text:
\section{Introduction}
\label{sec:introduction}
It has been a problem of longstanding theoretical and practical interest to model reaction pathways and transition mechanisms in generic chemical and biological systems.\cite{juraszek2013efficient,tiwary2017and,niu2018molecular,tsai2019reaction,lee2016multiple,roca2018monovalent,prinz2011markov} Due to recent progress in high performance computing, brute-force Molecular Dynamics (MD) simulations with all-atom resolution have enabled a possible way to do such analysis in femtosecond temporal and all-atom spatial precision, making it a useful tool for studying diverse phenomena. However this leads to a deluge of data resulting from explicit enumeration of all atomic coordinates over a very large number of MD timesteps. To make sense of such high-dimensional trajectories resulting from MD, it is a common practice to project them along low-dimensional coordinates identified with one of many dimensionality reduction schemes.\cite{piana2012protein,best2005reaction,hummer2015optimal,tribello2019using} However, more often that not in such schemes one ends up losing the kinetic connectivity of the high-dimensional landscape. This can thus lead to incorrect interpretation of MD trajectories, for example making molecular conformations appear closer to each other than they are and obfuscating interconversion pathways between them.\cite{altis2008construction} \\

In this work, we develop a formalism that learns a multi-dimensional yet minimally complex reaction coordinate (RC), such that when projected along this RC, all possible kinetically relevant pathways can be demarcated and the true high-dimensional connectivity is maintained. The central idea is to calculate the interconversion times between different pairs of metastable states, which can be defined \textit{a priori} or learnt on-the-fly,\cite{smith2018multi} and monitor how these distances change by adding additional dimensions to the RC. The procedure is stopped when the interconversion times do not vary with additional RC components. The interconversion times are calculated using the commute distance framework proposed by No\'{e}, Clementi and co-workers.\cite{noe2015kinetic,noe2016commute} While such a kinetic or commute distance based procedure is indeed already recommended best practice in the construction of Markov State Models (MSMs),\cite{husic2018markov} it is not directly amenable to rare event systems that might be undersampled, or accessible only through biased simulations. \\

To deal with this issue, in this work we combine the the commute distance\cite{noe2016commute,noe2015kinetic} with the Maximum Caliber based ``Spectral Gap Optimization of Order Parameters (SGOOP)" approach.\cite{tiwary2016spectral} This amounts to inducing a distance metric, which we call ``SGOOP-d" that preserves  kinetic truthfulness, and can be calculated from long unbiased simulations as well as biased simulations. Such biased simulations are often unavoidable in the study of rare events in chemical and biological physics. Here we use metadynamics\cite{valsson2016enhancing} as an example of the biasing method to illustrate the usefulness of SGOOP-d, while anticipating that the method directly applies to other biasing protocols as well.\cite{tiwary2016review}  We demonstrate the utility of the method by studying a range of model systems including conformational transitions in a small peptide Ace-Ala$_3$-Nme. In this system for instance, one has a total of at least 28 inter-state transitions. As we show here, with only two component-RC learnt from SGOOP-d we do accurately capture most of the 28 pairs of distances, with minimal improvement achieved by adding a 3rd component to the RC. Similar results are obtained on the basis of input trajectories coming from metadynamics simulations biased along pre-selected biasing variables.
Open-source software detailing the method has also been released.

\begin{figure}[t!]
  \centering
  \includegraphics[width=9cm]{flowchart}
  \caption
  { This flowchart describes the calculation of the $m$-th RC component $\chi^{(m)}, m \geq 1$ through multi-dimensional spectral gap optimization\textcolor{black}{. For each $m$ we calculate $d^{(m)}$} in Eq.~\ref{eq:cd_2RCs}, which represents the contribution to commute distance on the basis of this $m$-th component. The optimal RC $\chi^{(m)}$ will be fed to the next SGOOP calculation for finding $d^{(m+1)}$. This iteration will stop when we obtain convergence in state-to-state $d^2_{\rm comm}$ values with addition of RC components.
  The commute distance $d^2_{\rm comm}$ will be the sum of all the $d^{(m)}$ obtained in the iteration.
}\label{fig:flowchart}
\end{figure}

\section{Theory}
\label{sec:theory}
\subsection{Commute Distance and Commute Map}
\label{sec:commuted}
Our work builds upon the powerful advances first introduced by Clementi, No\'{e} and co-workers that allow quantifying a kinetically truthful distance metric between generic molecular configurations.\cite{noe2015kinetic,noe2016commute} One such notion of ``kinetic distance" was introduced in Ref. \onlinecite{noe2015kinetic}, which was then generalized in Ref. \onlinecite{noe2016commute} as the ``commute distance". Both of these distances amount to transformations of the input coordinate space into a new space wherein Euclidean distances directly correspond to interconversion times. Here we summarize the basic ideas which originated from diffusion maps~\cite{nadler2006diffusion,coifman2005geometric} but were later generalized to Markovian dynamics.\cite{noe2015kinetic,noe2016commute}

