text:
\section{Introduction}
\vspace{-0.05in}
Growing healthcare costs have drawn significant attention to the healthcare delivery system and its fragile and fragmented nature.  Similarly, the growing burden of illness has also directed attention to addressing patients' health needs.  The consequences of the growing burden of illness compounded by an increasingly expensive healthcare delivery system places grave consequences on our economy and way of life.

Efforts to affect positive change requires an understanding of the complex dynamics of healthcare delivery systems and patients' health.  Most modeling focuses on either the 1.) \emph{healthcare delivery system} that renders patients without state as they are pushed and pulled through the system (e.g., a patient with an acute condition in an ER) or 2.) \emph{patient health} without any consideration of its interface with the healthcare delivery system.  In order to develop a dynamic system model of a personalized healthcare delivery system in which individual health outcomes are managed, these two processes need to be linked.

\vspace{-0.2in}
\subsection{Dynamic Modeling of Healthcare Delivery Systems}
\vspace{-0.05in}
Efforts to quantitatively and dynamically model the healthcare delivery system originate from the field of production systems \cite{Zhong:2017:00}.  Production system modeling focuses on transporting operand-products one from location to another in the system.  The analogous extension to healthcare delivery system as a type of production system treats the patient as an operand-product as well.  In doing so, operand throughput and system efficiency in terms of cost and time can be quantitatively assessed and maximized.

Consequently, a large body of healthcare literature summarizes safety \cite{saxena2017design, Carayon:2006:00}, resource management \cite{Fanti:2013:00}, capacity planning \cite{Garg:2012:00, Green:2005:00}, and scheduling of various types including for outpatients\cite{Wang:2012:00, Cayirli:2003:00,Rose:2011:00, kim2006stochastic}, clinicians\cite{Cheang:2003:00, Burke:2004:00, Ernst:2004:00}, operating room\cite{Cardoen:2010:00, Erdogan:2011:00, Guerriero:2011:00}), work flow processes \cite{Zhong:2016:00, Combi:2014:BPA,wang2012emergency, chan2015quick} and patient-flows\cite{Hall:2006:00}.

Healthcare is well-suited to apply production modeling methods for patients with acute conditions.  The focus is on addressing the urgency of the patient's health state by quickly transporting the patient through the healthcare delivery system before the patient falls into more serious diagnoses.  Such modeling assumes that the operand's state can be described by its position in the system in much the same way a product's state can be inferred based upon its relative position in a production system.

Chronic conditions, however, have a much longer \emph{time-scale} and require a different approach.
Moving patients through the healthcare delivery system efficiently (i.e., faster) does not address disease understanding or affect long-term disease course.  For example, addressing pain for a patient with a chronic condition (e.g., rheumatoid arthritis, fibromyalgia, cancer), may prevent recurring emergency department visits all-together and consequently modeling transportation during these visits is entirely superfluous.  Processing the acute visit and moving the patient through the ER faster, however,  does not address the need for long-term pain care.  Understanding health state and factors affecting health status, be they physical or social determinants of health (e.g., socioeconomic status, physical environment, social support) \cite{WHO:2008:00}, is critical when understanding an individual's interaction with the healthcare delivery system.  Given that chronic conditions now account for 78\% of healthcare delivery system expenditures\cite{Anderson2004b}, it is most important that modeling efforts focus on the most essential features of chronic care.

\vspace{-0.15in}
\subsection{Dynamic Modeling of Health}

Health has been modeled at many levels of granularity; from the cell level to the disease level.  The field of systems biology focuses on continuous-time modeling at a cellular scale of bio-physical-chemical processes\cite{Kitano2001, Kitano2002}.  In contrast, clinical medicine generally focuses on discrete modeling of diseases(e.g., diabetes \cite{Palmer:2004:00}, cancer \cite{Newton:2012:00}).

\vspace{-0.15in}
\subsection{Paper Contribution}
This paper develops the dynamics for a system model for personalized healthcare delivery and managed individual health outcomes.  It utilizes a hetero-functional graph theory \cite{Schoonenberg:2017:ISC-BKR01} rooted in Axiomatic Design for Large Flexible Engineering Systems and Petri nets.  The dynamics of the model builds upon the developed systems architecture for healthcare delivery in \cite{Khayal:2017:HHS-J17}
which bears several analogies to the architecture of mass-customized production systems.  At its essence, the model consists of two synchronized Petri nets; one for the healthcare delivery system and another for indviduals' health state evolution.    The model applies equally to the care of both acute and chronic conditions, transparently describes health outcomes and links them to the evolution of the healthcare delivery system and its associated costs.

\vspace{-0.15in}
\subsection{Paper Outline}
The model's development rests upon a previously established architectural foundation\cite{Khayal:2017:HHS-J17}.  Section \ref{Sec:Background} presents the essential definitions and concepts from this foundation so that Section \ref{Sec:DynamicModel} may develop a conceptually consistent dynamic model.  Two illustrative examples are presented to demonstrate applicability to both acute care in Section \ref{Sec:ExampleAcute}, and chronic care in Section \ref{Sec:Example}.  Next, the discussion is presented in Section \ref{Sec:Discussion} and, finally, the conclusion in Section \ref{Sec:Conclusion}.  The work assumes prerequisite knowledge in model-based systems engineering \cite{Buede2011, Crawley2015, Weilkiens2011, Friedenthal2014}, graph theory \cite{Newman2010, VanSteen2010}, and discrete-event simulation \cite{Cassandras2008} which is otherwise gained from the cited texts.

\vspace{-0.1in}
\section{Background: Preliminaries}\label{Sec:Background}
The development of the dynamic model in Section \ref{Sec:DynamicModel} rests upon the recently developed architecture for personalized healthcare delivery and managed individual health outcomes.
That work drew upon a hetero-functional graph theory \cite{Schoonenberg:2017:ISC-BKR01} rooted in the Axiomatic Design for Large Flexible Engineering Systems and Petri nets.  The healthcare delivery system form is described by its resources in Section \ref{SystemForm}, and its system function is described by processes in Section \ref{SystemFunction}.  The processes are allocated to resources in the system concept as described by the system knowledge base in Section \ref{Concept-System}.
\vspace{-0.1in}
\subsection{System Form} \label{SystemForm}
The healthcare delivery system is composed of resources representing system form.  Four types of resources $\mathbb{R}=\mathbb{R}_F \cup \mathbb{R}_D \cup \mathbb{R}_M \cup \mathbb{R}_N$ have been defined \cite{Khayal:2017:HHS-J17}
:
\begin{defn}
\textbf{Transformation Resource}\cite{Khayal:2017:HHS-J17}:  A resource $\mathbb{r}_F \in \mathbb{R}_F$ capable of a transformative effect on its operand (e.g. the health state of an individual). They are the set union of human and technical transformation resources, $\mathbb{R}_F =  R_F \cup \mathscr{R}_F$.
\end{defn}
\begin{defn}
\textbf{Decision Resource}\cite{Khayal:2017:HHS-J17}:  A resource $\mathbb{r}_D \in \mathbb{R}_D$ capable of advising the operand, an individual, on how to proceed next with the healthcare delivery system.
They are the set union of human and technical decision resources, $ \mathbb{R}_D=R_D \cup \mathscr{R}_D$.
\end{defn}
\begin{defn}
\textbf{Measurement Resource}\cite{Khayal:2017:HHS-J17}: A resource $\mathbb{r}_M \in \mathbb{R}_M$ capable of measuring the operand: here the health state of an individual.  They are the set union of human and technical measurement resources, $\mathbb{R}_M =  R_M \cup \mathscr{R}_M$.
\end{defn}
\begin{defn}
\textbf{Transportation Resource}\cite{Khayal:2017:HHS-J17}:   A resource $\mathbb{r}_N \in \mathbb{R}_N$ capable of transporting its operand:  the individual themself.  They are the set union of human and technical transportation resources, $\mathbb{R}_N =  R_N \cup \mathscr{R}_N$. \\
\end{defn}

\vspace{-0.2in}
\begin{defn} \label{Def:RBuffer}
\textbf{Buffer Resource}\cite{Khayal:2017:HHS-J17}:  A resource $r \in \mathbb{R}_B$, denoting specified locations as a set union of transformation, measurement and decision resources,
where $\mathbb{R}_B=\mathbb{R}_F  \cup \mathbb{R}_D \cup \mathbb{R}_M$.
\end{defn}

In the cases where a specific resource is capable of performing several processes, it is must be uniquely classified, such that if $r \in R$ can \emph{Transform}; then $r \in R_F$, then if $r \in R$ can \emph{Decide}; then $r \in R_D$, then if $r \in R$ can \emph{Measure}; then $r \in R_M$, otherwise $r \in R_N$ and $\mathscr{r} \in \mathscr{R_N}$ .

\vspace{-0.1in}
\subsection{System Function} \label{SystemFunction}
The healthcare delivery system is composed of processes $P=P_F \cup P_D \cup P_M \cup P_N$ representing the system function.  Four types of processes have been defined \cite{Khayal:2017:HHS-J17}
:
\begin{defn}
\textbf{Transformation Process}:  A \emph{physical} process $p_{F} \in P_{F}$ that transforms the operand: specifically the internal health state of the individual (i.e. treatment of condition, disease or disorder).
\end{defn}
\begin{defn}
\textbf{Decision Process}:  A \emph{cyber-physical} process $p_{D} \in P_D$ occurring between a healthcare system resource and the operand:  the individual, that generates a decision on how to proceed next with the healthcare delivery system.
\end{defn}
\begin{defn}
\textbf{Measurement Process}:  A \emph{cyber-physical} process $p_{M} \in P_M$ that converts a physical property of the operand into a cyber, informatic property to ascertain health state of the individual.
\end{defn}
\begin{defn}
\textbf{Transportation Process}:  A \emph{physical} process  $p_{N} \in P_{N}$ that moves individuals between healthcare resources (e.g. bring individual to emergency department, move individual from operating to recovery room).\\

 \end{defn}
 \vspace{-0.2in}
\begin{defn}
\textbf{Non-Transportation Process}:  A combination of non-transportation processes representing transformation, decision and measurement process, $p_{B} \in P_{B}$ that is a set union of non-transportation processes, where $P_{B} = P_{F} \cup P_{D} \cup P_{M}$.
\end{defn}

\vspace{-0.2in}
\subsection{System Concept}
\label{Concept-System}
The system concept is defined as an allocated architecture composed of a bipartite graph between system processes and resources, that can be mathematically described as \cite{Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IES-J19,Farid:2013:IEM-C30,Farid:2015:IEM-J23,Schoonenberg:2016:TES-JR06}, $P=J_S\odot \mathbb{R}$,
where $J_S$ is the system knowledge base and $\odot$ is boolean multiplication.
\begin{defn}
\textbf{System Knowledge Base} \cite{Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IES-J19,Farid:2013:IEM-C30,Farid:2015:IEM-J23,Schoonenberg:2016:TES-JR06}: A binary matrix $J_S$ of size $\sigma(P)\times\sigma(\mathbb{R})$ whose element $J_S(w,v)\in\{0,1\}$ is equal to one when event $e_{wv} \in {\cal E_S}$ (in the discrete event systems sense \cite{Cassandras2008}) exists as a system process $p_w \in P$ being executed by a resource $r_v \in \mathbb{R}$.
\end{defn}
\noindent The healthcare delivery system knowledge base $J_S$ represents the elemental capabilities that \emph{exist} within the system.  These capabilities may not always be \emph{available} and therefore such constraints can be described in a similar structure called the system events constraints matrix.
\begin{defn}
\textbf{System Events Constraints Matrix}\cite{Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IES-J19,Farid:2013:IEM-C30,Farid:2015:IEM-J23,Schoonenberg:2016:TES-JR06}:  A binary matrix $K_S$ of size $\sigma(P)\times\sigma(\mathbb{R})$ whose element $K_S(w,v)\in\{0,1\}$ is equal to one when a constraint eliminates event $e_{wv}$ from the event set.
\end{defn}
The construction of $J_S$ and $K_S$ allow for the construction of a \emph{system concept matrix} $A_S$ describing the independent actions defining the available capabilities in the system \cite{Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IES-J19,Farid:2013:IEM-C30,Farid:2015:IEM-J23,Schoonenberg:2016:TES-JR06}, $A_S=J_S \ominus K_S$,
where $\ominus$ is Boolean subtraction.
The enumeration of these independent actions defines the healthcare system's structural degrees of freedom.
\begin{defn}
\textbf{Structural Degrees of Freedom}\cite{Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IES-J19,Farid:2013:IEM-C30,Farid:2015:IEM-J23,Schoonenberg:2016:TES-JR06}: The set of independent actions $\psi_i \in {\cal E_S}$ that completely defines the available processes in the system. It is given by:
\begin{align}\label{Eq:DOFS}
DOF_S=\sigma({\cal E}_S)&=\sum_w^{\sigma(P)}\sum_v^{\sigma(\mathbb{R})}A_S(w,v)
\end{align}
\end{defn}
\noindent From an architectural perspective, the structural degrees of freedom form the nodes of a hetero-functional network\cite{Farid:2016:IES-BC06, Farid:2015:IES-J19} that describes the structure of the healthcare delivery system.

