3}
	\begin{tabular}{r l p{0.7\linewidth}}
		\toprule
		& Moiety & Conserved quantity \\ \midrule
		\multicolumn{3}{l}{\textit{Conserved moieties common to all variants (A,B,C)}} \\ \midrule
		1 & K1 channel & $\mathrm{C_{K1} + O_{K1}}$ \\
		2 & K channel & $\mathrm{S_{00,K} + S_{10,K} + S_{20,K} + S_{01,K} + S_{11,K} + S_{21,K}}$ \\
		3 & Kp channel & $\mathrm{C_{Kp} + O_{Kp}}$ \\
		4 & Na channel & $\mathrm{S_{000,Na} + S_{100,Na} + S_{200,Na} + S_{300,Na} + S_{010,Na} + S_{110,Na} + S_{210,Na}}$ $\mathrm{ + S_{310,Na} + S_{001,Na} + S_{101,Na} + S_{201,Na} + S_{301,Na} + S_{011,Na}}$ $\mathrm{ + S_{111,Na} + S_{211,Na} + S_{311,Na}}$\\
		5 & LCC& $\mathrm{S_{000,LCC} + S_{010,LCC} + S_{020,LCC} + S_{100,LCC} + S_{110,LCC} + S_{120,LCC}}$ $\mathrm{ + S_{001,LCC} + S_{011,LCC} + S_{021,LCC} + S_{101,LCC} + S_{111,LCC} + S_{121,LCC}}$  \\
		6 & $\mathrm{Na^+}/\mathrm{K^+}$ ATPase& $\mathrm{P1_{NaK} + P2_{NaK} + P3_{NaK} + P4_{NaK} + P5_{NaK} + P6_{NaK} + P7_{NaK}}$ $\mathrm{ + P8_{NaK} + P9_{NaK} + P10_{NaK} + P11_{NaK} + P12_{NaK} + P13_{NaK}}$ $\mathrm{ + P14_{NaK} + P15_{NaK}}$ \\
		7 & NCX& $\mathrm{P1_{NCX} + P2_{NCX} + P3_{NCX} + P4_{NCX} + P5_{NCX} + P6_{NCX}}$\\
		8 & Troponin & $\mathrm{TRPN + TRPNCa}$ \\
		9 & Calmodulin & $\mathrm{CMDN + CMDNCa}$ \\ \midrule
		\multicolumn{3}{l}{\textit{Dynamic ion concentrations (A)}} \\ \midrule
		& Chemostats & MgADP, MgATP, Pi, $\mathrm{H^+}$\\
		10 & $\mathrm{K^+}$ ion & $\mathrm{K^+_i + K^+_e + 2P1_{NaK} + P2_{NaK} + P12_{NaK}+ 2P13_{NaK}+ 2P14_{NaK}}$ $+ \mathrm{2P15_{NaK}}$ \\
		11 & $\mathrm{Na^+}$ ion & $\mathrm{Na^+_i + Na^+_e + P4_{NaK} + 2P5_{NaK} + 3P6_{NaK}+ 3P7_{NaK}+ 3P8_{NaK}}$ $\mathrm{ + 2P9_{NaK}+ P10_{NaK} + 3P1_{NCX} + 3P6_{NCX}}$ \\
		12 & $\mathrm{Ca^{2+}}$ ion & $\mathrm{Ca^{2+}_i + Ca^{2+}_e + 2S_{001,LCC} + 2S_{011,LCC} + 2S_{021,LCC} + 2S_{101,LCC}}$ $\mathrm{ + 2S_{111,LCC} + 2S_{121,LCC} + P3_{NCX} + P4_{NCX} + TRPNCa}$ $\mathrm{ + CMDNCa}$\\
		13 & Charge & $\mathrm{Q - K^+_i - Na^+_i - 2Ca^{2+}_i + 2\mathrm{TRPN} + 2\mathrm{CMDN} + \Sigma}$ \\ \midrule
		\multicolumn{3}{l}{\textit{Dynamic intracellular ion concentrations (B)}} \\ \midrule
		& Chemostats & MgADP, MgATP, Pi, $\mathrm{H^+}$, $\mathrm{K^+_e}$, $\mathrm{Na^+_e}$, $\mathrm{Ca^{2+}_e}$\\
		10 & Charge & $\mathrm{Q - K^+_i - Na^+_i - 2Ca^{2+}_i + 2\mathrm{TRPN} + 2\mathrm{CMDN} + \Sigma}$ \\ \midrule
		\multicolumn{3}{l}{\textit{Constant ion concentrations (C)}} \\ \midrule
		& Chemostats & MgADP, MgATP, Pi, $\mathrm{H^+}$, $\mathrm{K^+_i}$, $\mathrm{K^+_e}$,  $\mathrm{Na^+_i}$, $\mathrm{Na^+_e}$, $\mathrm{Ca^{2+}_i}$, $\mathrm{Ca^{2+}_e}$\\	\bottomrule
	\end{tabular}
	\egroup
	\label{tab:cm}
\end{table}

\subsection{Chemostats influence the conserved moieties of cardiac action potential models}

Because the earliest models of the cardiac action potential did not include active transporters, they used constant intracellular concentrations to maintain ionic gradients across multiple cardiac cycles \cite{difrancesco_model_1985,luo_model_1991}. Later models incorporated ion transporters, allowing them to represent physiological conditions with dynamic intracellular ion concentrations, and constant extracellular ion concentrations to model washout from the circulatory system \cite{luo_dynamic_1994,faber_action_2000}. Under ischaemic conditions, washout is greatly inhibited, thus models of ischaemia use dynamic extracellular ion concentrations \cite{terkildsen_balance_2007}. We investigated the issue of drift in three classes of model: those with (A) dynamic ion concentrations on both sides of the membrane, representing models of myocytes under ischaemic conditions; (B) dynamic intracellular ion concentrations but constant extracellular ion concentrations, representing models of myocytes under physiological conditions; and (C) constant ion concentrations, representing models without transporters.

We used our bond graph model to represent these classes of models, selecting ions to fix at constant concentrations that resulted in three variants representative of the classes listed above. Conserved moieties of each variant were found using the left nullspace matrix of the stoichiometric matrix (\autoref{tab:cm}), and these include for example, the total amount of K1 channel (moiety 1). Because the channel is neither synthesised nor degraded in our model, the total amount of channel, i.e.~the sum of its closed ($\mathrm{C_{K1}}$) and open ($\mathrm{O_{K1}}$) states, remains constant over the course of a simulation.

Similarly, moiety 10 for variant (A) represents the total amount of K\textsuperscript{+} ions, which includes intracellular K\textsuperscript{+}, extracellular K\textsuperscript{+} and the K\textsuperscript{+} ions bound to Na\textsuperscript{+}/K\textsuperscript{+} ATPase. The total amount of K\textsuperscript{+} is constant when ion concentrations are dynamic. However, because fixing the concentration of K\textsuperscript{+} requires an additional external flux, the conservation law is broken in variants (B) and (C). Because the membrane capacitance is included in the stoichiometry of the system, our method automatically identifies a charge conservation law (moiety 13 for variant (A), and moiety 10 for variant (B)).