We consider a generic dynamical system undergoing Markovian dynamics in a finite state space $\Omega$. The local density $\rho_t(\mathbf{x})$, $\forall\mathbf{x}\in\Omega$ can be propagated in time $t$ through
\begin{align}
\rho_{t+\tau}(\mathbf{y})=\int_{\mathbf{x}\in\Omega}\rho_{t}(\mathbf{x})p_{\tau}(\mathbf{y}|\mathbf{x})d\mathbf{x} \equiv \mathcal{P}\circ\rho_{t}(\mathbf{x})
\label{eq:propagator}
\end{align}
where $p_{\tau}(\mathbf{y}|\mathbf{x})$ is the transition density of finding the system at state $\mathbf{y}$ at time $t+\tau$ given that we have started it at state $\mathbf{x}$ at time $t$. Equivalently, Eq. \ref{eq:propagator} defines a Markov operator $\mathcal{P}$ and describes how an initial distribution $\rho_t(\mathbf{x})$ at time $t$ propagates to the distribution $\rho_{t+\tau}(\mathbf{y})$ at a later time $t+\tau$. One usual assumption made here is that there exists a unique equilibrium distribution $\pi(\mathbf{x})$ which satisfies
\begin{align}
\pi(\mathbf{x})=\mathcal{P}\circ\pi(\mathbf{x})
\label{eq:stationary_state}
\end{align}
At the same time, we can write an equivalent equation for the weighted density $\nu_t(\mathbf{x})=\rho_t(\mathbf{x})/\pi(\mathbf{x})$
\begin{align}
\pi(\mathbf{y})\nu_{t+\tau}(\mathbf{y})=\int p_{\tau}(\mathbf{y}|\mathbf{x})\pi(\mathbf{x})\nu_t(\mathbf{x})d\mathbf{x}=\mathcal{T}\circ\nu_t (\mathbf{x})
\label{eq:backward_propagator}
\end{align}
where $\mathcal{T}$ is the corresponding backward operator, also called the transfer operator. With this formalism, following the literature on diffusion maps\cite{coifman2005geometric} one defines a distance measure $D^2_{\tau}(\mathbf{x}_1, \mathbf{x}_2)$ between two points $\mathbf{x}_1, \mathbf{x}_2$ in the state space of a random walk as
\begin{align}
D^2_{\tau}(\mathbf{x}_1,\mathbf{x}_2)=\int_{\mathbf{y}\in\Omega}\frac{|p_{\tau}(\mathbf{y}|\mathbf{x}_1)-p_{\tau}(\mathbf{y}|\mathbf{x}_2)|^2}{\pi(\mathbf{y})}d\mathbf{y}
\label{eq:kd}
\end{align}
This definition can be seen\cite{coifman2005geometric} as equivalent to (a) preparing two ensembles initially located at $\mathbf{x}_1$ and $\mathbf{x}_2$, (b) letting them evolve by a lag time $\tau$, and then (c) computing the difference between the subsequently resulting probability distributions. In order to make use of Eq.~\ref{eq:kd}, one needs the transition density $p_{\tau}(\mathbf{y}|\mathbf{x})$. To facilitate its computation,\cite{noe2015kinetic} we assume that the transfer operator $\mathcal{T}$ has $N$ discrete eigenpairs and assume reversible dynamics/detailed balance $\pi(\mathbf{x})p_{\tau}(\mathbf{y}|\mathbf{x})=\pi(\mathbf{y})p_{\tau}(\mathbf{x}|\mathbf{y})$:
\begin{align}
&p_{\tau}(\mathbf{y}|\mathbf{x})=\sum^{N-1}_{j=0}\lambda_j(\tau)\psi_j(\mathbf{x})\pi(\mathbf{y})\psi_j(\mathbf{y})
\label{eq:eigendecomp}
\end{align}
where $\lambda_j$ and $\psi_j$ are the corresponding eigenvalues and eigenvectors of the transfer operator $\mathcal{T}$. This allows calculation of Eq.~\ref{eq:kd} directly as:
\begin{align}
D^2_{\tau}(\mathbf{x}_1, \mathbf{x}_2)=\sum^{N-1}_{j=1}(\lambda_j\psi_j(\mathbf{x}_1)-\lambda_j\psi_j(\mathbf{x}_2))^2
\label{eq:kd_2}
\end{align}
 In Eq. \ref{eq:kd_2} the summation starts at $j=1$ since the $j=0$ eigenvector for the transfer operator $\mathcal{T}$ is a constant in $\mathbf{x}-$space. By further integrating out the lag time $\tau$ in Eq.~\ref{eq:kd_2}, we can make Eq.~\ref{eq:kd_2} insensitive to the choice of the lag time, and in this way we arrive at the definition of the commute distance $d^2_{\rm comm}$:
\begin{align}
&d^2_{\rm comm}(\mathbf{x}_1, \mathbf{x}_2)=\int^{\infty}_{0}D^2_{\tau}(\mathbf{x}_1, \mathbf{x}_2)d\tau \nonumber \\
&=\sum^{N-1}_{j=1}\left(\sqrt{\frac{t_j}{2}}\psi_j(\mathbf{x}_1)-\sqrt{\frac{t_j}{2}}\psi_j(\mathbf{x}_2)\right)^2
\label{eq:cd}
\end{align}
where $t_j = -{\tau \over \text{ln } \lambda_j}$ is the relaxation timescale associated with $j$th eigenvector. Often one uses the rate ${k_j}^{-1}=t_j$ instead of the timescale.\cite{perez2013identification} Eq.~\ref{eq:cd} now has a Euclidean distance form and a direct physical meaning: it is approximately the averaged time the system spends to commute between two states.\cite{noe2016commute} The  distance $d_{\rm comm}$ is thus called the ``commute distance", and the associated mapping
\begin{align}
\mathbf{x} \mapsto ( \sqrt{\frac{t_1}{2}}\psi_1, ..., \sqrt{\frac{t_{N-1}}{2}}\psi_{N-1})
\label{eq:cmap}
\end{align}
is called the ``commute map".

Assuming that the dynamics in the $\mathbf{x}-$space is Markovian and fully sampled giving access to eigenvalues and eigenvectors of $\mathcal{T}$, we can then use Eq.~\ref{eq:cd} to calculate a Euclidean distance which approximates the commute time in the $\mathbf{x}-$space.  It is also worth pointing out that in Eq. \ref{eq:cd} the timescales follow $t_1 \geq t_2 \geq ... 0$, which implies that the commute distance increases monotonically with consideration of further eigenvectors of $\mathcal{T}$, and that there is an increasingly vanishing contribution from every additional eigenvector that we consider.
If such a distance can be obtained through Eq.~\ref{eq:cd}, it is very useful for analyzing high-dimensional trajectories arising from well-sampled simulations as shown for instance in Ref. \onlinecite{noe2015kinetic,noe2016commute}. However many if not most real-world applications are characterized by rare events, wherein the system stays trapped in the part of the configuration space it was initiated from and rarely visits other regions. Adequate and reliable sampling of the underlying configuration space thus remains a longstanding challenge in computational chemistry and physics. This implies that the eigenvectors and eigenvalues needed to evaluate the various terms in Eq.~\ref{eq:cd} are simply not available or far from reliable. In fact, the dominant first few components of the commute map could even serve as biasing coordinates along which the sampling could be enhanced through methods such as umbrella sampling, metadynamics or others. This brings out the inverse nature of the problem wherein constructing an accurate commute distance depends on sufficient sampling of the eigenvalues and eigenvectors of the transfer operator, but the sampling itself could benefit greatly from the knowledge of the commute map.

 \subsection{Calculating commute distances for rare events}
\label{sec:commuted_rare}

In this section we develop a formalism for obtaining commute distances in poorly sampled rare-event systems where access to $\mathcal{T}$ and its eigenvectors/eigenvalues is not straightforward. The central idea is to perform biased sampling to accelerate exploration of the configuration space. Here we use metadynamics as the biased sampling method, but the developed formalism should be more generically applicable. While this basic idea is simple, there are however, at least two major, immediate difficulties when applying Eq.~\ref{eq:cd} with metadynamics or other similar enhanced sampling methods. First, the use of any sort of biasing corrupts the kinetics of the system, critical to calculating accurate eigenvalues and eigenvectors of the transfer operator $\mathcal{T}$. Second, the biasing itself needs access to the slow modes of the system, which are the dominant components of the commute map in Eq. \ref{eq:cmap}. \textcolor{black}{In SGOOP, we find these slow modes from such transition matrix but only look at its dynamics along 1-d coordinate, where} we refer to these slow modes as the reaction coordinate (RC) for the system.\cite{ma2005automatic,bittracher2018data} As mentioned in Sec. \ref{sec:commuted} the different components $\psi_i$ of the commute map have a vanishing relevance to the calculation of the commute distance as $i \gg 1$, and thus one can stop after the first few dominant components and bias these components in any biasing method of choice. However, without knowing the commute map, it is hard to calculate the dimensionality and components of the RC which would then be biased.