It is often useful to vectorize the knowledge base, where the shorthand $()^V$ is used to replace vec(). A projection operator may be introduced to project the vectorized knowledge base onto a one's vector to eliminate sparsity. $\mathds{P}(A_S)^V=\mathds{1}^{\sigma{(\cal{E_S})}}$
such that \cite{Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IES-J19,Farid:2013:IEM-C30,Farid:2015:IEM-J23,Schoonenberg:2016:TES-JR06}:
\begin{equation}\label{Eq:ProjMat}
\begin{array}{c}
\mathds{P} \\
\end{array}=
\left[\begin{array}{c}
e_{\psi_1}^{\sigma{(\cal{E_S})}}, \dots, e_{\psi_{\sigma{(\cal{E_S})}}}^{\sigma{(\cal{E_S})}} \\
\end{array}
\right]
\end{equation}
where $e_{\psi_1}^{\sigma{(\cal{E_S})}}$ is the $\psi_{i}^{th}$ elementary row vector corresponding to the first up to the last structural degree of freedom.

\noindent In summary, the variables in the healthcare delivery structural system model are summarized in Table \ref{Ta:SummaryBkgd}.
\vspace{-0.2in}
\begin{table}[h]
\caption{Healthcare Delivery Structural System Model Variables} \label{Ta:SummaryBkgd}
\vspace{-0.15in}
\begin{center}
\begin{tabular}{r l l}
\toprule
\multicolumn{1}{l}{\textbf{SYSTEM}} & \textbf{PERSONALIZED HEALTHCARE} \\
   & \textbf{DELIVERY SYSTEM} \\\toprule
\multicolumn{1}{l}{{\textbf{(A) System Form}}}  &  \\
	Resources & buffer($R_B$)[transformation($R_F$) $\cup$  \\
	&decision($R_D$) $\cup$ measurement($R_M$)] $\cup$ \\
        & transportation($R_N$) \\\midrule
	Resource Classification  & transform>decide>measure>transportation  \\\midrule
\multicolumn{1}{l}{\textbf{(B) System Function}}  & \\
        Processes & transformation($P_F$) $\cup$ decision($P_D$) $\cup$ \\
	& measurement($P_M$) $\cup$ transportation($P_N$)\\\midrule
\multicolumn{1}{l}{ \textbf{(C) System Context}} & \\
   	System Knowledge Base & $J_S$ = $ \begin{bmatrix} J_{F} & 0 & 0 & 0\\  J_{FD} & J_{D} & 0 & 0\\  J_{FM}  & J_{DM} & J_{M} &  0\\  J_{FN} & J_{DN} & J_{MN} & J_{N}\\ \end{bmatrix}$   \\\midrule
  	System Constraint Matrix & $K_S$ = $ \begin{bmatrix} K_{F} & 0 & 0 & 0\\  K_{FD} & K_{D} & 0 & 0\\  K_{FM}  & K_{DM} & K_{M} &  0\\  K_{FN} & K_{DN} & K_{MN} & K_{N}\\ \end{bmatrix}$   \\\midrule
	System Availability Matrix & $A_S=J_S \ominus K_S$ \\\midrule
	Structural Degrees & $DOF_S=\displaystyle\sigma({\cal E}_S)=\sum_w^{\sigma(P)}\sum_v^{\sigma(\mathbb{R})}A_S(w,v)$ \\
	of Freedom & \\
\bottomrule
\end{tabular}
\end{center}
\end{table}

\section{Dynamic Model Development} \label{Sec:DynamicModel}
The structural model presented in the previous section provides a skeleton upon which to develop the dynamic model in this section.  Because healthcare delivery systems are spatially distributed and evolve with discrete-event dynamics, the dynamic model utilizes Petri nets \cite{Cassandras2008}.  Two types are needed.  The first is called the \emph{Healthcare Delivery System Petri Net}.  It describes the evolution of the system processes and resources of the healthcare delivery system in Section \ref{Sec:DynamicsHDS}.  Section \ref{Sec:ChronicCare} then refines this default model to the care of chronic conditions.  The second Petri net is called the \emph{Health Net}.  It describes the `clinical' health state evolution of individuals  in Section \ref{Sec:DynamicsIndividual}.  As discussed in detail previously \cite{Khayal:2017:HHS-J15}, although the human body's health state evolves continuously via biological processes, the practice of clinical medicine discretizes this evolution into discrete states so as to facilitate diagnosis and decision-making.   With these two Petri nets in place, their respective dynamics are synchronized in Section \ref{Sec:DynamicsSync}.

\vspace{-0.2in}
\subsection{Healthcare Delivery System Dynamics} \label{Sec:DynamicsHDS}
The healthcare delivery system dynamics are described by a timed Petri net.
\begin{defn}
\textbf{Healthcare Delivery System Petri Net:} A bipartite directed graph represented as a 6-tuple:
\begin{equation}\label{Eq:SystemNet}
N= \{S, {\cal E}, {\cal M}, W, D, Q\}
\end{equation}
where:
\begin{itemize}
\item ${N}$ is the Healthcare Delivery System net.
\item $S$ is the set of places (or buffers) of size $\sigma{(\mathbb{R}_B)}$.
\item $\cal E$ is the set of transitions/events of size $\sigma{(\cal{E_S})}$.
\item $\cal M$ $\subseteq (S \times {\cal E}) \cup ({\cal E} \times S)$ is the set of arcs of size $\sigma{(\cal M)}$ from places to transitions and from transitions to places.
\item $W:$ ${\cal M} \rightarrow \{0,1\}$ is the weighting function on arcs.
\item $D$ is the set of transition durations.
\item $Q$ is a discrete state marking vector of size $\left(\sigma(\mathbb{R}_B) + \sigma(\cal{E_S})\right) \times \mathrm{1} \in \mathds{N}^{{\sigma{(\mathbb{R}_B)}}+\sigma(\cal{E_S})}$.
\end{itemize}
\end{defn}

In the model, there is exactly one \emph{place} for each healthcare system buffer.  As many healthcare systems may have hundreds or thousands of healthcare system buffers, it is often useful to form aggregated resources $\mathbb{\bar{R}}$\cite{Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IEM-J23,Khayal:2015:IES-J20}.
\begin{equation}\label{Eq:DPAgg}
\mathbb{\bar{R}}=A_R\circledast \mathbb{R}
\end{equation}
where $\circledast$ is an aggregation operator and $A_R$ is an aggregation matrix\cite{Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IEM-J23,Khayal:2015:IES-J20} and $A_R(i,j)$=1 iff $\mathbb{R}_j \in \mathbb{\bar{R}}_i$.  For example, a human resource such as a surgeon must be aggregated with a technical resource such as an operating room in order to make a functional surgical theatre.

In the model, there is exactly one \emph{transition} for every structural degree of freedom in the system.  This allows for all the capabilities of the healthcare delivery system to be potentially engaged by the patient population.  It is also important to note that the healthcare delivery system knowledge base can show process redundancies where a given process can be performed by multiple resources.   This critical distinction allows two different transitions to be fired and achieve the same process but engage entirely different resources at entirely different cost.   For example, the process of `perform skin suturing' performed by the resource `resident' vs. `plastic surgeon' have different costs associated with each transition.

The (directed) \emph{arcs} of the Petri net graph and their weightings define the Petri net incidence matrix ${\cal M}$.
\begin{defn}
\textbf{Petri Net Incidence Matrix} \cite{Farid2015}:  An incidence matrix $\cal M$ of size $\sigma{(\mathbb{R}_B)} \times \sigma{(\cal{E_S})}$ where:
\begin{equation}
{\cal M} = {\cal M}^+ - {\cal M}^-
\end{equation}
where ${\cal M}^+ (y,\psi) =  $w$(\epsilon_{wv}, r_y) $ and ${\cal M}^-(y,\psi)= $w$(r_y, \epsilon_{wv})$ and $\psi$ is a unique index mapped from the ordered pair $(w,v)$.
\end{defn}
\noindent The incidence out and incidence in matrices (${\cal M}^-$ and ${\cal M}^+$) form the negative and positive components of the Petri net incidence matrix respectively.   The incidence out matrix may be calculated straightforwardly \cite{Schoonenberg:2016:TES-JR06}.

\begin{align}\label{Eq:IncOutMat}
{\cal M}^-=\sum_{y1=1}^{\sigma(\mathbb{R}_{B})}&e_{y1}^{\sigma(\mathbb{R}_{B})}\left[\mathds{P}\left(X_{y_1}^-\right)^V\right]^T
\end{align}
where,
\begin{align}
X_{y_1}^-=\left[\begin{array}{ccc}
\mathds{1}^{\sigma(P_B)}e_{y1}^{\sigma(\mathbb{R}_{B})T} & | & \mathbf{0}^{\sigma(P_B) \times \sigma({\mathbb{R}_N})} \\\hline
e_{y1}^{\sigma(\mathbb{R}_{B})} & \otimes \mathds{1}^{\sigma(\mathbb{R}_{B})} & \otimes \mathds{1}^{\sigma(\mathbb{R})T} \\
\end{array}\right]
\end{align}
\noindent Equation \ref{Eq:IncOutMat} states that the incidence matrix is the linear superposition of $\sigma(\mathbb{R}_{B})$ matrices each associated with a given Petri net buffer $r_{y1}$.  For a given buffer $r_{y1}$, the outer product serves to link it to its associated structural degree of freedom or equivalently a Petri net transition.   Note that the matrix $X_{y_1}^-$ has the same size and structure as the system knowledge base $J_S$ and when projected by $\mathds{P}$ (in Equation \ref{Eq:ProjMat}) serves to select out the elements aligned with the structural degrees of freedom.  Finally, the $X_{y_1}^-$ matrix simply places filled elements at the structural degrees of freedom that 1.) occur at $r_{y1}$ and 2.) have $r_{y1}$ as its origin.  The incidence in matrix may be calculated analogously \cite{Schoonenberg:2016:TES-JR06}.