Finally, the overall amount of intracellular charge can be described as a sum of contributions from intracellular K\textsuperscript{+}, Na\textsuperscript{+}, Ca\textsuperscript{2+} (and its buffers) and Markov states from ion channels and transporters ($\Sigma$), similar to forms found in previous studies \cite{hund_ionic_2001,varghese_conservation_1997}. It should be noted, however, that when all ion concentrations were held constant charge conservation was broken, as indicated by the absence of a conserved charge moiety in the bottom partition of \autoref{tab:cm}. In general, holding the concentration of a species constant breaks conservation laws \cite{polettini_irreversible_2014} and the number of conserved moieties progressively decreases as more ions concentrations are modelled as chemostats. We discuss the consequences of this in later sections.

\begin{figure}
	\centering
	\includegraphics[width=0.9\linewidth]{stim_current_comparison}
	\caption{Effect of stimulus type and variable ion concentrations on model drift. \textbf{(A)} Dynamic ion concentrations; \textbf{(B)} Dynamic intracellular ion concentrations; \textbf{(C)} Constant ion concentrations. Results are shown for stimuli that conserve overall charge (blue) and those that do not conserve charge (red). Charge values are given as differences from the initial value of $-$5882.2 fmol. $T = \text{310 K}$. Definitions: $V_\text{dia}$, diastolic membrane potential; APD, action potential duration at 90\% repolarisation.}
	\label{fig:stim_currents}
\end{figure}

\subsection{Nonconservative stimulus currents cause drift in models with a charge conservation law}

An important feature of cardiac electrophysiology models is that they must be simulated for extended periods to examine physiologically relevant changes in behaviour, thus we tested how the type of stimulus current affected each variant of the cardiac action potential model by pacing at 1 Hz for 30 minutes. As illustrated (\autoref{fig:stim_currents}A,B), a nonconservative stimulus resulted in drift when the model had dynamic ion concentrations either for all compartments, or only within the intracellular compartment. The drift was particularly pronounced when all ion concentrations were dynamic (\autoref{fig:stim_currents}A), as extracellular concentrations changed faster than intracellular concentrations. In contrast, the model was resistant to drift from a nonconservative stimulus when all ion concentrations were held constant (\autoref{fig:stim_currents}C).

These results suggested that drift arose due to violations of the conserved charge moiety. Charge is a conserved moiety (\autoref{tab:cm}) in model variants where drift occured with a nonconservative stimulus. In this situation nonconservative stimulus currents cause drift because every stimulus causes a stepwise increase in the value of the conserved charge moiety (\autoref{fig:stim_currents}A,B bottom panels). However, because conservation laws are broken as more species are represented as chemostats \cite{polettini_irreversible_2014}, charge is no longer a conserved moiety when all ion concentrations are constant (\autoref{tab:cm}). Thus an observation which may not be obvious to intuition is that under these conditions charge is no longer constant between stimuli, and therefore free to return to its original value after each stimulus (\autoref{fig:stim_currents}C, bottom panel), allowing such models to achieve a steady-state limit cycle.

\begin{figure}
	\centering
	\includegraphics[width=\linewidth]{ss_comparison}
	\caption{Effect of initial conditions on steady-state behaviour. \textbf{(A)} Dynamic ion concentrations; \textbf{(B)} Dynamic intracellular ion concentrations; \textbf{(C)} Constant ion concentrations. The models were paced at 1Hz for 30 minutes using a conservative stimulus current. $\mathrm{[MgATP] = 6.95\ \si{mM} }$, $\mathrm{[MgADP] = 0.035\ \si{mM} }$, $\mathrm{[P_i] = 0.3971\ \si{mM} }$, $\mathrm{pH = 7.095 }$, $T = 310\ \si{K}$. Definitions: $V_\text{dia}$, diastolic membrane potential; APD, action potential duration at 90\% repolarisation.}
	\label{fig:ic_ss}
\end{figure}

\subsection{Initial conditions influence steady states through conserved moieties and chemostats}
Next, for different sets of conserved moieties (as determined by constrained/dynamic ionic concentrations) we tested how the steady-state behaviour of the cardiac action potential was altered under three different initial conditions (\autoref{fig:ic_ss}). The first set of initial conditions (IC1) are common values for comparison (Fig. 5; \textit{at bottom}). IC2 is the same as IC1 but with 1mM intracellular K\textsuperscript{+} exchanged for 1mM of intracellular Na\textsuperscript{+}, such that charge is conserved but K\textsuperscript{+} and Na\textsuperscript{+} are not conserved. Similarly, IC3 is IC1, but with some K\textsuperscript{+} extruded and an equal amount of Na\textsuperscript{+} moved into the cell such that charge, Na\textsuperscript{+}, and K\textsuperscript{+} are all conserved. When all ion concentrations are dynamic IC1 and IC3 lead to the same steady state, but IC2 results in a different steady state (\autoref{fig:ic_ss}A). If only intracellular ion concentrations are dynamic, however, IC1 and IC2 result in identical steady states, but IC3 leads to a different steady state (\autoref{fig:ic_ss}B). Finally, keeping all ion concentrations constant leads to different steady states for all initial conditions (\autoref{fig:ic_ss}C).

These results demonstrate that the summed amount for each conserved moiety and/or chemostat value determines the steady-state behaviour of cardiac action potential models. To investigate this further, we calculated the values for conserved moieties and chemostats that resulted from each initial condition (\autoref{tab:ic_cm}; \textit{differences from IC1 indicated in bold}). For two sets of initial conditions to achieve identical steady states, all conserved moieties and chemostats must have the same value. Thus under dynamic ion concentrations (\autoref{fig:ic_ss}A), IC3 results in the same steady state as IC1 because all conserved moieties have been preserved (\autoref{tab:ic_cm}), whereas, IC2 causes a different steady state because the $\mathrm{K^+}$ and $\mathrm{Na^+}$ conserved moieties take on different values. Similarly, when only intracellular ion concentrations are dynamic, IC2 preserves the value of all conserved moieties and chemostats, but IC3 changes the values of the chemostats corresponding to extracellular Na\textsuperscript{+} and K\textsuperscript{+} concentrations (\autoref{tab:ic_cm}), hence the different steady state. When all ion concentrations were held constant, changes in the chemostat values (\autoref{tab:ic_cm}) were associated with different steady states for all three initial conditions (\autoref{fig:ic_ss}C).

\begin{table}
	\caption{The values of conserved moieties and chemostats under different initial conditions. All values are in fmol. Chemostats are indicated with (cs). Values different from IC1 are shown in bold.}
	\centering
	\begin{tabular}{c c c c}
		\toprule
		& \multicolumn{3}{c}{Value} \\
		Moiety/Chemostat & IC1 & IC2 & IC3 \\ \midrule
		\multicolumn{4}{l}{\textit{Dynamic ion concentrations (A)}} \\ \midrule
		$\mathrm{K^+}$ & 5538.1 & \textbf{5500.1} & 5538.1 \\
		$\mathrm{Na^+}$ & 1105.6 & \textbf{1143.6} & 1105.6 \\
		Charge & $-$5882.2 & $-$5882.2 & $-$5882.2 \\  \midrule
		\multicolumn{4}{l}{\textit{Dynamic intracellular ion concentrations (B)}} \\ \midrule
		$\mathrm{K_e^+}$ (cs) & 27.98 & 27.98 & \textbf{38.35} \\
		$\mathrm{Na_e^+}$ (cs)  & 5510 & 5510 & \textbf{715.12} \\
		Charge & $-$5882.2 & $-$5882.2 & $-$5882.2 \\ \midrule
		\multicolumn{4}{l}{\textit{Constant ion concentrations (C)}} \\ \midrule
		$\mathrm{K_e^+}$ (cs)  & 27.98 & 27.98 & \textbf{38.35} \\
		$\mathrm{Na_e^+}$ (cs)  & 725.48 & 725.48 & \textbf{715.12} \\
		$\mathrm{K_i^+}$ (cs)  & 5510  & \textbf{5472} & \textbf{5500} \\
		$\mathrm{Na_i^+}$ (cs)  & 380 & \textbf{418} & \textbf{390.36} \\ \bottomrule
	\end{tabular}
	\label{tab:ic_cm}
\end{table}

\section{Discussion}
In this study, we developed a bond graph model of the cardiac action potential with the aim of resolving the issues of drift and non-unique steady states. Analysis using conserved moieties enabled the discovery of all conservation laws within the model. In addition to the conservation of charge law from previous studies \cite{varghese_conservation_1997,hund_ionic_2001,endresen_theory_2000}, we found conservation laws corresponding to ions, states of Markov models of channels and transporters, and buffers. Two key advantages of our approach over existing analyses are that it reveals all conservation laws in a comprehensive and systematic manner, and that it is general for all models of the cardiac action potential that can be represented as bond graphs. When simulated over long periods with a nonconservative stimulus our bond graph model displayed solution drift, but it became resistant to drift when ion concentrations were held constant, demonstrating that changes in the value of a conserved charge moiety drive model drift. We also found that two sets of initial conditions can lead to different steady states if the values of their corresponding conserved moieties and chemostats are different, suggesting a strong link between conserved moieties and the steady-state limit cycles of cardiac action potential models. To demonstrate that our approach is general, we tested how the selection of chemostats (i.e. fixed concentrations) influenced drift and steady-states by using variants of our model that were representative of existing models in the literature. Our approach shows that holding ion concentrations constant changes the conserved moieties of the model, which in turn has an effect on the susceptibility of a model to drift and non-unique steady states.