 \subsubsection{Commute distance calculation for rare events with SGOOP}
 \label{sec:commute_with_sgoop}
In this sub-section we develop an approach that circumvents both of the above described challenges. Our work builds on the RC discovery method ``Spectral Gap Optimization of Order Parameters (SGOOP)".\cite{tiwary2016spectral,tiwary2017predicting,smith2018multi} Summarily, SGOOP in its original form is a method for obtaining a one-dimensional RC given static and dynamic information about a multi-dimensional system by combining these information in a maximum Caliber or path entropy framework.~\cite{presse2013principles,ghosh2020maximum} Here we use SGOOP to induce a commute distance metric for complex high-dimensional systems that can be calculated from a combination of biased simulations and short  unbiased trajectories. SGOOP constructs the RC as a combination of pre-selected candidate order parameters $(s_1, ..., s_d)$, which can be thought of as a set of basis functions using which we are trying to describe our problem. The dimensionality $d$ is kept high enough so that dynamics in the high-dimensional $s-$space is likely Markovian, needed for the formalism described in Sec. \ref{sec:commuted}. The central ideas behind SGOOP\cite{tiwary2016spectral} in its original form can be summarized as the following three points: \newline
(i) It uses a reweighting protocol\cite{reweighting_jpcb_2015} to estimate the equilibrium distribution $P_0(s_1, ..., s_d)$ from an initial metadynamics simulation performed by biasing some trial RC. \newline
(ii) In addition, it uses short unbiased MD simulations to obtain dynamical observables pertaining to the system. These observables could be the position-dependent diffusivity or more typically, number of nearest-neighbor transitions along some binned trial RCs.\newline
(iii) By combining (i) and (ii) SGOOP constructs transition rate matrices along different putative RCs.

Different candidate one-dimensional RCs are then ranked in terms of the number of metastable states they demarcate, and then in terms of the timescale separation (or the spectral gap) between the slow and fast modes as projected on any RC. The optimal RC maximizes both of these. We recently introduced a multi-dimensional version of SGOOP \cite{smith2018multi} which makes it possible to extend the dimensionality of the RC in SGOOP. Each additional RC component $\chi^{(i)},i\geq 2$ is constructed in a way that it captures features indiscernible in the previous components through a conditional probability factorization described in Sec. \ref{sec:sgoop_details}. This de-emphasizes the features already captured by the components so identified. With multiple iterations of the SGOOP protocol one can identify a multi-dimensional RC $\chi = \{ \chi^{(1)},\chi^{(2)},...\}$. Assuming that a satisfactorily large number of components have been included in $\chi$, any two points $\{ \mathbf{x},\mathbf{x'}\} \in\Omega$ can then be mapped without substantial loss  of information to its values in the $\chi$ space as $\{ \chi,\chi' \} $. Whether the dimensionality of the RC $\chi$ is indeed sufficient or not is a non-trivial question to answer, which we will address later in this section and in Sec. \ref{sec:results}. We can then reformulate Eq.~\ref{eq:cd} as
\begin{align}
d^2_{\rm comm}(\mathbf{x},\mathbf{x'})
&= d^2_{\rm comm}(\chi, \chi') \nonumber \\
& =\sum^{N-1}_{j=1}\frac{1}{2k_j}\left[\psi_j(\mathbf{x})-\psi_j(\mathbf{x}')\right]^2 \nonumber \\
& =\sum^{N-1}_{j=1}\frac{1}{2k_j^{(1)}}\left[\psi_j^{(1)}(\mathbf{x})-\psi_j^{(1)}(\mathbf{x}')\right]^2
\label{eq:d_comm2}
\end{align}
In the above equation we have made use of the mapping $\mathbf{x} \to \chi$ learnt from SGOOP, but otherwise it still needs the eigenvalues and eigenvectors of the transfer operator $\mathcal{T}$. In the final line we have introduced a superscript $(1)$ to indicate the case where the first RC $\chi^{(1)}$ learnt from SGOOP is indeed sufficient for the system at hand. In such a case, SGOOP yields a Maximum Caliber based rate matrix $K^{(1)}$ for transitions between grid points along  suitably discretized $\chi^{(1)}$. Details of the construction of this rate matrix are described in Sec. \ref{sec:sgoop_details} while illustrative examples are provided in Sec. \ref{sec:results}. By diagonalizing the rate matrix $K^{(1)}$ we obtain the eigenvalues $k_1^{(1)}, k_2^{(1)},...$ and corresponding eigenvectors $\psi_1^{(1)}, \psi_2^{(1)},...$ to use in Eq. \ref{eq:d_comm2}.

The above commute distance so obtained can be understood as an estimate of true commute distance using the 1-dimensional projected RC $\chi^{(1)}$.  However, as shown in Sec. \ref{sec:results} and also emphasized in the literature on numerous occasions,\cite{altis2008construction} a 1-dimensional projection is often not kinetically truthful and does not reflect the connectivity of underlying high-dimensional space. We thus consider additional RC components $\chi^{(m)}$ from the SGOOP protocol, with eigenvalues $k_1^{(m)}, k_2^{(m)},...$ and corresponding eigenvectors $\psi_1^{(m)}, \psi_2^{(m)},...$, where $m\geq 1$ denotes which RC component we are looking at. Each such component induces its own contribution to the commute distance which we add to the contribution of the 1st component $\chi^{(1)}$ in Eq. \ref{eq:d_comm2} yielding the central equation of this work for a $M-$component RC:
\begin{align}
&d^2_{\rm{comm}}(\mathbf{x},\mathbf{x}') \nonumber \\
&=\sum^{M}_{m=1}\sum^{N-1}_{j=1}\frac{1}{2k^{(m)}_j}\left[\psi_j^{(m)}(\mathbf{x})-\psi_j^{(m)}(\mathbf{x}')\right]^2 \equiv\sum^{M}_{m=1}d ^{(m)}
\label{eq:cd_2RCs}
\end{align}
Here $d ^{(m)}$ is the contribution to the commute distance arising from the $m^{th}$ RC component, while $k^{(m)}_j$ and $\psi^{(m)}_j$ are the $j^{th}$ eigenvalue and eigenvector of the Maximum Caliber-based transition matrix $K^{(m)}$ calculated along along RC-component $\chi^{(m)}$ (Sec. \ref{sec:sgoop_details}).