\begin{align}
{\cal M}^+=\sum_{y2=1}^{\sigma(\mathbb{R}_{B})}&e_{y2}^{\sigma(\mathbb{R}_{B})}\left[\mathds{P}\left(X_{y_2}^+\right)^V\right]^T
\end{align}
where,
\begin{align}
X_{y_2}^+=\left[\begin{array}{ccc}
\mathds{1}^{\sigma(P_B)}e_{y2}^{\sigma(\mathbb{R}_{B})T} & | &\mathbf{0}^{\sigma(P_B) \times \sigma({\mathbb{R}_N})}  \\\hline
\mathds{1}^{\sigma(\mathbb{R}_B)} & \otimes e_{y2}^{\sigma(\mathbb{R}_B)} &\otimes  \mathds{1}^{\sigma(\mathbb{R})T}\\
\end{array}\right]
\end{align}

The Petri net structure leads directly to the definition of its timed discrete-event dynamics.
\begin{defn}
\textbf{Timed Petri Net (Discrete-Event) Dynamics} \cite{Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IES-J19,Farid:2013:IEM-C30,Farid:2015:IEM-J23,Schoonenberg:2016:TES-JR06}:
Given a binary input firing vector $U^+[k]$ and a binary output firing vector $U^-[k]$ of size both of size $\sigma{(\cal{E}_S}) \times 1$, and the positive and negative components $\cal{M}^+$ and $\cal{M}^-$ of the Petri net incidence matrix of size  $\sigma{(\mathbb{R}_B)} \times \sigma{(\cal{E}_S)}$, the evolution of the marking vector $Q$ is given by the state transition function $\Phi_T(Q[k],U[k])$:
\begin{equation}
Q[k+1] = \Phi_T(Q[k],U^-[k], U^+[k])
\end{equation}
where $Q = [Q_S; Q_{\cal{E}_S}]$ and
\begin{align}
Q_{S}[k+1]     &= Q_{S}[k] & + & &{{\cal M}^+} U^+[k] & & - &&{{\cal M}^-} U^-[k] \\
Q_{\cal{E}_S}[k+1] &= Q_{\cal{E}_S}[k] & - & &U^+[k] && + &&U^-[k]
\end{align}
\end{defn}

The state transition function breaks the discrete state $Q$ in two.  $Q_{S}$ tracks the locations of the tokens at the places $\mathbb{R}_B$ and $Q_{\cal{E}_S}$ tracks the locations of the tokens in the transitions $\cal{E}_S$ of the healthcare delivery system. The state transition function also distinguishes between input and output firing vectors so as to mark the entry and exit of tokens to and from transitions.  In practice, a scheduled event list is used to implement firing vectors and ensure the durations $D$ of each of the transitions.
\begin{defn} \label{Def:ScheduledEventList}
\textbf{Scheduled Event List} \cite{Cassandras2008}:
A tuple $\cal{S} =$ $(u_\psi[k], t_k)$ consisting of all elements $u_\psi[k]$ in firing vectors $U^-[k]$ and their associated times $t_k$.  For every element, $u_\psi^-[k] \in U^-[k]$, there exists another element $u_\psi^+[\kappa] \in U^+[\kappa]$ which occurs at time $t_\kappa$, $d_\psi$ time units later.  $t_\kappa=t_k + d_\psi$.
\end{defn}

{\color{black}
Now that the dynamics have been defined, an operating cost function can be calculated based on the firing vectors, $U^+[k]$, in the scheduled event list.     \begin{defn}
\textbf{Cumulative Operating Cost Function:}  Operating costs incur as transitions fire, representing the execution of capabilities in the healthcare delivery system.
Given a capability cost vector, $C$ of size $\sigma{(\cal{E}_S})\times1$, representing the cost for each capability and the input firing vector $U^+[k]$, the cumulative operating cost function, ${\cal C}$, is given by:
\begin{align}
{\cal C}[t] = \sum_{k=1}^{t}C^TU^+[k],
\end{align}
\end{defn}
}

\vspace{-0.2in}
\subsection{The Chronic Condition Care Abstraction}\label{Sec:ChronicCare}
The healthcare delivery system model presented in the previous subsection considered all of its inherent capabilities and integrated them within a Petri net model.   Such an approach is considered sufficient for acute care and is demonstrated in Section \ref{Sec:ExampleAcute}.  For chronic care, however, several additional considerations are required.  First, because chronic conditions continue well beyond a single visit to a healthcare facility, a resource entitled `outside clinic must be included in the model.  Naturally, this will require the addition of transportation processes so as to enter and exit the clinic.   Next, transportation degrees of freedom within the clinic are assumed to have a negligible duration and are therefore eliminated.  $K_S$ is modified accordingly.  By Equation \ref{Eq:DOFS}, the number of structural degrees of freedom changes as well.  Consequently, a new projection operator $\mathds{P}_C$ must be calculated such that:
\begin{align}
{\mathds{P}_C} (J_S \ominus K_S)^V = \mathds{1}^{\sigma({\cal{E}_S})}
\end{align}
\noindent Finally, the resources within the clinic are aggregated by Equation \ref{Eq:DPAgg} so as to yield to $\mathbb{\bar{R}}$=\{healthcare clinic, outside clinic\}.  Consequently, the healthcare delivery system Petri net incidence out and incidence in matrices become:
\begin{align}
{\cal M}^-=A_R\sum_{y1=1}^{\sigma(\mathbb{R}_{B})}&e_{y1}^{\sigma(\mathbb{R}_{B})}\left[\mathds{P_C}\left(X_{y_1}^-\right)^V\right]^T
\end{align}

\begin{align}
{\cal M}^+=A_R\sum_{y2=1}^{\sigma(\mathbb{R}_{B})}&e_{y2}^{\sigma(\mathbb{R}_{B})}\left[\mathds{P_C}\left(X_{y_2}^+\right)^V\right]^T
\end{align}
This hierarchical aggregation implements the chronic condition care abstraction.  The focus now becomes the various forms of transformation, decision, and measurement processes that the patient receives rather than transportation and queuing within the clinic.

\vspace{-0.2in}
\subsection{Health Net Dynamics} \label{Sec:DynamicsIndividual}
As mentioned previously, the Health Net
is introduced so as to represent the clinical health state of individuals.
\begin{defn}\label{Def:HealthNet}
\textbf{Health Net}\cite{Khayal:2017:HHS-J17}
: Given an individual $l_i$, that is part of a population $L=\{l_1, ..., l_{\sigma(L)}\}$, the evolution of their clinical health state can be described as a fuzzy timed Petri net\cite{Pedrycz2003, Ding2005, Ding2006}:
 \begin{equation}\label{Eq:HealthNet}
 {N}_{l_i}=\{S_{l_i},{\cal E}_{l_i},{\cal M}_{l_i}, W_{l_i}, D_{l_i}, Q_{l_i}\}
\end{equation}
where
\begin{itemize}
\item ${N}_{l_i}$ is the health net.
\item $S_{l_i}$ is the set of places describing a set of health states.
\item ${\cal E}_{l_i}$ is the set of transitions describing health events.
\item ${\cal M}_{l_i}$ $\subseteq (S_{l_i} \times {\cal E}_{l_i}) \cup ({\cal E}_{l_i} \times S_{l_i})$ is the set of arcs describing the relations of (health states to health events) or (health events to health states).
\item $W_{l_i}$ is the set of weights on the arcs describing the health transition probabilities for the arcs.
\item $D_{l_i}$ is the set of transition durations.
\item $Q_{l_i}$ is the Petri net marking representing the likely presence of the set of health states as a discrete probabilistic state.
\end{itemize}
\end{defn}

The Petri net structure leads directly to the definition of its discrete-event dynamics.
\begin{defn}\label{def:TPNDyn}
\textbf{Fuzzy Timed Petri Net (Discrete-Event) Dynamics}\cite{PopovaZeugmann:2013:00, Khayal:2017:HHS-J17}: Given a binary input firing vector $U_{l_i}^+[k]$ and a binary output firing vector $U_{l_i}^-[k]$ both of size $\sigma({\cal E}_{l_i}) \times 1$, and the positive and negative components ${\cal M}_{l_i}^+$ and ${\cal M}_{l_i}^-$ of the Petri net incidence matrix of size $\sigma(S_{l_i}) \times \sigma ({\cal E}_{l_i})$, the evolution of the marking vector $Q_{l_i}$ is given by the state transition function $\Phi(Q_{l_i}[k],U_{l_i}[k])$:
\begin{equation}\label{eq:Phi}
Q_{l_i}[k+1]=\Phi(Q_{l_i}[k],U_{l_i}^-[k], U_{l_i}^+[k])
\end{equation}
where $Q_{l_i}=[Q_{Sl_i}; Q_{{\cal E}l_i}]$ and
\begin{align}\label{eq:Q_B}
Q_{Sl_i}[k+1]=&Q_{Sl_i}[k] &+& & M_{l_i}^+U_{l_i}^+[k] & &-& & M_{l_i}^-U_{l_i}^-[k]\\\label{eq:Q_E}
Q_{{E}l_i}[k+1]=&Q_{{E}l_i}[k] &-& & U_{l_i}^+[k] & &+& &U_{l_i}^-[k]
\end{align}
\end{defn}
\noindent $Q_{Sl_i}$ is introduced to probabilistically mark Petri net places whereas $Q_{{E}l_i}$ is introduced to mark the likelihood that a timed transition is currently firing.
The transitions are fired based on a scheduled event list that combines the discrete events with a time interval as described in Definition \ref{Def:ScheduledEventList}.

{\color{black}
Now that the health net and its dynamics are defined.  An individual's health outcome function can be calculated.
\begin{defn}
\textbf{Health Outcome Function}:  An individual's health outcome is represented by the set of places describing health state, $S_{l_i}$.  Given a value vector that numerically represents health state, $V$ of size $\sigma(S_{l_i}) \times 1$, and the health state vector $Q_{Sl_i}[k]$, the health outcome function, ${\cal H}_{l_i}$, is given by:
\begin{align}
{\cal H}_{l_i}[k] = V^T Q_{Sl_i}[k]
\end{align}
\end{defn}
}
\vspace{-0.35in}
\subsection{Coordination of the Healthcare Delivery System Petri Net \& Individual Health Net Dynamics} \label{Sec:DynamicsSync}
As expected, the healthcare delivery system Petri net and the health net dynamics are inherently coupled.  Each transformation process in the healthcare delivery system induces its corresponding health event.  For each individual, $l_i$, this feasibility condition can be captured in a binary individual transformation feasibility matrix.
\begin{defn}
\textbf{Individual Transformation Feasibility Matrix} $\Lambda_{F_i}$ \cite{Khayal:2017:HHS-J17, Farid2007,Farid:2008:a1,Farid:2008:02,Farid:2015:IES-J19,Farid:2013:IEM-C30,Farid:2015:IEM-J23,Schoonenberg:2016:TES-JR06}:  a binary matrix of size $\sigma({\cal E}_{l_i}) \times \sigma(P_F)$, where $\Lambda_{F_i}(x,j) = 1$ if transformational process $p_{F_j}$ realizes the health event $e_{xl_i}$.
\end{defn}

An individual firing matrix is introduced to synchronize the healthcare delivery system Petri net firing vectors with those of the (individual) health nets.
\begin{defn}
\textbf{Individual Health Firing Matrix} \cite{Farid:2016:TES-J27, Schoonenberg:2016:TES-JR06}:  A binary individual health firing matrix ${\mathcal U}[k]$ of size $\sigma({\cal E}_S) \times \sigma(L)$, whose element $u_{{l_i}{\psi,l}}[k] =1$ when the $k^{th}$ firing timing triggers an individual $l$ to take structural degree of freedom $\psi$ for action.
\end{defn}

Consequently, the healthcare delivery system input firing vectors at a given moment $k$ become\cite{Schoonenberg:2016:TES-JR06}
\begin{equation}
U^-={\mathcal U}\mathds{1}^{\sigma({L})}
\end{equation}
and each health net firing vector at a given moment $k$ becomes\cite{Schoonenberg:2016:TES-JR06}
\begin{equation}
\Lambda_{F_i}^T \cdot U_{l_i} = {\cal A}_F \cdot {\cal U} \cdot e_{l_i}^{\sigma(L)T}
\end{equation}
and ${\cal A}_F$ serves to select out the structural degrees of freedom associated with transformation.