\subsection{Drift}
When paced with a nonconservative stimulus, variants of the model with a charge conservation law underwent drift (\autoref{fig:stim_currents}A,B) consistent with previous studies \cite{hund_ionic_2001,livshitz_uniqueness_2009}. By observing changes in the charge conserved moiety, the bond graph approach attributes drift to regular perturbations in charge that cannot be restored due to the presence of a conservation law. Whereas previous analyses relied solely on intuition to derive a conservation law corresponding to charge \cite{hund_ionic_2001,livshitz_uniqueness_2009}, we note that our approach automatically derives conservation laws and can detect other conservation laws that may be relevant for drift.

As demonstrated, the bond graph method requires construction of a stoichiometric matrix, providing a simple approach to check whether a stimulus current will cause drift. Let $v_s$ be a row matrix representing the stoichiometry of the stimulus current (with chemostats removed), $N^{cd}$ be the stoichiometric matrix after removing rows corresponding to chemostats, and $G$ be the left nullspace matrix of $N^{cd}$. To avoid altering any of the conserved moieties, the stimulus current must have zero contribution to them, i.e.~ $Gv_s = 0$ (or equivalently, $v_s$ needs to lie in the image of $N^{cd}$). Thus the model drifts if $Gv_s \neq 0$. While it is common practice to use K\textsuperscript{+} as the charge carrier for stimulus currents, it is likely that multiple species contribute to the current \cite{hund_ionic_2001,kneller_time-dependent_2002}. Thus the automated approach suggested here is well-suited for checking whether more complex stimulus currents satisfy conservation of charge, as well as other conservation laws within the model. It should be noted however, that while a model satisfying $Gv_s = 0$ will not drift due to violating conservation laws, drift may still occur due to an imbalance of currents throughout the action potential, for instance, in the absence of Na$^+$/K$^+$ ATPase, the ionic gradients would gradually disappear in a model with dynamic ion concentrations.

Finally, we believe that this analysis provides a link between the issues of drift and steady states. Our models show that drift due to a nonconservative stimulus current can be attributed to changes in the value of the charge conserved moiety with every stimulus, and accordingly the steady state of the model changes. Model drift then occurs as the solution continually chases a moving steady state.

\subsection{Effects of initial conditions on steady states}
We also found that initial conditions of cardiac action potential models change their steady states through the values of chemostats and conserved moieties (\autoref{fig:ic_ss}, \autoref{tab:ic_cm}). Accordingly, the same perturbation to initial conditions can have different effects on the steady state depending on which species are held constant. Therefore in addition to ensuring that the concentration of ions are physiological, care should be taken to correctly initialise each state of buffers and Markov models of ion channels and ion transporters, as they may contain a significant fraction of total ion abundance. For example, Ca\textsuperscript{2+} buffers and SERCA can sequester a significant amount of Ca\textsuperscript{2+} and they should be initialised with the correct amount of bound Ca\textsuperscript{2+} when multi-state models are used \cite{higgins_buffering_2006}. We note that the difficulty of manually deriving conservation laws increases exponentially as models of cardiac electrophysiology become more complex, and we believe that our approach extends on existing analyses \cite{hund_ionic_2001,livshitz_uniqueness_2009} to provide a general method for assessing steady-state behaviour by comparing the values of conserved moieties and chemostats that result from each initial condition.

In the field of biochemical network analysis, there is a well-established dependence of quiescent steady states on conserved moieties, and numerous mathematical techniques for assessing the uniqueness and stability of these steady states have been developed \cite{gross_algebraic_2016,feliu_variable_2012}. However, the influence of conserved moieties on limit cycles in an oscillating system that is regularly stimulated has yet to be investigated. Our results hint at similarities between these two fields, and while we only tested the uniqueness of steady states using relatively small perturbations to the initial conditions, it is possible that a set of conserved moieties may have multiple steady states, and greater perturbations may lead to other limit cycles.

\subsection{The ``differential'' and ``algebraic'' methods}
The discovery of conservation principles in cardiac electrophysiology has lead to a debate over whether to use the differential or algebraic methods of simulation \cite{hund_ionic_2001,fraser_quantitative_2007,livshitz_uniqueness_2009,varghese_conservation_1997,endresen_theory_2000}. The differential method is the calculation of membrane voltage by integrating total current, and the algebraic method is the calculation of membrane voltage using an algebraic relationship derived from charge conservation. We chose the differential method over the algebraic method since it better supports model reuse and modularity - in particular it is easier to modify the equations to select different species as chemostats, and to combine equations when two models are coupled. We note, however, that the algebraic method may reduce computational complexity \cite{gawthrop_energy-based_2014,hund_ionic_2001}. In bond graph modelling, the algebraic method can be implemented by using conserved moieties to turn the system of ordinary differential equations (ODEs) into an index-0 differential algebraic equation (DAE) (Eq. 3.48 of \cite{gawthrop_energy-based_2014}). This method generalises existing algebraic methods to reduce the system of differential equations by using all conserved moieties and not just the conserved charge moiety. While we did not use the algebraic approach, we emphasise that the choice of method relates to numerical approaches for model simulation rather than the underlying physics of the system \cite{hund_ionic_2001}. Therefore, the differential and algebraic methods are equivalent in conservative systems provided that the initial conditions and values of conserved moieties are consistent.

\subsection{Integration into whole-cell models}
Our bond graph model of the cardiac action potential is the first step towards a fully-integrated whole-cell bond graph model of a cardiomyocyte that couples electrophysiology, signalling, metabolism and mechanics. Modelling studies for the energetic regulation of a cardiac cell exist across the literature \cite{tran_regulation_2015}, but while some components used in these models are thermodynamically consistent \cite{tran_thermodynamic_2009,smith_development_2004}, existing whole-cell models are neither energy-based nor thermodynamically consistent throughout the entire model. Furthermore, because existing experimental and modelling studies use ATP consumption as a proxy for energy consumption, they can only estimate the energy consumption of major energy sinks: the Na$^+$/K$^+$ ATPase, SERCA, and crossbridge cycling \cite{schramm_energy_1994,tran_regulation_2015}. A bond graph approach may thus provide more detailed insights into how a cardiac cell uses energy downstream of ATP hydrolysis processes, and help to identify energy-consuming processes. Because the bond graph approach is energy-based it allows us to directly assess energy consumption of the model (in Joules). We found that when normalised against membrane area the cardiac action potential consumes approximately 76\% more energy than an action potential in the axon of a giant squid. To the authors' knowledge, this is the first account of energy consumed by electrochemical processes during the cardiac action potential.