We want to mention two important points here. Firstly, for any RC component $\chi^{(m)}$ for $m\geq 1$, the construction of the rate matrix $K^{(m)}$ as detailed in Sec. \ref{sec:sgoop_details} ensures that the rates are ordered as per $0 < k_1^{(m)} \leq k_2^{(m)} \leq \textcolor{black}{...} $. This leads to a useful property that the commute distance is a strictly monotonically increasing function of adding further RC components as well as further eigenvectors along any RC component. By monitoring how $d^2_{\rm{comm}} = d ^{(1)} + d ^{(2)}+...$ converges with addition of RC components, we can quantify the dimensionality of the RC needed for a given system at hand.  Secondly, the intuitive idea behind going from Eq. \ref{eq:d_comm2} to Eq. \ref{eq:cd_2RCs} is that different eigenvectors are orthogonal to each other allowing for a Euclidean distance measure. This is strictly true for the SGOOP-derived eigenvectors along a given RC component, i.e. the dot product of $\psi_j^{(m)}$ and $\psi_k^{(m)}$ is 0 $\forall j,k,m \geq 0$ as mentioned in Sec. \ref{sec:sgoop_details}. However when comparing $\psi_j^{(m)}\textcolor{black}{(\chi_m)}$ and $\psi_k^{(n)}\textcolor{black}{(\chi_n)}$ for $m \neq n$ i.e. for different RC components through multiple rounds of SGOOP\cite{smith2018multi} this is not strictly true, and thus we expect Eq. \ref{eq:cd_2RCs} to be an upper bound for the commute distance.

\subsubsection{Rate matrix estimates from Maximum Caliber based SGOOP}
\label{sec:sgoop_details}

In this sub-section we discuss further details of the construction of the rate matrix $K^{(m)}$ through SGOOP, which is central to calculating commute distance in Eq. \ref{eq:cd_2RCs}. Mathematically this can be written as follows. Once the first RC component $\chi^{(1)}$ has been learnt by SGOOP, we focus our attention on the probability distribution $P_1$ conditional on the knowledge of $\chi$ defined as:
\begin{align}
P_1(s_1, ..., s_d)&\equiv P_0(s_1, ..., s_d|\chi^{(1)}) \nonumber \\
&=\frac{P_0(s_1, ..., s_d)}{P_0(\chi^{(1)})}
\label{eq:CPF}
\end{align}
where we have used that the equilibrium probability $P_0(s_1, ..., s_d,\chi^{(1)} )=P_0(s_1, ..., s_d)$ as $\chi^{(1)}$ is a deterministic function of $(s_1, ..., s_d)$. The next round of SGOOP is then performed on data sampled from $P_1$ instead of $P_0$, which yields the second RC component $\chi^{(2)}$ that captures features missed by $\chi^{(1)}$. The procedure can be repeated for further RC components and can be performed using any enhanced sampling method.\cite{smith2018multi} Here we illustrate it using metadynamics. By performing well-tempered metadynamics simulation along $\chi^{(1)}$ where one builds a bias $V_b (\chi^{(1)})$, it can be shown that
\begin{align}
P_0(\chi^{(1)})& \propto e^{-\beta F(\chi^{(1)})} \propto e^{+\beta[\frac{\gamma}{\gamma-1}V_b(\chi^{(1)})]} \nonumber \\
P_1 \equiv \frac{P_0(s_1, ..., s_d)}{P_0(\chi^{(1)})}& \propto e^{-\beta[F(s_1, ..., s_d)+V_b(\chi^{(1)})]}
\label{eq:P0P1}
\end{align}
where $\beta=1/k_B T$, $\gamma$ is the bias factor for well-tempered metadynamics,\cite{valsson2016enhancing} and $F$ is the free energy of the system. Therefore, $P_1$ is simply the unreweighted/biased probability density obtained by sampling in the presence of bias potential $V_b (\chi^{(1)})$.
Following the strategy proposed in Ref. \onlinecite{smith2018multi}, the rate matrix along any putative RC $\chi$ can be built as follows:
\begin{align}
K^{(1)}_{mn}=
\begin{cases}
\textcolor{black}{-}\frac{\langle N\rangle}{\sum\sqrt{\pi_n\pi_m}}\sqrt{\frac{\pi_n}{\pi_m}}, & \text{if } n\neq m \\
-\sum_{k\neq m} K_{mk}^{(1)}, & \text{if } n=m
\end{cases}
\label{eq:sgoop_rate1}
\end{align}
where $\langle N\rangle$ is the total number of nearest-neighbor transitions per unit time, counted along a suitably discretized RC $\chi = \{\chi_n\}$ with $n$ indicating grid index and $\pi \equiv P_0 $ is the corresponding stationary density. For the first round of SGOOP to learn $\chi^{(1)}$, $\langle N\rangle$ is calculated from short unbiased MD simulations. The $K^{(1)}$ matrices are then constructed for different putative RCs and its eigenvalues used to screen for the best RC $\chi^{(1)}$ with highest spectral gap, as well as the eigenvalues and eigenvectors along this RC to be used in Eq. \ref{eq:d_comm2}.

For learning the second component $\chi^{(2)}$ and other higher order components, we generalize Eq. \ref{eq:sgoop_rate1} as follows:\cite{smith2018multi}
 \begin{align}
K^{(2)}_{mn}=
\begin{cases}
\textcolor{black}{-}\frac{{\langle N\rangle}^{(1)}}{\sum\sqrt{\pi_n^{(1)}\pi_m^{(1)}}}\sqrt{\frac{\pi_n^{(1)}}{\pi_m^{(1)}}}, & \text{if } n\neq m \\
-\sum_{k\neq m} K_{mk}^{(2)}, & \text{if } n=m
\end{cases}
\label{eq:sgoop_rate2}
\end{align}
In Eq. \ref{eq:sgoop_rate2}, $\pi^{(1)} \equiv P_1 $ is defined in Eq. \ref{eq:P0P1}. $\langle N\rangle^{(1)}$ denotes the average number of first-nearest neighbor transitions along a putative RC observed per unit time, but now measured in the biased simulation performed by sampling from this conditional probability density $P_1$. The procedure can then be easily generalized for constructing rate matrices $K^{(3)},K^{(4)},...$ for learning further RC components.  As mentioned previously in Sec. \ref{sec:commute_with_sgoop}, by diagonalizing the rate matrix $K^{(i)}, i\geq 1$ we obtain the eigenvalues $k_1^{(i)}, k_2^{(i)},...$ and corresponding eigenvectors $\psi_1^{(i)}, \psi_2^{(i)},...$ to use in Eq. \ref{eq:d_comm2}.