\section{Acute Care Illustrative Example} \label{Sec:ExampleAcute}
To demonstrate the model, an illustrative example of the acute care of an ACL injury and repair is chosen.  Section \ref{Sec:OrthoDescription} provides a narrative of the acute care episode.  Section \ref{Sec:OrthoSystem} then presents the healthcare delivery system model; first as a knowledge base, then in terms of a list of events, and finally as a Petri net.  Next, Section \ref{Sec:OrthoNet} presents the health net.  Finally, Section \ref{Sec:OrthoDyn} presents the coordination of the healthcare delivery system Petri net and individual health net dynamics.

\subsection{Description of Orthopedic Case}\label{Sec:OrthoDescription}
A typical example orthopedic case study of an ACL injury \& repair is described below; drawing from a textbook clinical case \cite{Guthrie2008}.
\vspace{-0.071in}
\begin{CaseStudy}\label{CS:Acute}
`Adam injured his left knee playing rugby when he fell forwards and sideways while the left foot remained fixed on the ground.  He felt immediate pain and was unable to continue with the game.  Pain and swelling increased over the next 2 hours.
He was seen in an emergency department (ED) and X-rays were negative for fractures.  He was prescribed anti-inflammatories, given elbow crutches and advice on ice, rest and elevation.  A clinic appointment to see an orthopedic consultant was arranged.

The orthopedic clinician (Ortho) evaluated the individual through a battery of special tests: anterior drawer test and valgus stress instability and active Lachman's test all of which were not conclusive due to pain and swelling.  The individual received an urgent MRI scan which showed a rupture of the left ACL and a medial collateral ligament tear.  Surgery was performed followed by an ACL post-operative rehabilitation protocol at physical therapy (PT)'.
\end{CaseStudy}

\vspace{-0.25in}
\subsection{Modeling the Healthcare Delivery System of the Orthopedic Case}\label{Sec:OrthoSystem}
\vspace{-0.39in}
 \begin{figure}[h]
  \begin{center}
   \includegraphics[scale=0.5, trim=2.1cm 5.9cm 1.81cm 6.1cm, clip=true]{JSOrtho}
   \vspace{-0.3in}
    \caption{\textbf{Acute Care Healthcare Delivery System Knowledge Base} $J_{S}$.  Filled elements represent allocated processes to resources.   For graphical simplicity, the $J_{FN}$, $J_{DN}$, $J_{MN}$ and $J_{NN}$ have not been shown.}
   \label{Fig:JSOrtho}
   \end{center}
   \vspace{-0.1in}
\end{figure}

\vspace{-0.1in}
The Case Study \ref{CS:Acute} text is interpreted so as to identify the healthcare delivery system processes and resources.   Each resource and process is then classified as either transformation, decision, measurement or transportation.  Additionally, an `outside clinic' resource is added to reflect the case's three clinical visits.  The resources and processes are used to construct the system knowledge base $J_{S}$ as shown in Figure \ref{Fig:JSOrtho}.  For graphical simplicity, $J_{FN}$, $J_{DN}$, $J_{MN}$ and $J_{NN}$ are not shown.   $J_{FN}$, $J_{DN}$, $J_{MN}$ are assumed to equal zero.  $J_{NN}$ introduces 20 transportation degrees of freedom within the clinic plus another 2 transportation degrees of freedom between the `reception' and `outside clinic'.  The text does not indicate any event constraints.  $K_S=0$.  The associated number of structural degrees of freedom is calculated from Equation \ref{Eq:DOFS}.  $DOF_S=36$.
 \begin{figure}[h]
  \begin{center}
   \includegraphics[width=2.5in]{EventListOrtho}

    \caption{\textbf{Acute Care Healthcare Delivery System Events} based on the Orthopedic Case narrative described in terms of the Healthcare Delivery System Events found in $J_S$.  The healthcare delivery transformational events are in bold. }
   \label{Fig:SystemeventsOrtho}

   \end{center}
\end{figure}

\vspace{-0.25in}
The Case Study \ref{CS:Acute} narrative is then rewritten as a string of healthcare delivery system events ${\cal E}_S$ as shown in Figure \ref{Fig:SystemeventsOrtho}.  Each event in ${\cal E}_S$ has a unique index and its associated combination of process and resource.  The transformational events are highlighted in bold.  These events are effectively an {\color{black}\emph{untimed}} scheduled events list and are used to generate the healthcare delivery system Petri net firing vectors.

 \begin{figure}[h]
  \begin{center}
   \includegraphics[width=3.25in, trim=0.009cm 0.0095cm 0.062cm 0.0532cm, clip=true]{HDSnetOrtho}
\vspace{-0.1in}
    \caption{\textbf{Acute Care Healthcare Delivery System Petri net}.  The places (\emph{circles}), represent buffer resources=\{outside clinic, reception, emergency room, imaging, physical therapy, orthopedic surgery\}.  The transitions (\emph{rectangles}), are numbered based on the healthcare delivery system structural degrees of freedom index  $\psi_i$.}
   \label{Fig:HDSnetOrtho}
   \end{center}
\vspace{-0.2in}
\end{figure}

The healthcare delivery system Petri net model is constructed as shown as in Figure \ref{Fig:HDSnetOrtho}.  A single Petri net place is shown for each of the 6 buffer resources.   A single transition is shown for each of the 36 structural DOF.   The places and transitions have been graphically situated to reflect their `physical' location in the healthcare clinic

\vspace{-0.2in}
\subsection{Modeling the Individual Health Net Episode of the Orthopedic Case}\label{Sec:OrthoNet}

The Case Study \ref{CS:Acute} narrative and its associated healthcare delivery system events now serve to determine the individual health net $N_l$ as shown in Figure \ref{Fig:OrthopedicNet}.
\begin{figure}[h]
\vspace{-0.2in}
  \begin{center}
   \includegraphics[scale=.34,trim=0.06cm 0.25cm 0.3cm 0.2cm, clip=true]{IndividualNetOrtho}
    \vspace{-0.1in}
   \caption{\textbf{Acute Care Individual Health Net}: visualizes the health state at the places \emph{(circles)} and the health events, causing the changes in health state, at the transitions \emph{(rectangles)}.}
   \label{Fig:OrthopedicNet}
   \end{center}
\vspace{-0.25in}
\end{figure}

The health net shows the individual's \emph{health states} at the places (circles) and the individual's \emph{health state transformations} or \emph{health events} at the transitions (rectangles).  These occur due to healthcare delivery system events $P_F$ or stochastic human processes $P_\varphi$.   As is common with acute conditions, there is a serial progression of events which when successful return the patient back to a normal health state.

\subsection{Modeling the Coordination of the Healthcare Delivery System Petri Net \& Individual Health Net of the Orthopedic Case}
\label{Sec:OrthoDyn}
To complete the model, the healthcare delivery system Petri net and individual health net must be coordinated.  The individual transformation feasibility matrix, shown in Figure
\ref{Fig:Ex1FeasibilityMatrix}, is constructed by linking the individual health net transitions (i.e. health events) to the corresponding healthcare delivery system transformational events (i.e. transformation process $P_F$).

\begin{figure}[h]
  \begin{center}
  \vspace{-0.1in}
   \includegraphics[scale=0.4, trim=1.38cm 6.86cm 2.3cm 2.11cm, clip=true]{OrthopedicExample_feasibility}
   \vspace{-0.26in}
    \caption{\textbf{Acute Care Individual Transformation Feasibility Matrix} $\Lambda_{F}$.}
   \label{Fig:Ex1FeasibilityMatrix}
   \end{center}
   \vspace{-0.2in}
\end{figure}

The synchronized dynamics of the healthcare delivery system Petri net and the individual net are shown in Figure \ref{Fig:DynamicTableOrtho} as two scheduled event lists side by side.

 \begin{figure}[]
  \begin{center}
   \includegraphics[width=3.5in]{DynamicTableOrtho}
  \vspace{-0.3in}
    \caption{\textbf{Acute Care Dynamics of the Two Petri nets}:  the healthcare delivery system Petri net and the individual net are now synchronized.  The scheduled events of each Petri net are shown side by side.}
   \label{Fig:DynamicTableOrtho}
   \end{center}
   \vspace{-0.295in}
\end{figure}

{\color{black} Finally, the healthcare delivery system operating cost and the individual health outcome dynamics for this Orthopedic acute case can be shown over time (k) in Figure \ref{Fig:Cost_HealthOutcome}.
 \begin{figure}[h]
  \begin{center}
   \includegraphics[width=3.in]{Cost_HealthOutcome}
      \vspace{-0.17in}
        \caption{\textbf{Acute Care Healthcare Delivery System Operating Cost in US dollars (top-blue) and Individual Health Outcome as \% healthy (bottom-red) over time k. }
        }
   \label{Fig:Cost_HealthOutcome}
   \end{center}
\vspace{-0.3in}
\end{figure}
}

\vspace{-0.2in}
\section{Chronic Care Illustrative Example} \label{Sec:Example}
In contrast to the previous example, a neuro-oncology case study is chosen to demonstrate the model's applicability to chronic conditions.  Section \ref{Sec:Description} presents the full narrative of the case as presented by Park et. al. \cite{Park2005}.  Section \ref{Sec:ModelHDS} then presents the healthcare delivery system model; first as a knowledge base, then in terms of a list of events, and finally as a Petri net.  Next, Section \ref{Sec:Modelindividual} presents the health net.  Finally, Section \ref{Sec:Dyn} presents the coordination of the healthcare delivery system Petri net and individual health net dynamics.

\vspace{-0.25in}
\subsection{Description of Neuro-Oncology Case} \label{Sec:Description}
\begin{CaseStudy}\label{CS:Chronic}`The patient was a 32-year-old, right-handed woman without significant past medical history who presented for evaluation of headaches and intermittent short-term memory loss. She also
reported mild nausea, but was otherwise asymptomatic. Her headaches had begun approximately 3 months before her presentation.  On neurologic examination, no deficit was appreciated.  She underwent a head CT with the finding of a large, poorly enhancing right occipital-parietal mass that appeared to be located within the lateral ventricle. Subsequent MR imaging scanning confirmed the location of the tumor in the trigone with local expansion of the ventricle.  Similar to the CT, minimal enhancement was noted. On the  basis of the imaging characteristics, a low-grade astrocytoma was felt to be the most likely diagnosis. In light of the size of the tumor and its location, a parietooccipital surgical approach was performed. The tumor appeared grayish and was predominantly firm, necessitating piecemeal removal. The tumor was not particularly vascular, and a distinct plane between tumor and ependyma was identified, but there were several areas where the tumor appeared to infiltrate into adjacent brain parenchyma. Frozen-section pathologic analysis was described as abnormal and cellular but was not specifically diagnostic.  Tumor resection was continued until a near-total removal was accomplished. Postoperatively, the patient remained without neurologic deficit. Follow-up MR imaging showed near-total removal of the tumor.