\subsection{Limitations}
Because of physical restrictions imposed by the framework not all model components can be directly converted into a bond graph form. Accordingly, we were forced to model ion channels and transporters using Markov states to faithfully represent their underlying physics, however, this produced a model that had numerous states compared to the number of biological processes. While it is reassuring to find that our method of identifying conserved moieties remained robust despite this complexity, simulation of the model was computationally expensive. For the purpose of integrating this action potential model into a larger whole-cell model, it would be useful to have simple model components that reduce computational cost. While current methods for reducing biochemical models in the bond graph framework are not advanced enough to apply to the biological components in this study, we note that bond graphs provide a useful foundation for applying model simplification while ensuring that thermodynamic consistency is maintained \cite{gawthrop_energy-based_2014}.

We also decided to limit the transport processes included in our model to those considered essential for producing a cardiac action potential, while maintaining a limit cycle using dynamic ion concentrations. Our bond graph model omitted many ionic currents due to their small amplitudes, however these channels may have greater contributions under conditions which vary from those tested here. Thus an obvious extension of this work would be the integration of other electrogenic processes within the cardiac membrane. It would be interesting to investigate whether coupling other models requires further tuning of parameters \cite{babtie_how_2017}, and whether the presence of physical bond graph parameters changes this process.

When formulating the structure and parameters for a bond graph model of the cardiac action potential (or most other processes), it is possible to either fit against existing mathematical models or the underlying experimental measurements. For all processes in this study excluding the NCX, we developed our bond graph model to reproduce the behaviour of an existing model, in an attempt to re-use existing knowledge about these processes. This approach poses constraints on the bond graph structure used, especially for gating structure. Therefore it would be interesting to develop an approach that assesses bond graph structures as well as bond graph parameters, based on their fits to data \cite{babtie_how_2017}. Such an approach may provide a better fit to the data, and uncover insights into the physical mechanisms of ion channels.

\section{Conclusion}
In this study we have developed a bond graph model of the cardiac action potential and used this to explore the issues of drift and non-unique steady states. We demonstrate that the analysis of conserved moieties generalises the concept of charge conservation used in earlier studies, and found that changes in conserved moieties can explain drift as well as changes in steady state behaviour. Importantly, holding ion concentrations constant can have significant consequences on both drift and steady states as they change the conserved moieties in the model. Our approach is sufficiently general that it can be applied to any cardiac action potential model which can be represented as a bond graph. We hope that the bond graph approach outlined here will prove useful for the development of future cardiac electrophysiology models, and eventually whole-cell models of the cardiomyocyte.

\textbf{Data access:}
The code associated with this study is available from GitHub (\url{https://github.com/uomsystemsbiology/bond_graph_cardiac_AP}), and archived on Zenodo (\url{https://doi.org/10.5281/zenodo.1172205}) \cite{pan_supporting_2018}. The code contains MATLAB (The MathWorks, Natick, MA) that generate the figures, CellML code containing parameters, initial conditions and equations of the model, and full details of the bond graph structure.

\textbf{Author contributions:}
M.P., P.J.G., J.C. and E.J.C. developed the theory. M.P. performed the research. K.T. provided conceptual advice and helped interpret the results. All authors contributed to the text of the manuscript and gave final approval for publication.

\textbf{Competing interests:}
We have no competing interests.

\textbf{Funding:}
M.P. would like to acknowledge financial support provided by an Australian Government Research Training Program Scholarship. P.J.G. would like to thank the Melbourne School of Engineering for its support via a Professorial Fellowship. K.T. is supported by the Heart Foundation of New Zealand (Research Fellowship 1692) and the Marsden Fund Council from Government funding, managed by Royal Society Te Apārangi (Marsden Fast-Start 17-UOA-300).

\bibliographystyle{RS}
\small

redpajama_set_name: RedPajamaArXiv


The future is now. From self-driving cars to paying with your thumbprint, we're able to do things now that we could only dream of 20 years ago. One area of technology that has seen wild growth is virtual and augmented reality. 74% of VR users are interested in travel and tourism applications. At the end of 2017, I wrote a blog about my predictions for social media marketing trends to watch this year. Of those predictions, two dealt with virtual reality. So let's talk more about VR tourism.
A few weeks ago Nicole wrote a blog on whether travel technology was a disrupter or the new industry norm. (Spoiler alert: it's the norm.) That got me thinking about how VR has made its way into our lives- without us really being aware of it. These changes also have a large impact on how we travel.
In January, I visited One World Trade Center in New York City. It was a stunning piece of architecture- but that's not what really caught my eye. The World Trade Center provides almost 360-degree views of the city and New Jersey. There's so much to look at, it could easily be overwhelming. But the World Trade Center counteracts that by offering rentals of a very special piece of technology.
Available for rent is an iPad called the One World Explorer. Just pick a compass direction, hold it to the window, and see the names of the buildings you're looking at. Not only that, but you can also tap on select buildings and watch a short video about the history of that building and what it does now. This was an invaluable tool for myself and my family, and well worth the $15 rental fee. It enhanced the experience by telling me exactly what I was looking at.
Watch for this technology to spread in the next year. Other attractions with a view, like the CN Tower in Toronto and the Willis Tower in Chicago, would benefit from incorporating technology like this (if it isn't already in the works!).
The Museum of Natural History has gone one step further and incorporated VR into their app development. Since their Bones exhibit opened in 1881, it has remained largely the same experience- until now. They developed an app called Skin & Bones that works within their exhibit to show you what animals would have looked like when they were alive. Just hold the phone up to the case and voila! You can see what a Steller's Sea Cow looked like before it went extinct. The app also has interactive games to test your knowledge of natural history as well as educational videos.
VR tourism can also take people to places previously unimaginable- like space itself. Startup company SpaceVR is currently in the process of sending virtual reality cameras into space. Their goal is to give anyone the ability to experience space firsthand. While the project is still in testing, you can pre-order a year's worth of access to the universe for just $35. It's incredible to think there are people alive today who witnessed the launch of the first rocket and the moon landing, and we can explore the universe from our homes and our phones- thanks to VR tourism. And while I don't expect to see an uptick in room nights on the ISS, this opens a door that wasn't built even two years ago.
More platforms than ever are integrating VR, AR, or a mixture of both, called mixed reality, into their viewing platforms. Facebook did it first (of course) with their 360 photos, and now YouTube allows VR and 360 videos. You can dive with dolphins in South Wales or take in the view from the top of the Eiffel Tower– all from the comfort of your couch (or desk, if you need a brain break at work).


Any fastener attached to a wall supporting structural member.
Distortion due to changes in moisture content.
A metal disc placed under a bolt or nut.
A fitting, which conveys waste or water from a fixture or floor to pipe network.
A pipe which conveys the discharge from waste fixtures.
The treatment of walls and floors to make them impervious.
The natural level of ground water.
A gap in a perpend of a masonry wall, just above the flashing to allow any water in the cavity to drain out.


text:
Q: Why is the use of (>100) partial application? This code illustrates the use of partial application through the use of an operator section :
gt100 :: Integer -> Bool
gt100 x = x > 100

greaterThan100 :: [Integer] -> [Integer]
greaterThan100 xs = filter gt100 xs

greaterThan100_2 :: [Integer] -> [Integer]
greaterThan100_2 xs = filter (\x -> x > 100) xs

greaterThan100_3 :: [Integer] -> [Integer]
greaterThan100_3 xs = filter (>100) xs

The operator section (>100) partially applies the operator to one
of its two arguments. So the operator in this case is >
Why is this partial application as the > operator is being applied
to the entire Integer list ?
How is this different from lambda expression (\x -> x > 100) which
apparently is not partial application ?
Taken from http://www.seas.upenn.edu/~cis194/spring13/lectures/04-higher-order.html
Update :
Thanks to answers this appears clearer.
So here now is my understanding :
*Main> :t (>)
(>) :: Ord a => a -> a -> Bool

Is not applied at all as it accepts two parameters "a -> a" but they are not applied.
*Main> :t (>100)
(>100) :: (Ord a, Num a) => a -> Bool

Is partially applied as a function of type "a -> Bool" is created
*Main> :t (3>100)
(3>100) :: Bool

Is evaluated to type Bool which is the return type of operator (>) as illustrated by :t (>)

A:
Why is this partial application as the > operator is being applied to the entire Integer list ?