\section{Results}
\label{sec:results}
In this section we demonstrate the usefulness and reliability of the  SGOOP\cite{tiwary2016spectral,smith2018multi} based commute distance\cite{noe2015kinetic,noe2016commute} protocol developed in Sec. \ref{sec:theory}, which we label ``SGOOP-d" for convenience,  by applying it to a range of analytical potentials, as well as to small molecules with rare conformational transitions between different metastable states. Low-dimensional projections of these high-dimensional potentials can in general lead to a spurious number of barriers and inter-basin connectivity.\cite{altis2008construction,tsai2020learning} Here we show how to use SGOOP-d to ascertain the minimal dimensionality of the RC that preserves the kinetic aspects of the underlying high-dimensional landscape. To do so we calculate the state-to-state commute distances, and monitoring how these change and eventually converge with increase in RC dimensionality. This is done using either biased or long unbiased simulations. We can also use the RC so learnt to perform further efficient and reliable biased simulations. We consider different types of unbiased and biased trajectories to demonstrate the general applicability of our proposed framework. Numerical and computational details of these systems have been provided in the Supplementary Information (SI).

\begin{figure*}[t!]
  \centering
  \includegraphics[width=0.9\textwidth]{dK_3s4s}
  \caption
  {(a)-(c) show the analytical 3-state and 4-state potentials 4A, 4B respectively.
  In (a)-(c) we have also provided the two RC components  $\chi^{(1)}$ (solid red lines) and $\chi^{(2)}$ (dashed blue lines) evaluated using Eq.~\ref{eq:dK}. Contours in all plots are separated by $k_B T$. In (d)-(f) the estimated commute distances $d_K$ between different pairs of states (in arbitrary units) are plotted as function of $K$, where the benchmark parameter $K^{\ast}$ in each case is specified as the vertical black dashed line. The insets in (d)-(f) show the commute distance between each metastable states at $K=K^{\ast}$. As explained in Sec. \ref{sec:analytical}, using $K=K^{\ast}$ gives the right kinetic connectivity between different metastable states for each of the model potentials.
}\label{fig:dK_3s4s}
\end{figure*}

\begin{figure*}[t!]
  \centering
  \includegraphics[width=0.9\textwidth]{dK_aladip}
  \caption
  {(a) Free energy surface as function of $\phi$ and $\psi$ obtained by reweighting metadynamics simulation biasing along 1-d RC $\chi^{(1)}$ specified in Table. \ref{tab:RCala} . The positions of three metastable states are specified. (b) shows the corresponding $d_K$ as a function of $K$ for each pair of metastable states obtained from the biased simulation. (c) shows the same information generated from a long unbiased simulation. In both (b) and (c) the benchmark parameter $K^{\ast}$ is shown through a vertical black dashed line, while empty circles correspond to the expected best estimates of commute distances.}
  \label{fig:dK_aladip}
\end{figure*}

\begin{figure*}[t!]
  \centering
  \includegraphics[width=0.9\textwidth]{dK_alatetra}
  \caption
  {In this figure, (a) provides the molecular structure of Ace-Ala$_3$-Nme with the corresponding dihedral angles. The corresponding metastable states are detailed in SI. (b) provides the estimated commute distances using one-dimensional, two-dimensional and three-dimensional RC respectively (blue  triangles, blue circles and blue squares, left axis). Corresponding to their calculation, these are labelled respectively $k^{(1)}_1d_{K=0}$, $k^{(1)}_1d_{K^{\ast}}$ and $k^{(1)}_1d_{K^{\ast},L^{\ast}}$ (in arbitrary units).  (b) also provides the estimated commute time $(t_{\rm comm}$ (red triangles, right axis) calculated from long unbiased simulation of Ace-Ala$_3$-Nme. }
  \label{fig:dK_alatetra}
\end{figure*}

\subsection{Analytical potentials}
\label{sec:analytical}
 The analytical potentials used here are originally inspired from Ref. \onlinecite{altis2008construction}. These are built with two degrees of freedom $x$ and $y$, but with varying number of metastable states and barriers separating them. Thus a 1-d projection is not always guaranteed to be kinetically truthful. Specifically we consider a 3-state potential and three 4-state potentials labeled 4A and 4B (Figs. \ref{fig:dK_3s4s} (a)-(c)). For each of these we build inter-state commute distances using one-dimensional and two-dimensional RCs, with different components expressed as linear combinations of $x$ and $y$. Since the underlying dimensionality is two, here we will demonstrate the results with up to two-dimensional RC.
In such a case we can simplify Eq.~\ref{eq:cd_2RCs} by introducing
\begin{align}
\hat{d}^{(m)}&=k^{(m)}_1d^{(m)}
\label{eq:simplify_dK}
\end{align}
and then writing
\begin{align}
d_{\rm comm}(\mathbf{x}_1, \mathbf{x}_2)&=d^{(1)}+d^{(2)} \nonumber \\
&=\frac{1}{k^{(1)}_1}\hat{d}^{(1)}+\frac{1}{k^{(2)}_1}\hat{d}^{(2)}
\label{eq:cd_2RCs_1eval}
\end{align}

To see how good a job the RC components do at reconstructing the state-to-state connectivity, we further parameterize Eq.~\ref{eq:cd_2RCs_1eval} by using a tunable parameter $K$ for the ratio of eigenvalues $\frac{k^{(1)}_1}{k^{(2)}_1}$, yielding
\begin{align}
k^{(1)}_1 d_{\rm comm}(\mathbf{x}_1, \mathbf{x}_2) \equiv k^{(1)}_1 d_K\equiv\hat{d}^{(1)}+K\hat{d}^{(2)}
\label{eq:dK}
\end{align}
We highlight here that in our framework $K$ is not a free parameter that needs to be tuned. Instead, it can be approximated on the basis of Maximum Caliber based rate matrices (Sec. \ref{sec:sgoop_details}) as:
\begin{align}
K^{\ast}\equiv\frac{k^{(1)}_1}{k^{(2)}_1}
\label{eq:K_ast}
\end{align}
However, as the Maximum Caliber based rate estimates are approximate and might depend on choice of the dynamical constraints and quality of sampling,\cite{ghosh2020maximum} we can vary $K$ around $K^{\ast}$ and ascertain the sensitivity of the calculation of commute distance with respect to the accuracy of $K$.

Fig.~\ref{fig:dK_3s4s} and Table. \ref{tab:RC3s4s} detail the two RC-components $\chi^{(1)}$ and $\chi^{(2)}$ so obtained for the different model potentials. Here using $K=0$ is equivalent to using only the first component $\chi^{(1)}$ to determine the commute distance, while increasing non-zero values of $K$ captures increasing contributions from the second component $\chi^{(2)}$ through Eq. \ref{eq:dK}. As can be seen for the 3-state system (Fig. \ref{fig:dK_3s4s} (d)), considering only the first component $\chi^{(1)}$ would lead to an erroneous conclusion that the pairs of states AB, AC and BC are all kinetically equidistant. This is not consistent with the high-dimensional data sampled shown in Fig. \ref{fig:dK_3s4s} (a), where the barrier experienced between the states BC is much lower than for AB and AC. By adding the second component $\chi^{(2)}$ to the kinetic distance in Eq. \ref{eq:dK} using $K=K^{\ast}$, we recover this correct picture. Furthermore the picture is relatively insensitive to the exact choice of $K^{\ast}$ thereby showing the robustness of the procedure to possible inaccuracies in the Maximum Caliber estimate. Similar conclusions regarding kinetically truthful picture consistent with the data can be drawn for the remaining three 4-state potentials shown in Fig. \ref{fig:dK_3s4s}.  In both Fig. ~\ref{fig:dK_3s4s} (e) and (f), using only the 1-d RC $\chi^{(1)}$, AB, BC, and CD are equally short, while AD is the slowest transition. This erroneous connectivity has been corrected after adding a second component of RC $\chi^{(2)}$, where AB and CD are equally shortest at $K=K^{\ast}$. Note that in both insets AD is slightly lower which shows the noisy nature in the Maximum Caliber based estimation of transition rates.