Histologic sections were examined by light microscopy. The neoplasm was hypercellular with necrosis and endothelial cell proliferation, hallmarks of GBM, World Health Organization (WHO) classification grade IV (9, 10). Gemistocytes were distributed throughout the neoplasm with rare mitoses. These cells had hyaline, eosinophilic cytoplasm, and eccentric, hyperchromatic nuclei, some of which were large and pleomorphic. Immunostains for glial fibrillary acidic protein (GFAP), S-100 protein, vimentin, and neurofilament were positive, whereas immunostains for muscle-specific actin, alpha smooth muscle, and synaptophysin were negative. MIB-1 was positive, with a low proliferation index. The morphology and GFAP positivity suggested a diagnosis of diffuse gemistocytic astrocytoma; however, the tumor necrosis and microvascular proliferation raised the tumor grade to grade IV GBM. Because of the unusual radiographic appearance and location, the histologic slides were also reviewed by physicians at the Armed Forces Institute of Pathology (Bethesda, MD), who confirmed the initial diagnosis. Whole-brain radiation and chemotherapy were subsequently instituted. At 2-year follow-up, the patient complained of headaches but remained neurologically intact with no evidence of tumor progression on MR imaging.' \cite{Park2005}
\end{CaseStudy}

\vspace{-0.23in}
\subsection{Modeling the Healthcare Delivery System of the Neuro-Oncology Case}\label{Sec:ModelHDS}
The Case Study \ref{CS:Chronic} text is interpreted so as to identify the healthcare delivery system processes and resources.  They are modeled at a level of aggregation typical of clinical narratives.  For example, the narrative states `... a parietoccipital surgical approach was performed' \cite{Park2005}.  Here, the healthcare delivery system process is aggregated to `Perform surgery' and the `neurosurgery' resources describes the aggregation of human and technical resources including the neurosurgery team, room and equipment.  Second, an `outside clinic' resource is added to reflect the individual entering and exiting the healthcare delivery system in the case's six clinical visits.  As discussed in Section \ref{Sec:ChronicCare}, the transportation capabilities within the clinic are assumed to be always available, of relatively short duration, and of sufficient capacity.   They are eliminated from the knowledge base so as to focus on the more valuable healthcare delivery capabilities of transformation, decision and measurement.  Therefore, the transportation processes are reduced to `Enter clinic' and `Exit clinic'.  Furthermore, given the long term nature of this example, the decision processes of care planning and care scheduling are combined.

\vspace{-0.1in}
 \begin{figure}[h]
  \begin{center}
   \includegraphics[scale=0.485, trim=1.66cm 15.98cm 1.39cm 1.79cm, clip=true]{JS}
         \vspace{-0.26in}
    \caption{\textbf{Chronic Care Healthcare Delivery System Knowledge Base} $J_{S}$ with allocated processes to resources (dark filled).}
   \label{Fig:JS}
   \end{center}
   \vspace{-0.2in}
\end{figure}

\vspace{0.05in}
The resources and processes are classified as either transformation, decision, measurement or transportation and used to construct the system knowledge base $J_{S}$ shown in Figure \ref{Fig:JS}.  For simplicity, the system is assumed to not have any event constraints, $K_S=0$.  The system availability matrix and consequently the structural degrees of freedom can be calculated using Equation \ref{Eq:DOFS} such that $DOF_S=7$.

The Case Study \ref{CS:Chronic} narrative is then rewritten as a string of healthcare delivery system events ${\cal E}_S$ as shown in Figure \ref{Fig:EventList}.  Each event in ${\cal E}_S$ has a unique index and its associated combination of process and resource.  The transformational events are highlighted in bold.  These events are effectively an \emph{untimed} scheduled events list and are used to generate the healthcare delivery system Petri net firing vectors.

 \begin{figure}[h]
       \vspace{-0.1in}
  \begin{center}
   \includegraphics[width=3.in]{EventList}
      \vspace{-0.1in}
    \caption{\textbf{Chronic Care Healthcare Delivery System Events} based on the Neuro-Oncology Case narrative in terms of the Healthcare Delivery System Events found in $J_{S}$.  The healthcare delivery transformational process events are in bold.}
   \label{Fig:EventList}
   \end{center}
   \vspace{-0.2in}
\end{figure}

Finally, the healthcare delivery system Petri net is constructed.  As discussed in Section \ref{Sec:ChronicCare}, the chronic care abstraction is utilized to abstract the many healthcare delivery system resources to a single `healthcare clinic' resource.  Figure \ref{Fig:HDSnet} shows the Petri net of the healthcare delivery system superimposed on a light-grey physical layout.

 \begin{figure}[h]
  \begin{center}
   \includegraphics[scale=0.48, trim=0.009cm 0.0095cm 0.062cm 0.0532cm, clip=true]{HDSnet}
      \vspace{-0.126in}
    \caption{\textbf{Chronic Care Healthcare Delivery System Petri net}.  The places (\emph{circles}), represent  1=`outside clinic' and 2=`healthcare clinic'.  The transitions (\emph{rectangles}), are numbered based on the healthcare delivery system structural degrees of freedom index $\psi_i$.}
   \label{Fig:HDSnet}
   \end{center}
\vspace{-0.2in}
\end{figure}

\vspace{-0.1in}
 \begin{figure}[h]
  \begin{center}
   \includegraphics[width=3.25in, scale=0.335, trim=0.cm 0.0cm 0.02cm 0.0cm, clip=false]{IndividualNet}
   \vspace{-0.14in}
    \caption{\textbf{Chronic Care Individual Net}: visualizes the health states at the places \emph{(circles)} and the health events at the transitions \emph{(rectangles)} representing the stochastic human process or the healthcare delivery system transformational process firing.}
   \label{Fig:IndividualNet}
   \end{center}
   \vspace{-0.25in}
\end{figure}

\vspace{-0.12in}
\subsection{Modeling the Individual Health Net of the Neuro-Oncology Case} \label{Sec:Modelindividual}
The Case Study \ref{CS:Chronic} narrative and its associated healthcare delivery system events now serve to determine the health net for the neuro-oncology patient as shown in Figure \ref{Fig:IndividualNet}.  The health states are identified based on typical clinical outcomes of the healthcare transformational processes:  `Perform surgical resection' and `Perform radiation \& chemotherapy treatment'.

Because the health net is fuzzy, the outcome of any given transition is probabilistic.   For example, after a tumor resection three different outcomes are possible to describe the extent of resection:  gross-total resection [GTR], near-total resection [NTR] and sub-total resection [STR]).  For simplicity, the probabilities of these outcomes are assumed to be equal and in practice would be validated with clinical data of surgery outcomes.  Next, three transitions occur in parallel to represent radiation \& chemotherapy of the tumor/cancer in its current condition.   This leads to four possible treatment response outcomes based on the McDonald criterion \cite{Wen2010} (i.e. complete response [CR], partial response [PR], stable disease [SD], progressive disease [PD]).  These lead to states associated with further tumor progression, or no measurable tumor progression followed by an asymptomatic state.  In this case, the health net, as a fuzzy-timed Petri net, not only shows the dynamic evolution of an individual's distributed health state in the clinical sense but it's stochastic nature lends itself to Bayesian statistics.

\vspace{-0.25in}
\subsection{Modeling the Coordination of the Healthcare Delivery System Petri Net \& Individual Health Net of the Neuro-Oncology Case}
\label{Sec:Dyn}

To complete the model, the healthcare delivery system Petri net and the individual health net must be coordinated.  The individual transformation feasibility matrix, shown in Figure \ref{Fig:FeasibilityMatrix}, is constructed by linking the individual health net transitions (i.e. health events) to the corresponding healthcare delivery system transformational events (i.e. transformation process $P_F$).  Note that the radiation and chemotherapy transformation process is tied to three health events; not just one.  This is because the individual's health evolves differently to the same stimulus depending on their current condition.
 \vspace{-0.1in}

 \begin{figure}[h]
  \begin{center}
   \includegraphics[scale=0.34985, ]{FeasibilityMatrix}
      \vspace{-0.1in}
    \caption{\textbf{Chronic Care Individual Transformation Feasibility Matrix} $\Lambda_{F}$.}
   \label{Fig:FeasibilityMatrix}
   \end{center}
      \vspace{-0.2in}
\end{figure}

The synchronized dynamics of the healthcare delivery system Petri net and the individual net are shown in Figure \ref{Fig:DynamicTable} as two scheduled event lists side by side.

 \begin{figure}[]
  \begin{center}
      \includegraphics[width=3.5in]{DynamicTable}
     \vspace{-0.25in}
    \caption{\textbf{Chronic Care Dynamics of the Two Petri nets}:  the healthcare delivery system Petri net and the individual net are now synchronized.  The scheduled events of each Petri net are shown side by side.}
   \label{Fig:DynamicTable}
   \end{center}
   \vspace{-0.2in}
\end{figure}

{\color{black} Finally, the healthcare delivery system operating cost and individual health outcome dynamics for this Neuro-Oncology Chronic case can be shown over time (k) in Figure \ref{Fig:Cost_HealthOutcome2}.

 \begin{figure}[h]
  \begin{center}
   \includegraphics[width=3in]{Cost_HealthOutcome2}
   \vspace{-0.2in}
    \caption{\textbf{Chronic Care Healthcare Delivery System Operating Cost in US dollars (top-blue) and Individual Health Outcome as \% healthy (bottom-red).}}
    \label{Fig:Cost_HealthOutcome2}
   \end{center}
   \vspace{-0.25in}
\end{figure}
}

\vspace{-0.2in}
\section{Results \& Discussion} \label{Sec:Discussion}

The illustrative examples demonstrate the dynamic model for personalized healthcare delivery and managed health outcomes.  Such a model has several important aspects.  It applies equally to the care of both acute and chronic conditions, it transparently describes health outcomes, and it transparently links cost and outcomes.

First, the two illustrative examples demonstrate the model's applicability to both acute and chronic care.  The acute care dynamic modeling resembles those commonly found in industrial engineering and operations research literature \cite{Gunal2010, Jacobson2006, Turkcan2012, Alvarado2012}.  It emphasizes the importance of scheduling and minimized queuing.  At the timescale of a clinic visit, acute care decision processes like care planning and scheduling are critical.   The timeliness of decision-making was highlighted in the acute care of the orthopedic case.  Acute care requires a more granular resolution of healthcare delivery system capabilities (i.e. structural degrees of freedom).  Consequently, many more are utilized per visit relative to chronic care.   The utilization of spatially distributed transformative, decision, and measurement capabilities within a short period of time naturally raises questions of transportation (e.g. in emergency rooms) and queues (e.g. in patient care).  In chronic care, these concerns are diminished.  The model abstracts away transportation so as to focus on the coordination of transformation, decision and measurement processes.

The health net in this model is an important contribution that serves to transparently describe health outcomes.  In acute care, the health net tends to cycle back to an initially healthy state in a fairly short period of time; and perhaps within a single visit.  In chronic care, not only are multiple clinical visits required but the state of the individual's health must be tracked in the meantime.  While in some chronic conditions a return to a healthy state is possible, in most instances the healthcare delivery system must actively track and manage its degradation.