It is not applied to the entire list, as a whole, but to the individual elements, one by one. When the > is partially applied over 100, it creates a new function.
Prelude> :type (> 100)
(> 100) :: (Num a, Ord a) => a -> Bool

Now, the function accepts an argument and returns Bool. This function is applied to all the elements in the list by the filter function.

How is this different from lambda expression (\x -> x > 100) which apparently is not partial application ?

> is a function which needs two operands to operate. You are already passing one of them, as 100. To completely execute the function, you need one more argument. So, the function > is partially applied with 100.
In the second case, you are creating a new function which needs only one argument to execute. Once you pass that argument, your function will be executed. So, the lambda function is not applied partially.

A:
How is this [(<) 100] different from lambda expression (\x -> (<) 100 x) which apparently is not partial application? [1]

I think it is important to draw a distinction between semantic properties and syntactic properties. The two terms you suggested are semantically identical -- that is, there is no Haskell function you can write that reduces to one thing when applied to (<) 100 and reduces to a different thing when applied to (\x -> (<) 100 x).
However, partial application is a syntactic property -- that is, it is a property not of the behavior of a term but of the particular implementation chosen. (In analogous terms to my definition of a semantic property, a syntactic property is about whether you could write a Haskell function that reduces to one thing when applied to the string "(<) 100" and reduces to a different thing when applied to the string "(\x -> (<) 100 x)", which is eminently possible.) If I had to define it, I would define it this way: partial application is an application term with an arrow type. [2] Both of your terms are well-typed and have arrow types. But (<) 100 is an application term, whereas \x -> (<) 100 x is a lambda term (that has an application in its body).
As for operator sections like (100<) and (>100), it is not immediately obvious what to do with these. One choice is to simply decree that all operator sections are partial applications (or to simply decree that no operator sections are partial applications, of course). Another is to treat them as shorthand for (<) 100 and flip (>) 100, respectively, in which case we would still consider them partial applications (since they are application terms and have arrow types). [3] Yet a third is to treat them as shorthand for \x -> (<) 100 x and \x -> (>) x 100, respectively, in which case one might claim they are not partial applications.
But the distinction is, in my opinion, not too important: generally, semantic properties are more interesting and useful than merely syntactic ones.
[1] To avoid muddying the waters, I have used (<) 100 instead of (>100). We will discuss this distinction shortly.
[2] There is some question about what to do if the type is polymorphic. Let's punt on that question for now.
[3] This differs from simply decreeing that all operator sections are partial applications; consider some one-argument operator (!) and its section (100!), which we would then be treating as shorthand for (!) 100. This is an application term, but does not have an arrow in its type.

redpajama_set_name: RedPajamaStackExchange


text:
package com.ycombinator.news.dto;

import android.support.annotation.NonNull;
import android.support.annotation.Nullable;
import com.fasterxml.jackson.annotation.JsonCreator;
import com.fasterxml.jackson.annotation.JsonValue;

public class ItemId
{
    @NonNull public final Long id;

    @JsonCreator public ItemId(long id)
    {
        this.id = id;
    }

    @Override public int hashCode()
    {
        return id.hashCode();
    }

    @Override public boolean equals(@Nullable Object other)
    {
        return other instanceof ItemId
                && ((ItemId) other).id.equals(id);
    }

    @SuppressWarnings("UnusedDeclaration")
    @JsonValue Long serialise()
    {
        return id;
    }
}

redpajama_set_name: RedPajamaGithub


text:
This Pa. school suspended fewer students by using a restorative model
Sara Schneider, WESA
Fifth-graders Thomas Medley, (left), and Devin Walker study their training materials as they learn to become student leaders at Woodland Hills Intermediate in 2017. (The University of Pittsburgh)
Suspensions among 4th-6th graders are down at Woodland Hills School District. That can be attributed, in part, to a restorative practice program created by the University of Pittsburgh, according to school district administrators. The team supporting the work recently released a report reviewing the past two years of the strategy's implementation.
School staff were trained to think of discipline differently. They were asked to find out why students are disruptive rather than remove them from school. Managing behavior relies on community building and conflict resolution instead of suspensions, they found.
The approach has many names: Pittsburgh Public Schools calls it Restorative Practice. Woodland Hills uses Just Discipline, created by Pitt's Center on Race and Social Problems.
James Huguley, an assistant professor of social work, said it's all about building and repairing relationships when there's a conflict. That mediation often happens in meetings called "circles" that bring the offender and victim together.
"Oftentimes tears were shed, people hug. Because, you know, they've never really been — or haven't been — exposed enough to ways to peacefully resolve conflict," he said.
More schools nationally are using similar approaches. Huguley's team based their work on discipline reforms in Oakland, Calif., Houston, and New York City. He said there is little evidence that taking kids out of school is effective in changing behavior. Often, students of color and students with disabilities are disproportionately targeted.
"It's basically a recipe for disaster all around. The challenge is that we have not found an alternative — on a large scale — alternatives that were viable, and useful and ready to be implemented at the school level until recent years," he said.
While Huguley said no formal policy was issued reflecting a change in disciplinary practices, the message was that suspension would not be the default solution.
"The collaboration with the Just Discipline Program helped to maintain a positive learning environment and gave the staff and teachers a sense of community," intermediate principal Allison Kline said in a press release.
Individual student suspensions decreased in grades 4, 5 and 6 by 28 percent since 2017.
Pitt received a $450,000 grant from the Heinz Endowments to support programming, training and to hire a school coordinator.
This story originally appeared on WESA, which receives funding from the University of Pittsburgh.
Spotlight PA
Head of Pa.'s public university system to examine historic roots of racism in state schools
Chancellor Daniel Greenstein said he was "ashamed to admit" he had not studied how the university system has historically perpetuated racial inequity.
Long ignored, private online schools see golden opportunity in pandemic
Cyber charters get the most attention, but there's a niche world of private online academies. Could they be having a moment?
Listen 5:03
Pa.'s free pre-K program provides a meaningful math and language boost, says new study
Those results were consistent across the state, in urban and rural areas alike. And they remained evident in the second half of kindergarten.

redpajama_set_name: RedPajamaCommonCrawl


Jessica V. Jan 05 .
This restaurant serves mainly tipical plates from Colombia. The place has very nice decoration. The food is served fast and the staff are very friendly. I would recommend this place to everyone because the food is delicious.