\begin{table}[]
    \centering
    \begin{tabular}{|c|c|c|c|}
    \hline
         \multicolumn{2}{|c|}{Systems} & $\theta^{(1)}/\pi$ & $\theta^{(2)}/\pi$ \\ \hline
         \multicolumn{2}{|c|}{3-state} & 0.00  & 0.21 \\ \hline
         \multirow{3}{*}{4-state}
         & 4A (Fig. \ref{fig:dK_3s4s}(b)) & 0.15 & 0.84  \\ \cline{2-4}
         & 4B (Fig. \ref{fig:dK_3s4s}(c)) & 0.15 & 0.84 \\ \hline
    \end{tabular}
    \caption{ In this table, we have shown the first and second components of the reaction coordinate $\chi^{(1)}$ and $\chi^{(2)}$  found for each model analytical potential. The angles $\theta^{(1)}$ and $\theta^{(2)}$ in the table define $\chi^{(i)}=\cos(\theta^{(i)})x+\sin(\theta^{(i)})y$.
    }
    \label{tab:RC3s4s}
\end{table}

\begin{table*}[]
    \centering
    \begin{tabular}{|c|c|c|}
    \hline
         Systems & RCs & Coefficients \\ \hline
         \multirow{2}{*}{Alanine dipeptide}
         & $\chi^{(1)}$ & $(0.643,0.778,-0.133,-0.088,-0.221,-0.165)$ \\
         \cline{2-3}
         & $\chi^{(2)}$ & $(0.827,1.166,-0.120,0.578,0.013,0.240)$ \\ \hline
         \multirow{3}{*}{Ace-Ala$_3$-Nme}
         & $\chi^{(1)}$ & $(0.187, -1.127, -0.228, -2.362, 0.230, 1.176)$ \\
         \cline{2-3}
         & $\chi^{(2)}$ & $(1.174, 0.738, 0.132, 0.716, 0.356, 2.827)$ \\
         \cline{2-3}
         & $\chi^{(3)}$ & $(-0.037, -0.839, 0.557,  1.454,  1.693, 1.624)$ \\
         \cline{2-3}
         \hline
    \end{tabular}
    \caption{ This table shows the reaction coordinates found for alanine dipeptide and Ace-Ala$_3$-Nme. For alanine dipeptide, two RC components both expressed as $\chi=a\cos\phi+b\sin\phi+c\cos\psi+d\sin\psi+e\cos\theta+f\sin\theta$ with their 6 respective coefficients are listed. For Ace-Ala$_3$-Nme, three RC components all expressed as $\chi=a\cos\phi_1+b\sin\phi_1+c\cos\phi_2+d\sin\phi_2+e\cos\phi_3+f\sin\phi_3$ with their 6 respective coefficients are listed.
    }
    \label{tab:RCala}
\end{table*}

\subsection{Alanine dipeptide}
\label{sec:aladi}
The next system we use to illustrate our method is the well-studied alanine dipeptide. Here we consider the molecule as characterized by three dihedral angles $\phi$,$\psi$ and $\theta$. This molecule has three metastable configurations (Fig. \ref{fig:dK_aladip}(a)) which can be characterized by using only $\phi$ and $\psi$, while $\theta$ plays a role in characterizing the transition between the metastable states.\cite{tiwary2013metadynamics} Here we express the different RC components as linear combinations of 6 order parameters, namely cosines and sines of the 3 aforementioned dihedrals, with the final optimized coefficients listed in Table. \ref{tab:RCala}. The spectral gap in SGOOP is optimized using a basin-hopping algorithm.~\cite{wales2003energy,wales1997global,li1987monte} These RC components and associated information are then plugged into Eq. \ref{eq:dK} to estimate the commute distance $d_K$. In Figs. \ref{fig:dK_aladip}(b)-(c) we show the commute distance so calculated using an input biased trajectory and a benchmark long unbiased trajectory respectively. The biased trajectory was generated by doing well-tempered metadynamics along 1-d RC $\chi^{(1)}$ defined in Table. \ref{tab:RCala}. See SI for further details of both the biased and unbiased simulations.

For this simple system, the commute distances $d_K$ show similar connectivities for $K=0$ and $K=K^{\ast}$, which shows that one RC is indeed sufficient to describe the system in terms of recovering state-to-state connectivity between all 3 metastable states. Both types of input trajectories show a near degenerate structure with two pairs of states kinetically separated from each other, while one pair very close.

\subsection{Ace-Ala$_3$-Nme}
\label{sec:alatri}
 In this final section, we demonstrate our method on a more complicated molecular system, namely the peptide Ace-Ala$_3$-Nme with a much larger number of metastable states, and an even larger number of state-to-state transitions.~\cite{rydzewski2020multiscale} Simulation details are provided in SI. As discussed in Ref.~\onlinecite{rydzewski2020multiscale} the three dihedral angles $\phi_1$, $\phi_2$, $\phi_3$  are sufficient to characterize the $2^3=8$ dominant metastable states corresponding to positive and negative parts of the Ramachandran diagram for the 3 central Alanine residues. The RC components used in computing SGOOP-d distances are calculated as linear combination of cosines and sines of these 3 dihedral angles, thereby amounting to a total of 6 order parameters. We consider the 8 most dominant metastable states labelled $S_1$,..., $S_8$ and the associated $\binom{8}{2} = 28$ inter-state transitions. The corresponding dihedral angles for these 8 states are tabulated in the SI. Here we consider up to three RC components, and demonstrate that after considering 3 components the commute distances converge especially for the slower state-to-state transitions.  They are also in agreement with the benchmark calculations on this system through counting transitions in the higher dimensional underlying space from a long unbiased trajectory.  The final optimized solutions for all three RC components are shown in Table.~\ref{tab:RCala}. Here in order to add a third RC component we generalize Eq.~\ref{eq:dK} by introducing an additional parameter $L$:
\begin{align}
    k^{(1)}_1 d_{K,L}\equiv\hat{d}^{(1)}+K\hat{d}^{(2)}+L\hat{d}^{(3)}
\label{eq:dK3}
\end{align}
Similar to what was done for $K^{\ast}$ in Eq. \ref{eq:K_ast} we can approximate $L^{\ast}$ as
\begin{align}
    L^{\ast}\equiv\frac{k^{(1)}_1}{k^{(3)}_1}
\label{eq:L_ast}
\end{align}
With a long enough unbiased MD trajectory, we can also calculate the commute time $t_{\rm comm}$ between two metastable states through a simple counting protocol (see SI and Ref.~\onlinecite{tsai2020learning}). In Fig.~\ref{fig:dK_alatetra}, we show SGOOP-d distances calculated using Eq. \ref{eq:dK3} with 1, 2 and 3 RC components, and compare them with the corresponding 28 $t_{\rm comm}$ values between these 8 metastable states in the same plot. It can be seen from plot that with only the use of two RC components SGOOP-d already provides a good estimate of relative inter-state connectivity and commute distances between 23 of the 28 pairs of states. However, in order to get the correct connectivity for the remaining 5 pairs of states as well, we have to include the third RC component. We emphasize that in Fig. \ref{fig:dK_alatetra} the slowest 8 transitions have the same reference commute time as we were to observe any such transition events even in the 1 $\mu$s long unbiased simulation. Thus the reference commute times for these states serve as approximate lower bounds to the true values.