Indeed, the most important aspect of the model is its coherence between the healthcare delivery system and the individual's health state.  The states of the Petri nets are tied directly and should ideally be coordinated in order to deliver effective care.  Whether for acute or chronic conditions, time is of the essence.   Because the health nets have stochastic processes that will fire spontaneously, the healthcare delivery system must take timely and coordinated action to avoid adverse and negative health outcomes.

Finally, it is important to recognize that each healthcare delivery system degree of freedom incurs a cost every time it is fired.  Therefore, as the two Petri nets evolve simultaneously, the discrete event simulation transparently reveals the accumulation of incurred cost versus the evolution of health outcomes   {\color{black} as shown in Figures \ref{Fig:Cost_HealthOutcome} and \ref{Fig:Cost_HealthOutcome2}.}

\vspace{-0.1in}
\section{Conclusion \& Future Work} \label{Sec:Conclusion}

In conclusion, this paper develops the dynamic system model for personalized healthcare delivery and managed individual health outcomes.  The dynamics of the model rests upon the developed systems architecture from prior work.  This work draws upon a hetero-functional graph theory rooted in Axiomatic Design for Large Flexible Engineering Systems and Petri nets.
The dynamic model coordinates the healthcare delivery system and individual net.  The healthcare delivery net evolves as the transitions fire when the system is utilized, while the individual net evolves as the individual's health state evolves due to the spontaneous firing of stochastic process and as the individual receives transformative processes by the healthcare delivery system.    The dynamic model was then demonstrated for two illustrative examples: an acute care and chronic care.  The contrast of the two examples shows the versatility of the model to handle the queueing needs of acute care and the coordination needs of chronic care.  {\color{black} Furthermore, the dynamic model was used to produce two parametric functions of time dynamically showing healthcare delivery system operating cost over time and patient outcome values over time.  These could be used to understand what healthcare capability utilizations or utilization patterns lead to better patient outcome values.}

The development of the model opens several new avenues for future work.   The Petri net firing vectors indicated as inputs to the model provide an opportunity for the development of rigorous decision-making algorithms.  Second, the model may be applied to new case studies of potentially larger scope.   The clear trade-offs between cost and health outcomes is likely to be of interest to many healthcare delivery system stakeholders including clinicians, healthcare facility administrators, insurance companies, and regulators.
Finally, as the need for such a model matures, new approaches to automated model building that integrate with healthcare enterprise information systems or capture health state information through Internet-of-Things enabled sensor devices is likely to grow.

\bibliographystyle{IEEEtran}

redpajama_set_name: RedPajamaArXiv


I have been tagged by Darlene of Darlene's Hodgepodge to do a Meme. Darlene began blogging at the very young age of 82!
YES! I did say 82.
Since then despite a fall and hip surgery she has returned to living alone and blogging. A very wise and humorous lady, I could learn plenty just sitting at Darlene's feet.
The rules are to pick the book nearest to you, turn to page 161 and copy the fifth sentence. I know I have done this sort of thing before, but I do manage to read and complete at least one book a year! 🙄 You don't believe me?
Seriously now the book to hand is 'From here, you can't see Paris' by Michael Sanders.
This entry was posted in Blogging on September 13, 2009 by Grannymar.


text:
Q: How to add Face Id Authentication in Xamarin forms for the Android I'm looking for the solution in Xamarin forms to implement Face Id authentication. If the user has enabled Face Id on their mobile, there will be a prompt to scan their face for authentication. I have tried a lot but not found any solution.

A: Unless I'm mistaken Android devices don't have the hardware to do this. Sure, you could use the camera and sprinkle AI over it to determine if there is a face in the picture and if the eyes are looking at the screen, but that will be a big undertaking.
iOS has Face ID which has all of this built-in, not just in it's software, but also in their hardware with a variety of sensors to support this scenario.
If you want to look into making fingerprint and Face ID usage easier, check out the Xamarin Biometrics plugin.

redpajama_set_name: RedPajamaStackExchange


text:
Q: Need help to create mysql query for multiple selects for specific conditions
I need some help to make a SQL query.
I have table 'stock_exchange' which records the stock interchanged between four different stores/sites.
It records

date, item_id, qty, price, total_price, from_site, to_site

Now I need to create a query to run for one of the stores/site which will return total price for the stock sent and received between other three stores.
For example: there are Store1, Store2, Store3, Store4
If I need to check for Store1, it should return:

Store Name____Total Sent____Total Received Store2_________90.90_______50 Store3_________120_______100.40
  Store4_________400_______200

I tried myself, but was only able to get sum of either stock sent or received.
Here is the fiddle
EDIT:
I changed the table to record store id (1,2,3,4....) now instead of store alias (crw, chc, cal_rav....), and the code(in answer) I accepted, has stopped working. I tried this amendment in the code to find matching rows by store id, but does't return anything:
SELECT GREATEST(t2.name, t3.name) AS from_store,
       LEAST(t2.name, t3.name) AS to_store,
       SUM(CASE WHEN t2.name < t3.name THEN t1.total_price ELSE 0 END) AS total_sent,
       SUM(CASE WHEN t2.name > t3.name THEN t1.total_price ELSE 0 END) AS total_received
FROM stock_exchange t1
INNER JOIN sites t2
    ON t1.from_site = t2.id
INNER JOIN sites t3
    ON t1.to_site = t3.id
GROUP BY GREATEST(t2.name, t3.name),
         LEAST(t2.name, t3.name)
HAVING MAX(GREATEST(t2.id, t3.id)) = '1'

Here is the updated fiddle.

A: In my opinion, while there is possibility to have much wider combinations of multiple stores, I prefer using rather more queries that are more simple (and usually even faster to execute):
SELECT name, SUM(total_price) as total_sent_to FROM stock_exchange se
LEFT JOIN sites ON sites.alias = se.to_site
WHERE from_site = 'crw' GROUP BY from_site, to_site;
SELECT name, SUM(total_price) as total_received_from FROM stock_exchange se
LEFT JOIN sites ON sites.alias = se.from_site
WHERE to_site = 'crw' GROUP BY from_site, to_site;

Result:

... so I would test it against bigger data amounts and compare solutions before using in production.
For counting totals:
SELECT *, (SELECT SUM(total_price)
                  FROM stock_exchange se
                  WHERE se.from_site = sites.alias
                  GROUP BY se.from_site)
                as total_sent_sum,
                (SELECT SUM(total_price)
                  FROM stock_exchange se
                  WHERE se.to_site = sites.alias
                  GROUP BY se.to_site)
                as total_received_sum
                FROM sites;

A: Here is a query which shows the sent and received amounts from Cafe Rosewood to all other stores:
SELECT GREATEST(t2.name, t3.name) AS from_store,
       LEAST(t2.name, t3.name) AS to_store,
       SUM(CASE WHEN t2.name < t3.name THEN t1.total_price ELSE 0 END) AS total_sent,
       SUM(CASE WHEN t2.name > t3.name THEN t1.total_price ELSE 0 END) AS total_received
FROM stock_exchange t1
INNER JOIN sites t2
    ON t1.from_site = t2.alias
INNER JOIN sites t3
    ON t1.to_site = t3.alias
GROUP BY GREATEST(t2.name, t3.name),
         LEAST(t2.name, t3.name)
HAVING MAX(GREATEST(t2.name, t3.name)) = 'Cafe Rosewood'

If you want to see transactions between all stores, just remove the HAVING clause.  This query employs a trick of taking GREATEST(from_site, to_site) to group together two stores.
SQLFiddle