text:
Tesla's shares drop after execs resign, video of Musk smoking marijuana circulates
By Hamza Shaban
Hamza Shaban
Technology reporter
Tesla shares plummeted Friday after two executives announced their departures from the company and video of chief executive Elon Musk smoking marijuana and drinking whiskey on a popular podcast began to circulate on social media.
The resignations of Tesla's accounting and human resources chiefs were just the latest in a string of troubles for the electric carmaker, which has been hit in recent months by several more staff exits, as well as production struggles, lawsuits and federal investigations. The turmoil comes as investors and analysts have called on the company's board to replace Musk with a more predictable chief executive, or to offload his responsibilities to a capable manager.
Musk smoked marijuana with comedian Joe Rogan at the end of a 2½-hour interview on "The Joe Rogan Experience," which featured a wide-ranging discussion on topics that included artificial intelligence, Musk's technological ambitions and personal hardship.
After discussing the artistic and engineering merits of wristwatches, Rogan brought out a blunt, telling Musk that it was a mix of tobacco and marijuana. "You ever had that?" Rogan asked, noting that Musk probably had not smoked one "because of stockholders."
"I mean, it's legal, right?" Musk asked before taking a puff. The show took place in California, where recreational marijuana consumption is legal.
The podcast episode arrived at a tumultuous moment for Tesla and Musk. Last month, Musk alarmed shareholders, among others, by announcing on Twitter that a deal to take Tesla private was all but certain, only to abandon the plan 17 days later. The abrupt U-turn on the proposal still leaves Tesla to contend with federal probes, shareholder lawsuits and whistleblower complaints sparked by the initial announcement.
The company is facing a Securities and Exchange Commission probe into whether Musk had purposely misled investors to manipulate the company's stock price and another tied to potentially misleading investors about Model 3 production problems, according to the Wall Street Journal.
Musk has also acknowledged that his intense workload of 120-hour weeks was taking a toll on his physical health, according to an emotional interview with the New York Times last month. Musk's detractors have criticized his impulsiveness and recent behavior. But even those close to him have expressed worry. Musk told the Times, "I've had friends come by who are really concerned."
Some board members have also raised the issue of Musk's use of Ambien, a prescription sedative, according to the Times. Musk said in the interview that he takes the drug to help him sleep. In a tweet last year Musk said, "A little red wine, vintage record, some Ambien . . . and magic!"
On the same day that the podcast was published, two executives announced their resignations from the company. Tesla's chief accounting officer, Dave Morton, said he was leaving after considering the level of attention Tesla has received and the "pace within the company."
"I want to be clear that I believe strongly in Tesla, its mission, and its future prospects, and I have no disagreements with Tesla's leadership or its financial reporting," he said. Morton worked for the company for only a month.
Shortly after Morton's announcement, Bloomberg reported that Tesla's "chief people officer," Gabrielle Toledano, would not return to the company after a leave of absence.
At least 48 executives have left the company this year. But Tesla has said that the departures are at a rate typical of any large company.
Tesla did not respond to requests for comment.
In a report published Friday, Musk told the Guardian that smoking marijuana is not necessarily prohibited by company rules. "Our policy allows trace amounts of THC [an ingredient of cannabis] during work times, provided they are below the safety limit (much like a minimum alcohol level)," he said, according to the report.
Carl Tobias, a law professor at the University of Richmond, said that Musk's lighting up was not normally an issue because "people do that all the time." But Musk's marijuana incident appears to follow a pattern of questionable behavior, Tobias said, and is further evidence of bad judgment. "It's troubling. It may be especially troubling for board members or shareholders," he said. "We do expect our CEOs of major companies to behave differently than ordinary people."
Earlier this week, Musk doubled down on an incendiary allegation against a British cave explorer who helped save 12 boys trapped in a flooded cavern in Thailand this summer. After the explorer criticized Musk's efforts to participate in the cave rescue, calling it a "PR stunt," Musk retaliated on Twitter. In the July tweet, he called the explorer, Vernon Unsworth, a "pedo guy." Musk later apologized for labeling Unsworth as a pedophile. But investors were rattled. Musk's critics have said that his bitter feuds with journalists, employees, rivals and others have interfered with Tesla's mission to transform the auto industry.
And, according to an email published by BuzzFeed this week, Musk has not put the cave diver incident behind him. He repeated his attacks on Unsworth in an email to a reporter, again raising questions about his decision-making and state of mind.
The long-term viability of the $50 billion automaker hinges on the success of the Model 3, a mass-market battery-powered vehicle envisioned as the pathway to Tesla's profitability. But the Model 3 had been plagued by production delays. Recent months at the company's Fremont, Calif., plant were defined by an urgent, all-hours flurry, which Musk has described as "production hell."
Tesla has not made an annual profit in 15 years, but Musk has pledged that will end in the second half of the year. After reaching a long-delayed goal in June of producing 5,000 Model 3 sedans per week, Tesla said last month that the company should be able to sustain that pace throughout the third quarter.
Tesla's stock closed down more than 6 percent Friday.
Drew Harwell contributed to this report.
Hamza Shaban Hamza Shaban is a technology reporter for The Washington Post. Previously, he covered tech policy for BuzzFeed. Follow
Today 0.2%
S&P 2,995.3
Last Updated:12:24 PM 07/19/2019


text:
NINEby9
COMMITTED TO ACHIEVING
GENDER PARITY BY 2030
FIONA MCKAY
Fiona is the CEO of the Asian Academy Creative Awards, Asia Pac's most prestigious awards for creative excellence for TV/Film. Under Fiona's guidance, the Asian Academy also runs year-round skills development programmes under its Academy Campus.
She is a highly regarded experienced media and corporate lawyer, with over 25 years of legal experience working in law firms, public listed companies, and multi-national companies and major international TV networks.
Prior to Asian Academy Creative Awards, she headed the legal department for OTT platform Viu (based in Singapore), where she managed all legal and corporate matters for Viu's operations across Singapore, Malaysia, India, Indonesia, Middle East and Myanmar.
Fiona started her legal career practicing law in a medium sized boutique law firm, after graduating from University of Malaya. Her first in-house legal career started with Star Cruises, Malaysia. Her career in media started with the largest Malaysian based TV & Radio broadcaster, Astro. She was then head hunted to be the general counsel for the Australian ASX listed global network broadband service provider, Speedcast Ltd, before joining the international TV networks, RTL CBS, as head of legal in Singapore.
Stay up to date on our research and insights
Copyright 2021 © NINEby9 Pte Ltd
NINEby9 Pte Ltd (UEN: 202117245Z) is a non-profit organisation incorporated in Singapore
as an exempt company limited by shares. All rights reserved.


Wassily Kandinsky (1866-1944) was a Russian painter who visualised musical compositions with abstract forms and colours. His intricate and dynamic works of art combined colour and spontaneous shapes. He once wrote, "Colour directly influences the soul. Colour is the keyboard, the eyes are the hammers, the soul is the piano with many strings". Credited as having painted the first pure abstract works, Kandinsky remains a pioneer of modern art.


The Pacific Northwest region spans Oregon and Washington, with a combined tidal shoreline of 4,436 miles. Commercial and recreational fishing along the outer coast, in rivers, and inland waters results in lost fishing gear, which often requires removal by professionals fishers and divers. Most marine debris washing up along the sparsely populated coast of the Pacific Northwest comes from all across the Pacific Rim, a testimony to the global nature of the marine debris problem. It is volunteer effort that removes most of this marine debris. Marine debris removal is difficult in remote and largely inaccessible coastal areas in the region, especially in the fall and winter when storms bring more debris on the beaches, yet make removal much more challenging.
NOAA Marine Debris Program partner Washed Ashore gave a webinar on February 28th on their efforts to educate about marine debris through art. Check out the recording of the webinar.
The Northwest Straits Foundation, with support from the NOAA Marine Debris Program, created five short videos to educate crabbers. The videos go over topics like setting your crab pots so they don't get lost and adding weight to your pots. Check them out!
The Northwest Straits Initiative's 10 year effort to remove derelict fishing nets from the Puget Sound will soon be complete. Read more about the project.
To learn more about Japan tsunami marine debris in this region, visit our webpage. You can also find information on Oregon Parks and Recreation Department's website and Washington Department of Ecology's website.
Now that some tsunami debris has arrived, what do you expect to happen in the future?
Tsunami debris began arriving on U.S. shores in the winter of 2011-2012 and has continued washing ashore in a scattered fashion ever since, mixing in with chronic marine debris. This pattern will likely continue. Beachgoers may notice an increase in debris on beaches, in addition to marine debris that normally washes up, depending on where ocean currents carry it.