\section{Conclusion}
\label{sec:conclusion}
In summary, in this work we have developed a computationally efficient formalism labeled "SGOOP-d" and summarized in the flowchart in Fig. \ref{fig:flowchart}, that can help towards solving a longstanding important problem in chemical physics and physical chemistry. Namely, how many dimensions should a projection from high-dimensions into low-dimensional reaction coordinates (RC) have, so that (1) the projection is kinetically and thermodynamically truthful to the underlying landscape, and (2) these minimal number of components can then be used to perform biasing simulations without fear of missing slow degrees of freedom. The formalism here makes the best of two different approaches, namely commute map \cite{noe2016commute} and SGOOP \cite{tiwary2016spectral}. This way it induces a distance metric which we call SGOOP-d that is applicable to biased rare event systems as well as unbiased trajectories with arbitrary quality of sampling. The kinetically truthful RC learnt here can then also be used to improve the sampling quality of the biased simulation itself\cite{bussi2020using} or as a progress coordinate in path-based sampling methods.\cite{zuckerman2017weighted,elber2020milestoning,votapka2017seekr,jiang2018forward,defever2019contour} We thus believe that going forward our work represents a useful tool in the study of kinetics in rare event systems with multiple states and interconnecting pathways.

\section{Acknowledgments}
\label{sec:acknowledgements}
The authors thank Yihang Wang, Dedi Wang, Luke Evans, Shashank Pant, En-Jui Kuo and Yixu Wang for discussions. This work was supported by the National Science Foundation, Grant No. CHE-2044165. ZS was supported by University of Maryland COMBINE program NSF award DGE-1632976. Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research (PRF 60512-DNI6). We also thank Deepthought2, MARCC and XSEDE (projects CHE180007P and CHE180027P) for computational resources used in this work. SGOOP and SGOOP-d code are available at \url{github.com/tiwarylab}.

\bibliographystyle{unsrtnat}

redpajama_set_name: RedPajamaArXiv


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redpajama_set_name: RedPajamaCommonCrawl


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text:
Drives-U-Crazy
Used Everywhere
Vancouver Auto Show: It's Not Just About Glitz on Wheels…
by Alexandra Straub on Monday, March 23rd, 2015
"You can still get a great vehicle, with a fully warranty, AND some perks for under $20,000…"
Subaru Impreza Sedan ($19,995)
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Contact: alexandra [dot] straub [at] drivewaybc [dot] ca
Andrew Ross { Enjoyed your Forest of Bowland in the BMW X5M, particularly the photo of the BMW in front of the main part of Stonyhurst College where... }
Davd Randall { Bantam designed the Jeep, not Willy's or Ford. The American military gave the original Bantam prototype to Willys and Ford to copy. There is plenty... }
Elliott Parodi { All Escalades come with a 6.2-lilter V8 engine that produces 420 horsepower. A six-speed automatic is the only transmission offered and drives the rear wheels.... }
Ev { Alexandra is an excellent journalist. }
Journey to a 'Sparkling' Luxury Okanagan Resort "Four lucky readers will put a Dodge Journey's weekend-... 20 comments
The Need For Speed: Hike Those Highway Limits More than half of those polled believe the province sho... 18 comments
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Readers Respond: The Pros and Cons of Increasing B.C. Speed Limits Increasing the speed limits will only increase risk to... 9 comments
Honda CR-V Review: The Compact Crossover To Get Things Done The CRV is a very stylish and aerodynamic crossover veh... 8 comments
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My heart dropped when I heard thoughts of the podcast going away! Please never every have those thoughts again! JD I love your pod casts!
My heart dropped when I heard thoughts of the podcast going away! Please never ever have those thoughts again. JD, I love your pod casts!
Thank you Dusty! We never really talked about what went down but we probably will. Thank you for your support.