SCP/TAPS represent a diverse family of proteins in eukaryotes, including pathogens. An analysis of structure-based amino acid sequence alignments of SCP/TAPS proteins (also called activation-associated proteins, ASPs) from the blood-feeding hookworm, A. caninum, reveals at least three distinct groups. This analysis combined with comparative modelling showed that all known ASPs have an equatorial groove, suggesting that it binds extended structures, such as peptides or glycans. The topology seen in the crystal structure of a representative group 2 ASP (designated Ac-ASP-7) is consistent with pathogenesis-related proteins, with the N-terminal domain adopting the SCP/TAPS fold, and the C-terminal extension resembling the fold of the Hinge domain. By anomalous diffraction, a new metal binding site in the C-terminal extension of the protein was observed (Ca2+, Mn2+). In solution, Ac-ASP-7 is in a monomer-dimer equilibrium, and crystal packing analysis identified a dimeric structure which may resemble the homo-dimer in solution. The dimer interaction interface includes a novel binding site for divalent metal ions, proposed to serve as a binding site for proteins involved in the parasite-host interplay at the molecular level.
Alpha-giardins constitute the annexin proteome (group E annexins) in the intestinal protozoan parasite Giardia, and as such represent the evolutionary oldest eukaryotic annexins. alpha-1 giardin localises to the plasma membrane of Giardia trophozoites and has recently been identified as a vaccine target.
The structure was solved using the anomalous signal of the tantalum bromide cluster [Ta6Br12]2+ synthesised in house. Structure determination further involved the hybrid modelling-replacement approach provided by ROSETTA and Phenix.
The structure of Anx24 from bell pepper was the first structure of any plant annexins to be solved. Hydrophobic and basic residues on the convex (membrane-binding) side of the protein are responsible for a second, calcium-independent membrane binding mode which seems to be a characteristic feature of several plant annexins that distinguishes them from their vertebrate relatives.
Human annexins A3 and A5 were complexed within the crystals with BDA452, a new 1,4-benzodiazepine derivative. BDA452 binds to a cleft which is located close to the N-terminus opposite to the membrane binding side of the proteins. Biophysical studies of the interactions of various benzodiazepine derivatives with annexins were performed to analyse the binding of benzodiazepines to annexins and their effects on the annexin-induced calcium influx into phospholipids vesicles. Benzodiazepines modulate the membrane effects of annexins allosterically.
The crystal structure of calcium-free recombinant human annexin VI shows two similar halves closely resembling annexin I connected by an -helical segment and arranged perpendicular to each other. The calcium and membrane binding sites assigned by structural homology are therefore not located in the same plane. Analysis of the membrane-bound form of annexin VI by electron microscopy shows the two halves of the molecule coplanar with the membrane, but oriented differently to the crystal structure and suggesting a flexible arrangement (see also structure by Kretsinger's group: PDF).
Using structure-based amino acid sequence alignments, we identified a structural feature shared by several (but not all) annexins from parasitic organisms that presents a novel element of those annexins and is thus absent from any of the mammalian annexins. Many schistosome annexins, and those from T. solium (annexins B1, B2, B3), C. elegans annexin B36, as well as alpha12- and alpha19-giardin possess an unusually long linker segment between repeats II and III on the concave side of the protein.
The crystal structure of annexin B22 confirms the presence of the previously predicted alpha-helical segment in the II/III linker and reveals a covalently linked head-to-head dimer. From the calcium-bound crystal structure of this protein, canonical type II, type III and B-site positions are occupied, and a novel binding site has been identified. The dimer arrangement observed in the crystal structure suggests the presence of two prominent features, a potential non-canonical membrane binding site and a potential binding groove opposite to the former.
Crystals of annexin B22 required dehydration to achieve diffraction up to 2.2 Å. The structure was solved with Pr-MAD.
The structure indicates that canonical calcium binding is geometrically possible within the membrane loops in domains I and II. The tryptophan residue in the IAB loop, which is highly conserved in plant annexins, is in a surface-exposed position, half way between both conformations observed in Anx24(Ca32). An unusual sulphur cluster formed by two cysteines and a methionine in domains II and III with S-S distances of about 5 Å might form the molecular basis for annexin function in oxidative stress response.
The crystal structure of beta-glucosidase A (BglA, EC. 3.2.1.21) from the halothermophilic bacterium Halothermothrix orenii has been determined at a resolution of 3.0 Å. The structure with two molecules in the asymmetric unit was solved by molecular replacement using a library of known glucosidase structures. A Ni2+ ion, presumably acquired during purification, was found in the active site.
Plant annexins show distinct differences when compared to their animal orthologues. In particular, the endonexin sequence, which is responsible for coordination of calcium ions in type II binding sites, is only partially conserved in plant annexins. The crystal structure of calcium-bound cotton annexin Gh1 was solved at 2.5 Å resolution, and shows three metal ions coordinated in the first and fourth repeat in type II and III binding sites. While the protein has no detectable affinity for calcium in solution in the presence of phospholipid vesicles, we determined a stoichiometry of four calcium ions per protein molecule using isothermal titration calorimetry. Further analysis of the crystal structure shows that binding of a fourth calcium ion is structurally possible in the DE loop of the first repeat. Data from this study are in agreement with the canonical membrane-binding of annexins which is facilitated by the convex surface associating with the phospholipid bilayer by a calcium bridging mechanism. In annexin Gh1, this membrane-binding state is characterised by four calcium bridges in the I/IV module of the protein, and direct interactions of several surface-exposed basic and hydrophobic residues with the phospholipid membrane.
A new class of carbonic anhydrase (CA) inhibitor was designed to selectively target the extracellular domains of the cancer-relevant CA isozymes. The aromatic moiety of the classical zinc binding sulfonamide CA inhibitors is absent from these compounds and instead they incorporate a hydrophilic mono- or disaccharide fragment directly attached to the sulfonamide group to give S-glycosyl primary sulfonamides. We solved the crystal structures of three anomeric sulfonamides and the sugar sulfamate drug topiramate in complex with human recombinant CA II. From these structures we have obtained valuable insights into ligand-protein interactions of these novel carbohydrate-based sulfonamides with CA.
A survey of genomic shows that P. aeruginosa possesses two TPP proteins, one with chromosomal and one with extra-chromosomal location. Notably, the occurrence of both proteins is mutually exclusive; all P. aeruginosa strains for which information is available to date possess either the chromosomal (Paer-chTPP) or the plasmid-encoded (Paer-ecTPP) trehalose 6-phosphate phosphatase. The crystal structure of Paer-chTPP shows that the protein adopts the general fold known from other halo-acid dehydrogenase (HAD) superfamily (IPR023214) enzymes. The structure reveals a homodimer where the central β-sheet of the core domain is extended to a twelve-stranded β-sheet and the dimer interface is further expanded by the formation of a four-helix bundle. An intriguing novel structural element is the first connector between the HAD core and the cap domain. Whereas the segments connecting cap and core domains in TPPs are typically short extended/unstructured loops, the N-terminal connector is replaced here by a long bent α-helix with Trp111 at the bending point. This connector fold constitutes a rather rigid attachment of the cap to the core domain owing to the inherent directional stability of the helical fold.
CAP is a highly conserved and widely distributed protein that links the nutritional response signalling to cytoskeleton remodelling. We solved the orthorhombic crystal structure of the N-terminal domain of CAP that occurred due to auto-proteolytic cleavage in preparations using the full-length protein. Comparison with other CAP structures reveals variable modes of dimerisation of this domain, but the presence of a common interface for the side-to-side dimer.
Crystals of cyclic green fluorescent protein (cGFP) engineered by the split intein technology in the group of A Plückthun were obtained and the structure was solved using molecular replacement. Although the core of the protein can unambiguously be fitted from the first to the last residue of the genuine sequence, the electron density in the region of the linker peptide is rather poor owing to the high water content of the crystals. Therefore, it is concluded that this part of the protein is highly disordered in the present structure and is very flexible. Nevertheless, the density is consistent with the loop being intact, as confirmed by mass spectroscopy of dissolved crystals. This structure contains an antiparallel cGFP dimer where the dimer interface is clearly different from other crystal structures featuring two GFP molecules. The cylinder surface of GFP is rather versatile and can employ various polar and non-polar patches in protein-protein interactions.
The oxidised structure of cyclic nucleotide phosphodiesterase (CPDase) from Arabidopsis thaliana was the first one to be solved for any member of this family of 2H phosphodiesterases. The name stems from the signature tandem motif constituted by two H-X-T/S-X sequences.
CPDase possesses six cysteine residues, four of which are involved in forming two intra-molecular disulfide bridges. One of these bridges, between Cys-104 and Cys-110, is opened in the semireduced CPDase, whereas the other remains intact. This change of the redox state leads to a conformational rearrangement in the loop covering the active site of the protein. While the native structure shows this partially disordered loop in a coil conformation, in the semireduced enzyme the N-terminal lobe of this loop winds up and elongates the preceding alpha-helix. The semireduced state of CPDase also enabled co-crystallization with a putative inhibitor of its enzymatic activity, 2',3'-cyclic uridine vanadate.
The main target of this plant protein is ADP-ribose 1'',2''-cyclic phosphate, a product of the tRNA splicing reaction.
The first crystals of this protein were obtained accidentally during our efforts to crystallise native annexin 24(Ca32) purified from bell pepper. Subsequently, the cDNA of this protein was prepared, and the complete gene encoding paprika ferredoxin-NADP(+) reductase (pFNR) precursor was sequenced and cloned. The overall structure of pFNR is similar to other members of the ferredoxin-NADP(+) reductase family, the major differences concern a long loop that forms part of the FAD binding site and some of the variable loops in surface regions.
A library of natural products and their synthetic derivatives has been investigated for enzyme inhibition against carbonic anhydrases (CAs), comprising the two human alpha-family CAs I and II and two Mycobacterium tuberculosis beta-family CAs. In support of this study, the structures of several compounds from this library were determined in their enzyme-boudn forms, using human CAII.
Hookworm activation-associated secreted proteins (ASPs) can be structurally classified into at least three different groups. The hallmark feature of Group 1 ASPs is a prominent equatorial groove, which is inferred to form a ligand binding site. Furthermore, a conserved tandem histidine motif is located in the centre of the groove and believed to provide or support a yet to be determined catalytic activity. We solved the three-dimensional crystal structures of Na-ASP-2, an L3-secreted ASP from the human hookworm, which demonstrate transition metal binding ability of the conserved tandem histidine motif. We further identified moderate phosphohydrolase activity of recombinant Na-ASP-2, which relates to the tandem histidine motif. By panning a random 12-mer peptide phage library, we identified a peptide with high similarity to the human calcium-activated potassium channel SK3, and confirm binding of the synthetic peptide to recombinant Na-ASP-2 by differential scanning fluorimetry. Potential binding modes of the peptide to Na-ASP-2 were studied by molecular dynamics simulations which clearly identify a preferred topology of the Na-ASP-2:SK3 peptide complex.
Chemical probing of the mycobacterial β-carbonic anhydrase Rv1284 using protein crystallography and stopped-flow enzyme assays show that the catalytic activity can be reversibly inhibited by oxidation. These findings link conditions of oxidative stress to pH homeostasis of the pathogen, and also support the notion that mycobacterial carbonic anhydrases can be targeted with non-classical inhibitors binding at the protein surface.
Ac-SLP-1 and Na-SLP-1 are non-orthologous proteins. Both proteins share the property of membrane binding. In contrast to Na-SLP-1, the three-dimensional structure of Ac-SLP-1 suggests that membrane interactions are most likely initiated by a unique tryptophan residue that has previously been implicated in membrane interactions in other SAPLIPs. With Ac-SLP-1 we analysed 4 native and 12 derivatised crystals with 7 heavy atom compounds. The crystal structure was solved with Pt-SIRAS.
Saposin-like proteins (SAPLIPs) from soil-transmitted helminths play pivotal roles in host-pathogen interactions and have a high potential as targets for vaccination against parasitic diseases. Na-SLP-1 adopts the general SAPLIP fold which is comprised of a four- or five-helix bundle, where a kink in the third helix can lead to occurrence of two helices. In total, four datasets of native crystals, as well as 29 datasets of crystals derivatised with 12 heavy atom compounds were collected. The structure was solved with Pt-SIRAS. The structure shows that initial membrane contact of the monomeric Na-SLP-1 is most likely by electrostatic interactions between the membrane surface and a prominent basic surface patch.


Struggling to complete an interval session? Got a few nagging pains on the bike? Dealing with low energy levels? Coach Chris Mayhew with JBV Coaching is here to help you get proper help in today's Training Tuesday column.
Training shouldn't be unpleasant. Cyclocross is really nice in that a majority of the pre-season training takes place when the weather is nice and the days are long. However, I have had some experiences that have really driven home the truth that if training causes you pain (as opposed to just the discomfort of going hard), it's a sign that something is wrong. You shouldn't have to endure or hope the pains will get better. "If you keep doing the same thing you keep getting the same thing" is some of best advice I've ever received. If some aspect of your training is working, that's great! Keep it. But if it's not, don't be glued to it. Try something different and seek some help, because there's probably a solution to your problem other than what you're currently doing.
The first example when you're dealing with pain while training. For weeks my knees had been killing me. Then it slowly started working up into my hips, then down to my feet. I could mediate the pain with yoga or foam rolling, and each individual day wasn't that bad, but after weeks on end it wasn't getting better and was cumulatively becoming more uncomfortable. Then, after talking with Jeff Jacobs, it occurred to me I couldn't remember the last time I'd purchased new insoles for my summer cycling shoes. It turns out I was long past due to replace them. When I finally did, the change in comfort after buying some was immediate.
As a practical point, keep track of when you purchase consumable items like that. Shoes, insoles, cleats and saddles wear out over time. I've taken to writing the date I buy insoles on the bottom of them, for easy reference. All those contact points can wear out and the changes can creep up on you over time. If you're experiencing discomfort or pain, check the basics and make sure nothing is worn out.
Related to contact points and wear items, never be afraid to evaluate your fit. I've taken to asking all my clients on intake "when's the last time you had a fit and who did it?" If the answer is anything less than "last year with local respected fitter" I try and steer them in the direction of a fit. There are so many good resources out there these days, there's really no excuse to not get one. Even though they're not cheap, in our expensive sport, the cost is worth it and needs to be viewed in context of the value you place on injury-free or pain-free riding, not as an expense that keeps you from buying a new tubular tire. What good is a new tire if you're injured and can't race it?
A good fit will enable you to ride longer and harder with more comfort. We all have had nagging issues on the bike, and most pains can potentially be addressed by a fit. Fit isn't a static thing either. We change as we age and as we engage in different activities, and that comes out in our form on the bike. Years of yoga allowed me to get back to the position I'd had when I was in my 20's. The last few months of Crossfit seem to have limited some of my flexibility. Because of this change, I raised my stem 5mm and became so much more comfortable. This small change allowed me to use the drops much more. Even if you've had a fit it's good to reevaluate it from time to time, especially if you're experiencing new pains.
An expert opinion can help you in aspects of training beyond just bike fit and training plans. Recently I, and some my clients, have been struggling to get through rides or finish intervals strongly. I hired Kristen Arnold to look at my nutrition and it's been an area of huge gains for me. I've been able to do more work per week than in years past. Additionally, working with her has enabled me to recover from rides a lot faster.
So many athletes have to transition directly from a hard ride to family obligations other activities. In that scenario, proper nutrition goes a long way towards enabling recovery and a positive mood. This pays back doubly because a happy family means it's less stressful to get out for a quick ride at some other point down the road. Calories make everyone happy, more or less. Make sure you're consuming enough to train, and more importantly, to be human afterward.
Don't be afraid to bring someone else in to have a look at what you're doing and consuming. Objective eyes are always a plus, even if they're telling you things you already know, and they can hold you accountable. As with fit, small changes can often make a big difference.
Why don't people seek help? Cyclists are taught to be tough. We crash and get right back into the race. We ride a million miles and get up again and do it again the next day, day after day. It's ingrained in the sport to some extent to shrug things off and keep going. And that feeds right into the Type A personality many of us have. Sayings like "Ain't got time to bleed" and "What doesn't kill us makes us a stronger" ring through our brains. We see it as weakness to admit we have a problem we can't solve and to seek out help. However, perspective helps. As I often counsel clients, you can spend a couple of days off the bike now, when it doesn't really matter, dealing with this, or you can spend a month off the bike in July, when it does matter, trying to deal with the damage that's already done. Deal with whatever issues you're having now when they're not that big, and when they're more easily dealt with.
Don't see seeking help as weakness. Think of it as spending time on yourself, like a day at the spa. No one thinks you're weak because you got a massage, do they?
A few hours with your bike fitter is no different than dropping your clothes off with a tailor. Do you think of Dr. Kristen Keim's long list of clients (including at least three cyclocross national champions) as weak? What's really stronger: bonking on every ride because you don't want to fuel sufficiently, or seeking some help so you can smash your way through the end of every ride? The strength and bravery is in admitting your weakness, being vulnerable, and seeking help, not in being tough and riding yourself into injury or hampering your training load.
If you can remove the obstacles to your training, day in and day out, you'll be able to put maximum effort into the intense workouts. I'm a big fan of Jocko Willink for some pre-ride inspiration, but whatever it takes, make the most of your intervals and specific training. If you're out there to smash it, smash it. If you can't bring intensity on a hard effort day, maybe it's time for something else that day, or nothing at all. The intensity of your work, or the overall volume of your training, should be where the toughness comes into play. Don't be pretend-tough and wind up hampering your daily and weekly training loads. That almost never ends well in the long run. As I'm fond of telling runners, that's how running makes cyclists.
Seeking help will make you stronger. Get some people around you who can get some expert eyes on you and the things you're trying to change, and make the most of what you're doing as a result.
Can't get enough? Browse all of our Training and Technique Tuesday pieces here from coaches Mayhew and others. Mayhew expects to contribute Training Tuesday installments every two weeks in the off-season.