text:
You are here > Home > Inspire Me > Birmingham Blog > New year, new openings
on Jan 02 2020
In Press & Media, Events, Blogs
New year...new openings. From restaurants to hotels, 2020 will welcome even more fabulous destinations this year, adding to Birmingham's ever-growing leisure and tourism offering. Keep your eyes peeled and discover what the city has to offer.
Paradise is the latest chapter in Birmingham's compelling history, a location rich in British heritage and charm and where the old and the new sit side by side. Delivering one of the UK's most important city centre developments and an entirely new destination, it is placemaking at its very best.
Ten brand new high-quality buildings
Three new public squares
£700m investment into the city
1.74m sq ft of contemporary office space
120,000 sq ft of retail and leisure space
550 car parking spaces
4-star hotel with 250 bedrooms and over 22 floors
Dishoom
Dishoom Birmingham will open in Spring 2020 - located in the heart of the city at One Chamberlain Square, part of Paradise Birmingham. The team, led by co-founders Shamil and Kavi Thakrar, are truly delighted to be moving into this new home, where they will enjoy the company of the city's most beautiful and historic buildings.
Executive Chef Naved Nasir's menu of Bombay comfort food will be served all day, from breakfast-time until late. Bringing together the food of all Bombay, dishes cooked in Hindu, Muslim, Irani and Parsi traditions willall jostle for space on the table, and a new chef's special will be created especially for Dishoom Birmingham (particulars forthcoming in due course). The restaurant will also have a Permit Room bar, serving Dishoom's award-winning cocktails, teetotal tipples, chai, coolers and more.
Craft English Garden
In January 2020, the team behind Craft Dining Rooms and Aktar Islam will be launching the Craft English Garden, a stunning garden terrace and inside dining room bringing a unique drinking and dining space. Located on the Canalside at the ICC alongside the critically acclaimed Craft Dining Rooms, the site will be centred around a beautifully designed bar and crafted dining pods for groups to enjoy.
Indoors will still see the best of Britsh dining being served in Craft Dining Rooms as well as spirits, ale, soft drinks and iover 100 different wines.
The new Eastside development will feature both an on-site hotel and pub linked directly to meeting and events spaces. It will sit within the heart of what's being called the 'Knowledge Quarter' - alongside Birmingham's universities. It will be walking distance from the city centre, canal network and cultural attractions making it the perfect location to access key spots in Birmingham.
The 195-room Aloft Hotel will accomodate a mixture of standard and luxury suite options with an on-site pub!
Affinity Suite
Eastside's main venue space will be the city's largest pillar free banqueting space, capable of seating upto 1200 delegates. It features its own welcome reception, state of the art AV and technical capabilities and floor to ceiling dividers that can slice the room in two.
Attrium & Belmont Suite
Outside of the Affinity Suite there is breakout capacity capable of housing the 1,200 delegates that can fit into the main space.
The first of which is the Belmont Suite, itself capable of hosting up to 400 delegates, and with similar roof to floor dividers that can turn it into four separate rooms. The Belmont Suite also sits within a larger atrium, which floods the space with natural light and makes for an easy business networking and relaxation area.
The eastside rooms also has a number of smaller meetings and events spaces, hosted on floors one and two of the venue, all with their own dedicated reception and food and beverage servicing areas.
Opening January 2020, Moxy Birmingham NEC will be filled with stylish nods to the music industry displayed through its interior design. The hotel is located at the heart of the NEC and within walking distance of Resorts World and Resorts World Arena. Expect an affordable boutique hotel with spacious, cosy rooms, 42" LCD Tvs and free Wi-Fi throughout your stay.
Nobody has commented on this post yet, why not send us your thoughts and be the first?
Attractions(19)
Blogs(51)
By train(5)
Canals(2)
Cricket World Cup(12)
History(1)
Parks & Countryside(3)
Press & Media(89)
Theatre & Performance(2)
Sept 2019(8)
Feb 2019(7)


Intricately engraved guns honoring states and cities across america.
Centennial Classic Arms is proud to announce the production of the Kan..
Centennial Classic Arms is proud to announce the production of the Texas&nb..
Centennial Classic Arms is proud to announce the production of the Wyoming ..
Join us as we celebrate the Golden Anniversary of Alaska's Statehood. Our S..
Kansas Statehood Sesquicentennial Only 150 Kansas Statehood Layaway is av..
Special Edition Marlin 1895 High Grade Stainless Steel For Blued Ver..
Ruger Vaquero For 125 years the hard working people of Wyoming hav..
Special Edition Marlin 1895 Blued For Stainless Steel Version Click ..


Deeply missed by her loving daughters Sonia Olivier of Texas – Skomman Consulting Group, Inc.
hermes blanket replica Greenwood, Eldon T. Age 88 of Shakopee. Eldon was a loved son, husband, father, grandfather, great grandfather, uncle and friend. Living to the amazing age of 96, she was predeceased by her parents, siblings John, Stella and Mary, her nephew Richard, as well as her husband Wasyl. Remembering her fondly are her two sons Mark of Toronto and Boris (wife Irene) of Sudbury, as well as nephews Bob of British Hermes Replica Belt Columbia and Ron and Barry hermes belt replica aaa of Alberta and second nephew Russell of Michigan. She was always a deeply caring wife and special mother, and throughout her many years, when not at her best in the kitchen cooking and Hermes Birkin Replica baking especially the greatest cinnamon buns ever to Hermes Handbags come out of the oven, enjoyed all the time she could spend with family and friends, sometimes playing card games, but always in conversation hermes blanket replica.


text:
TV program. Eddy Mitchell and Laurent Gerra reunited on C8, do we skip or watch?
The evening will open with the song "C'est un rocker". C8 is broadcasting this Saturday evening "On credit and in stereo", an evening filmed on May 27, 2021 at the Théâtre du Gymnase, in Paris, and broadcast live on Facebook. Singer Eddy Mitchell, comedian Laurent Gerra and comedian Chicandier alternate songs, accompanied by nine musicians, and moments of fun.
About twenty songs will be performed, including Eddy Mitchell's must-haves: "Mint-colored eyes in the water", "No boogie-woogie", "Lèche-botte blues", "Nashville ou Belleville", "The last session "," The elephant cemetery ", and of course" On credit and in stereo ".
Laurent Gerra will imitate a dozen personalities
But other famous singers or personalities will invite themselves in the evening thanks to the talent of imitator of Laurent Gerra. Enrico Macias, Patrick Bruel, Renaud, Francis Cabrel and Serge Gainsbourg will thus come to push the song.
Other songs, such as "The country where I come from" and "Je reviens te rire" by Gilbert Bécaud, "Les bals populaire" by Michel Sardou, or even "Vieille canaille" by Serge Gainsbourg, will be performed at the occasion of the imitations of Laurent Gerra.
Jokes about Covid and vaccination
Between two titles, the imitator will have fun interpreting other personalities such as Fabrice Lucchini, Jean-Pierre Foucault, or even François Hollande. With registration taking place in May, the jokes about the Covid, vaccination and bar closings will be rife. When we know that the slight lull of summer has given way to a new wave in recent months, we could laugh yellow in front of the television.
The three men exchange frank laughs and crazy moments, in good humor from start to finish. We still regret a few beautiful jokes that go on forever, and the recurring theme (even if it is of the second degree) of "it was better before".
"Laurent Gerra and Eddy Mitchell on credit and in stereo", Saturday January 8 at 9:05 pm on C8.
PrevMan arrested after finding dead woman in Lier
NextThe syringe suppresses the psychosis for a period of time. More and more people are being forced into mental health care.


Do you have an important event that you need to keep in mind while working on your project? Or perhaps there are particular due dates or submission deadlines? To help you stay on target to meeting your overall job deadlines, the milestone feature in WorkflowMax will ensure you're always ahead of the game.
The milestone dates that you set up for a job are completely separate to the tasks or job start and finish dates. They can be added when you're setting up a job, as part of a job template, or at any time during the duration of a job as they pop up.
For example, you might have a date that your first draft is due, or you may need to contact a supplier by a certain date in order to schedule in their services for the project, or you may need sign-off from your client on the first stage of the job by a certain deadline. These milestones can be seen by those working on the job, and also, if you choose to, you can make this visible to clients using the client login by selecting 'public' when you set up a new milestone.
In the video below, we take you through the steps you need to know to add, edit, and manage milestones, as well as understand the notifications which can be assigned to a milestone.