In same start position and with same weight, turn palm forward and raise to 3 on right and 9 on left, thumb toward ceiling. slowly lower back to 6 straight with the feet.
Next, raise arms to your side, slightly in front of you. Do one arm at a time, bringing right arm to 2 and left to 10. This is more advanced that is why we only do one arm at a time. be careful and again if there is pain only go as high as you can without pain. Slowly you can regain your range of motion in many cases.
This can help with pinched nerves, arthritis, frozen shoulders and muscle tightness! Good Luck!
I have been suffering from a slight shoulder happened due to lifting bed when we were changing the settings of the room. And i used to do these exercises they are really effective.


Discus and support Update Error in Windows 10 Installation and Upgrade to solve the problem; my pc was updated automatically and now it shows me an annoying message every time it says error code 0x80096004. How can I get rid of that message?... Discussion in 'Windows 10 Installation and Upgrade' started by BrianMorris9, Apr 15, 2019 at 11:12 PM.
my pc was updated automatically and now it shows me an annoying message every time it says error code 0x80096004. How can I get rid of that message?
^ what they said will both work. i suggest updating directX, and in the future please try and list the exact error message... and i want a muffin.
Can't update to windows 10 with Iso error 0xC19100101?
update failed error code 0x80246008.


text:
Q: Powershell: how to backup a list of databases I have a script which successfully backups all databases in SQL Server:
cd SQLSERVER:\SQL\MyServer\DEFAULT\Databases
foreach($database in (Get-ChildItem))
{
$dbName = $database.Name
Backup-SqlDatabase -Database $dbName -BackupFile "C:\Backup\$dbName.bak"
}

I want to to backup a limited list of databases, instead of all of them.
How do I do that?

A: You need the list that you want to backup, or some way to filter the databases, and then just toss a simple If/Then in there.
cd SQLSERVER:\SQL\MyServer\DEFAULT\Databases
$DBList = Get-Content 'C:\Path\To\DBList.txt'
foreach($database in (Get-ChildItem))
{
    $dbName = $database.Name
    If($DBList -contains $dbName){
        Backup-SqlDatabase -Database $dbName -BackupFile "C:\Backup\$dbName.bak"
    }
}

Or you can alter the If/Then to use some logic if you prefer (every DB that starts with VM):
If($dbName -like "VM*")

or everything that references Server008 or Server006
If($dbName -match ".*?Server00(6|8).*")

A: cd SQLSERVER:\SQL\MyServer\DEFAULT\Databases
foreach($database in (Get-ChildItem))
{
    $dbName = $database.Name
    If ($dbName -eq "databaseName" –OR $dbName -eq "anotherDatabaseName")
    {
        Backup-SqlDatabase -Database $dbName -BackupFile "C:\Backup\$dbName.bak"
    }
}

A: You can set the names of the databases in the $arrDBName.
$arrDBName = @("Name1","Name2","Name3")
cd SQLSERVER:\SQL\MyServer\DEFAULT\Databases
foreach($database in (Get-ChildItem))
{
$dbName = $database.Name
If ($arrDBName -contains $dbName) {
    Backup-SqlDatabase -Database $dbName -BackupFile "C:\Backup\$dbName.bak"
}
}


Alfred Welch, the 'A' of A. Welch & Sons was born in 1876. Like his father and grandfather before him Alfred became a coachman. Alfred married Ellen Tritton and they had 8 sons and 2 daughters. In time 5 of the sons joined their father in business, and so A. Welch & Sons was born, carrying out household removals, taxi work and supplying horses, carriages and coffin bearers to the four local funeral directors in Herne Bay.
One of the sons, Harold, also assisted one of the funeral directors, initially with coffin making and later with arranging and conducting funeral services. When the sons returned from the second World War, and, in 1948 the family decided to undertake funeral arrangements in their own right alongside the other work the company was doing.
When motor vehicles replaced the horse and carriage our stables were converted into workshops, timber stores and a Chapel of Rest. In 1960 the decision was taken to concentrate solely on funerals. Our premises were continually updated and improved, refrigerated storage facilities and an embalming theatre were installed and we became the first fully equipped funeral directors in the Herne Bay, Beltinge and Canterbury district. During the seventies we had 4 private viewing chapels and a private service chapel built. In 1994 we opened a second branch in Canterbury.
Our premises undergo regular improvements and modernisation. 2012 saw the completion of an extensive refurbishment of our Mortuary and Chapel facilities. Our funeral vehicle fleet is regularly replaced and we currently run a fleet of bespoke Ford vehicles purchased in 2016. A. Welch & Sons remains a family owned, independent funeral directors. The current Managing Director is Tim Welch, Alfred's great-grandson. Mr. Peter Welch, Alfred's grandson, is retained as a valuable consultant following his retirement in 2006, having served 40 years in the business.
We have three full-time funeral directors, six full-time funeral service operators, a full-time Pre-Paid funeral specialist, two part-time receptionists and an in house bereavement counsellor. We consider it a great privilege when we are entrusted with arranging a funeral for a family. We are also very aware of the huge responsibility we have to that family. A funeral is one of the most important, stressful and emotional experiences a family or individual has to endure so it is essential that the arrangements are handled professionally.
All our funeral directors are fully qualified members of the BIFD (The British Institute of Funeral Directors) and hold the Diploma in Funeral Directing. Tim Welch, the current Managing Director is also a fully qualified embalmer and member of the BIE ( British Institute of Embalmers). In addition, We are members of the NAFD (National Association of Funeral Directors) giving our clients the peace of mind that we operate within the NAFD's strict Code of Practice Principles and giving them access to the Funeral Arbitration Scheme.
Our philosophy is a simple one: every funeral we arrange is the most important funeral we have ever conducted because it is so important to you. Every person whose funeral arrangements are entrusted to us is somebody's son or daughter, and, in most cases somebody's mother or father so we care for them as we would want our own children or parents cared for.
It is a fact that a funeral will always be a sad occasion but that doesn't mean that it has to be miserable. A funeral should be a celebration of that person's life, a time to remember the joy they brought into your lives and the happiness they shared with you in their life. It is our aim to help you achieve that goal and assist you to make the funeral service as comforting as possible.
We are always glad to Help and Advise.
We can guide you through the whole process, using the experience we have gained by arranging 28,000 funerals in the last 70 years, but ensuring that you retain control of how the funeral is to be conducted.
I am the 4th generation of the Welch family to be entrusted with running the family company. I joined A. Welch & Sons Ltd in 1992 as a driver/bearer. I qualified as an embalmer in 1996 and was accepted as a member of the British Institute of Embalmers. I then studied for the Diploma in Funeral Directing, passed those exams in 2004 and became a licensed member of the BIFD.The driving force behind our business is customer service. I am constantly aware of the huge responsibility we have to our clients and my aim is to make the process of arranging and attending the funeral of your loved one as easy and as comforting as possible through maintaining high professional standards, continually looking for ways to improve our services and, perhaps most importantly, simply caring deeply about the funerals we provide and the families we serve.
I started my funeral career in 1990 at the Cooperative Funeral Service and am now in my nineteenth year within the profession. I joined A Welch & Sons Ltd. in 2000.On joining A. Welch & Sons I was given the opportunity to study for the Diploma in Funeral Directing and successfully passed the examinations in 2004. This has also enabled me to become a Licensed Member of the British Institute of Funeral Directors - The BIFD.
I have since enjoyed the friendly family atmosphere that the company promotes from the staff right through to the families we look after. Working to provide an excellent service, with the highest standards of customer care, guidance and help for families at a very stressful time of their lives is what provides the rewards that drive me to excel within this profession.
I started my career in the funeral profession in 2003 when I joined A Welch & Sons as a driver/bearer. In 2011 I was given the opportunity to become a Funeral Director and started to study for the Diploma in Funeral Directing.I successfully completed the course in March 2013, was awarded my Diploma and also became a Licensed Member of the British Institute of Funeral Directors. I enjoy the friendly atmosphere in which I work and it reflects in the way we look after the families who use our services.We make sure that we give families as much help and guidance as possible, through what is a very upsetting and distressing time. Providing our clients with guidance and comfort at this stressful time is what makes the job so worthwhile and very rewarding for me.
On leaving school I knew I wanted to pursue a career in counselling. I attended Canterbury College study A level Psychology, Biology and English. On completion of my A levels life took me on different path resulting in me starting a family so my career took a back seat.I started working at A Welch & Sons, initially as an administrator. I decided to embark on a Diploma Course in Grief and Bereavement Counselling in 2010. I completed this course successfully and received my qualification in 2012.
I have enjoyed working as part of the 'Welch team' since 2009. We provide an excellent service to our families at a time of great stress and vulnerability and our aim is to keep that service at the highest possible standard. Part of that service can now continue beyond 'the funeral'.As a counsellor I aim to provide individuals and families, if necessary, support and help at a time it is often most needed but also often over looked: after the funeral when life is supposed to go 'back to normal' but very often doesn't.
Read more about our Bereavement Counselling service. For Free consultation please call us on 01227 374 995 or Send us an E-mail.
We're very proud of our brand-new Ford fleet but we are also able to organise mobility vehicles and vintage vehicles so please speak to us about your requirements and we'll always do our best to meet them.


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