Mon- Sun 08:30am to 6 pm.
Karma Group operates and/or has under development 29 properties located in Australia, Bahamas, Brazil, France, Germany, Greece, India, Indonesia, Japan, Philippines, Thailand, UK and Vietnam.
Karma Group is an award-winning international travel and lifestyle brand offering extraordinary experiences and exclusive curated entertainment in the world's most beautiful locations. Karma Group operates and/or has under development 29 properties located in Australia, Bahamas, Brazil, France, Germany, Greece, India, Indonesia, Japan, Philippines, Thailand, UK and Vietnam.


Lines, connectors, arrows, transitions - these are the glue that hold diagrams together. Styling your connectors will help make your diagrams more readable, and that's easy to do in draw.io!
Sometimes you don't want to connect to any particular connection point, but to the edge of a shape. And perhaps you want one end of a connector to move and the other to stay in one position. There are two types of connections, indicated with blue and green frames in draw.io.
If you draw additional lines between shapes in a diagram, they won't move with your shapes when you move them around the drawing area. By using actual connectors (not lines), your diagram becomes much more flexible and easy to work with. There are four different ways you can create connectors between shapes and quickly extend your diagrams in draw.io.


text:
Switzerland and Bulgaria
Living in Bulgaria
Embassy of Switzerland in Bulgaria
Swiss Contribution Office Sofia
Coordinates funding and projects on the ground
All consular services and visa issues are provided by the Regional Consular Centre South-eastern Europe in Bucharest/Romania.
Travel advice for Bulgaria
Contact the Regional Consular Centre South-East Europe in Bucharest when you want to register or unregister as a resident, when you need a new pass, have moved or wish to apply for citizenship. The entire selection of services offered can be found in the dropdown to the right.
Bilateral relations Switzerland–Bulgaria
Projects in Bulgaria
Switzerland supports 15 projects in Bulgaria with its EU enlargement contribution
Bilateral Framework Agreement with Bulgaria
Switzerland has concluded a bilateral framework agreement with Bulgaria. Switzerland decides in consultation with Bulgaria and independently of the EU which projects it will support.
News, highlights and information on the projects in Bulgaria
Thematic Funds in Bulgaria
In Bulgaria the SDC is working with thematic funds in the areas of public security, the participation of civil society and integration of the Roma and other minorities.
Results in Bulgaria
Switzerland uses its enlargement contribution to promote vocational education and training in an effort to reduce youth unemployment, enable care for the elderly following the Swiss Spitex model and ensure that old pesticides are disposed of in an environmentally friendly way.
The Swiss Abroad Act governs the fundamental rights and obligations of Swiss nationals living abroad. It also defines a variety of services that Switzerland can offer its citizens who are living and/or working abroad permanently or temporarily.
Pursuant to the Swiss Abroad Act, Swiss nationals living abroad are Swiss citizens who are not domiciled in Switzerland and are registered with their competent representation.
The Swiss Abroad Act governs support from the Confederation for institutions related to Swiss nationals living abroad.
Swiss nationals living abroad can apply for social welfare, subject to certain conditions. They can also exercise various political rights that are specified in the Swiss Abroad Act.
Registration within 90 days
Within 90 days of relinquishing domicile in Switzerland, Swiss citizens aged 18 or over must register with the representation responsible for their new place of residence. Individuals who, on the one hand, have acquired Swiss citizenship through birth abroad and, on the other, reached the age of 18 abroad can register with a representation to avoid losing their citizenship.
Consular protection
The Swiss Abroad Act governs consular protection for Swiss nationals abroad who require emergency assistance or are situated in a crisis or disaster area. It specifies the assistance that is provided to Swiss nationals domiciled in Switzerland and, to a certain extent, to Swiss nationals living abroad.
Consular protection is also available to legal entities, subject to certain conditions. However, there is no legal entitlement to consular protection. Cases are always assessed on an individual basis.
The Swiss Abroad Act governs additional consular services of which Swiss nationals living abroad make particular use, e.g. authentication of documents and confirmations.
Services based on other federal acts
Some services are prescribed in other federal acts. For example, the Federal Act on Identity Documents for Swiss Nationals governs the issue of passports abroad.
Numerous other federal acts and ordinances also include provisions on the rights and obligations of Swiss nationals abroad, which is why such pieces of legislation are also worth consulting, e.g.:
The Ordinance on Voluntary Old-Age, Survivors' and Disability Insurance
This piece of legislation only governs the insurance scheme of the same name, which Swiss nationals domiciled outside the EU and EFTA can join, subject to certain conditions.
Ordinance on Voluntary Old-Age, Survivors' and Disability Insurance
The Ordinance on Military Administration, chapter 5
This piece of legislation governs the exemption from military service while abroad of individuals who are subject to the notification obligation in accordance with the Military Act.
Ordinance on Military Administration
Bilateral and multilateral agreements
In certain circumstances, the rights and obligations of Swiss nationals abroad are ultimately also determined on the basis of applicable bilateral and multilateral agreements. The 1999 Agreement on the Free Movement of Persons between Switzerland and the EU is of relevance for many Swiss nationals living abroad.
Agreement between the European Community and its Member States, of the one part, and the Swiss Confederation, of the other, on the free movement of persons


This nicoise salad can be meal prepped two ways: in a mason jar or a meal prep container. It's filling, flavorful and loaded with protein but is still light and easy to digest. Don't skip the fresh dill! Gluten-free.
We made it to Friday! Day 5 of Salad Week! I have loved seeing all of your mason jar salads. Seriously, I do a little happy dance every time you post one of my recipes! Thanks for making my day (and week)! Keep tagging me @eatingbirdfood and hashtagging #saladeveryday.
For some reason, I've always thought nicoise salads sounded so fancy. Maybe it's because I never took French (I was a Spanish girl), or maybe it's because I still question whether I'm pronouncing it correctly every time I say it. Either way, I'm always game for anything that makes me feel fancy but is actually super simple. You with me?
This salad screams spring and summer to me. The veggies are so refreshing and the tuna gives it plenty of protein but still keeps it nice and light. I can't wait to pack up this salad for a bike ride or park day with Isaac!
I also have to note that you can't skip the fresh dill because it takes this nicoise salad to the next level. Although, I'll be honest — I think fresh dill takes all salads to the next level! We literally just planted a little herb garden with dill on our back deck, so you can expect to see lots of dill action on the blog this summer!
How did this salad challenge go for you? Are you on the #saladeveryday train? Who's going to keep up with this habit over the next few months? I know I'll be doing it all summer because I truly love the way it makes me feel and it totally simplifies my healthy eating routine.
I'm so excited because I'm currently working on a new salad-focused program you can use any time you feel like you need a reset — maybe after an indulgent vacation or weekend, before a big event or just any time you want to get back on track with healthy eating. I'm still building out the content for the program and testing it out on myself so I'll be sharing more details soon! Can't wait.
Spread chopped sweet potatoes on a baking sheet with 1 teaspoon of oil. Toss and then roast for about 20-30 minutes or until tender. Note: you can also steam the sweet potatoes if you'd like!
While the potatoes are roasting, set a steamer basket insert into a large saucepan and fill with water just below the steamer. Bring to a boil. Add green beans and asparagus, and steam for approximately 5 minutes (or until desired level of tenderness). Let all the veggies cool.
For a mason jar: Add 2-3 Tablespoons of dressing into a large, wide-mouth mason jar, then start layering ingredients in this order: olives, green beans, asparagus, sweet potatoes, tomatoes, canned tuna, arugula, hard-boiled egg, dill.
For a meal prep container: Line bottom of container with arugula and layer all ingredients in columns/sections on top. Store dressing in a separate container.