mind to acquire property. He is sacrificing his eternal interest for treasures upon the earth. He believes the truth, he loves the principles of truth, and loves to see others prospering in the truth; but he has made himself so thoroughly a slave to mammon that he feels bound to serve this master as long as he shall live. But the longer he lives the more devoted will he become to his love of gain, unless he tears away from this terrible god, money. It will be like tearing out his vitals, but it must be done if he values heaven.
He needs the censure of none, but the pity of all. His life has been a terrible mistake. He has suffered imaginary pecuniary want, while surrounded with plenty. Satan has taken possession of his mind and, exciting his organ of acquisitiveness, has made him insane upon this subject. The higher, nobler powers of his being have been brought very much into subjection to this close, selfish propensity. His only hope is in breaking the bands of Satan and overcoming this evil in his character. He has tried to do this by doing something after his conscience has been wrought upon, but this is not sufficient. This merely making a mighty effort and parting with a little of his mammon, and feeling all the time that he is parting with his soul, is not the fruit of true religion. He must train his mind to good works. He must brace against his propensity to acquire. He must weave good works into all his life. He must cultivate a love for doing good, and get above the little, penurious spirit which he has fostered.
God is blasphemed by some on account of this close, penny dealing. Angels turn away in disgust. Everything in heaven is noble and elevated. All seek the interest and happiness of others. No one devotes himself to looking out and caring for self. It is the chief joy of all holy beings to witness the joy and happiness of those around them.
When these angels come to minister to those who shall be heirs of salvation, and witness the exhibition of selfishness, of covetousness, of overreaching, and benefiting self at others' disadvantage, they turn away in grief. When they see those who claim to be heirs to an immortal inheritance so penurious in dealing with those who do not profess any higher ambition than to be laying up treasures on earth, they turn away in shame; for holy truth is reproached.
In no way could the Lord be better glorified and the truth more highly honored than for unbelievers to see that the truth has wrought a great and good work upon the lives of naturally covetous and penurious men. If it could be seen that the faith of such had an influence to mold their characters, to change them from close, selfish, overreaching, money-loving men to men who love to do good, who seek opportunities to use their means to bless those who need to be blessed, who visit the widow and fatherless in their affliction, and who keep themselves unspotted from the world, it would be an evidence that their religion was genuine. Such would let their light so shine that others seeing their good works would be led to glorify their Father which is in heaven. This fruit would be unto holiness, and they would be living representatives of Christ upon the earth. Sinners would be convicted that there is in the truth a power to which they are strangers. Those who profess to be waiting and watching for the appearing of their Lord should not disgrace their profession by bantering in deal and standing for the last penny. Such fruit does not grow upon the Christian tree.
Brother I, the Lord is not willing that you should perish, but would rather that you should take hold of His strength and make peace with Him by a conformity of your will to His divine will. If a faithful picture of your course in money getting could be presented before you, you would be terrified. You would be disgusted with your closeness, your penuriousness, your love of money. You would make it the effort of your life to obtain the transforming grace of God, which would make you a new man. The means which came to you from relatives was a curse to you. It only increased your money-loving propensity, and was an additional weight to sink you to perdition.
"The love of money is the root of all evil." When men employ their powers of mind and body in obtaining riches, and are content with the pleasure of laying up wealth which they can never use, and which will prove an injury to their children, they abuse the powers which God has given them. They show that their characters have been made sordid by the absorbing pursuit of gain. Instead of realizing happiness, they are miserable. They have shut up their souls to the wants of the needy, and have given evidence that they had no compassion for the suffering.
I: What are you going to do with your money? You are God's steward. You possess talents of means and can do much good with them. You can deposit in the bank of heaven by being rich in good works. Bless others with your life. "Lay not up for yourselves treasures upon earth, where moth and rust doth corrupt, and where thieves break through and steal: but lay up for yourselves treasures in heaven, where neither moth nor rust doth corrupt, and where thieves do not break through nor steal: for where your treasure is, there will your heart be also."
Remember that the treasures laid up in heaven are not lost. They are secured to yourselves by a judicious use of the means of which Heaven has made you stewards. "Charge them that are rich in this world," says the apostle, "that they be not high-minded, nor trust in uncertain riches, but in the living God, who giveth us richly all things to enjoy; that they do good, that they be rich in good works, ready to distribute, willing to communicate; laying up in store for themselves a good foundation against the time to come, that they may lay hold on eternal life."
last, you will know what proved your ruin--the love of money. You will cry in bitter anguish: "Oh, the deceitfulness of riches! I have lost my soul. I sold it for money. My soul and body I bartered for gain. I sacrificed heaven, fearing that I should have to sacrifice my money to obtain it." From the Master will be heard: Take ye the unprofitable servant, bind him hand and foot, and cast him into outer darkness. We hope this will not be your fate. We hope you will remove your treasure to heaven, and transfer your affections, and fasten them upon God and the immortal treasure.
I have seen that the entire family were in danger of partaking, in a degree, of the father's spirit. Sister I, you have already partaken of this spirit. God help you to see it and make an entire change. Cultivate a love for doing good; seek to be rich in good works. In many things you can do more than you do. You have an individual responsibility before God. You have a duty to do, from which you cannot be excused. Maintain a close walk with God; pray without ceasing. You will have close work if you save your soul. Seek to have a counteracting influence in your family. Take your stand nobly for God. Your organization is unlike your husband's, and you will be condemned of God unless you act for yourself. Make diligent work in saving your own soul, and in exerting an influence to save your family. Let your example show that your treasure is in heaven, that you have invested all in a better home and a better life, which are eternal. Train your mind to value heavenly things, to be elevated, to love God, and to manifest a willing obedience to His will.
faith. Much more depends upon you than you realize. You should put the armor on. Spend not your precious strength in exhaustive labor which another can do. Encourage your daughter to engage in useful employment and to aid you in bearing the burdens of life. She needs discipline. Her mind is vain. She needs to render all to God; then she can be useful and please her Redeemer.
My sister, work less, and pray and meditate more. Eternal interests should be primary with you. God forbid that your children should be molded into money lovers. True refinement and gentleness of manners can never be found in a home where selfishness reigns. The truly refined always have brains and hearts, always have consideration for others. True refinement does not find satisfaction in the adornment and display of the body. True refinement and nobility of soul will be seen in efforts to bless and elevate others. The weight of eternal things rests very lightly upon your children. May God arouse them before it shall be too late, and they exclaim in anguish: "The harvest is past, the summer is ended, and we are not saved."
Brother J, your case was presented before me. You occupy a responsible position. You are entrusted with talents of money and of influence. To every man is given a work-- something todo, not merely to engage his brain, bone, and muscle in common labor; it means more than this. You are acquainted with this work from a worldly point of view, and have some experience in it in a religious capacity. But for a few years past you have been losing time, and now you will have to work fast to redeem the past. To possess talents is not enough; you must so use them as to advantage not merely yourself but Him who bestowed them. All that you have is a loan from your Lord. He will require it again at your hand with interest.
Christ has a right to your services. You have become His servant by grace. You are not to serve your own interest, but the interest of Him who has employed you. As a professed Christian you are under obligations to God. It is not your own property that is entrusted to you for investment. Had it been so, you might have consulted your own pleasure in regard to its use. The capital is the Lord's, and you are responsible for its use or abuse. There are ways in which this capital can be so invested--put out to the exchangers--that it shall be earning the Lord something. If it is allowed to be buried in the earth, neither the Lord nor you will be benefited, and you will lose all that was entrusted to you. May God help you, my brother, to realize your true position as God's hired servant. By His own suffering and death He has paid the wages to secure your willing service and ready obedience.
During the trials of the past few years, you have suffered in mind, and have felt it a relief to turn your attention more fully to the things of the world, to the work of acquiring property. God, in His great love and mercy to you, has again gathered you into His fold. New duties and responsibilities are now laid upon you. You have a strong love for this world. You have been laying up treasures upon the earth. Jesus now invites you to transfer your treasure to heaven; for where your treasure is, there will your heart be also. In all your deal with your brethren and with unbelievers, guard yourself. Be true to your profession, and maintain true nobleness of soul, which shall be a credit to the truth which you profess.
ones lack in many things, and if they are faithful in the humble service the Master requires of them they will have all that they can do. They cannot afford to waste their time in anxiously fearing lest their neighbor, who has a larger work entrusted to him, shall fail to do his work well. While they are so interested in the case of another, their own work is neglected, and they are really slothful servants. They were anxious to do their neighbor's work instead of that committed to themselves to do.
They think that if they only had the five talents to handle, they could do much better than the one to whom these talents were entrusted. But the Master knew better than they. None need mourn that they cannot glorify God by talents He never gave them and for which they are not responsible. They need not say: "If I were in another's position in life I would do a great amount of good with my capital." God requires no more of them than to improve upon what they have, as stewards of His grace.
The one talent, the humblest service, if wholly consecrated, and exercised to promote the glory of God, will be as acceptable as the improvement of the weightiest talent. The varied trusts are proportioned to our varied capabilities. To every man is given according to his ability. None should slight his work, considering it so small that he need not be particular to do it well. If he does this he trifles with his moral responsibilities and despises the day of small things. Heaven apportions to all their work, and it should be their ambition to do this work well, according to their capabilities. God requires that all, the weakest as well as the strongest, fulfill their appointed work. The interest expected will be in proportion to the amount entrusted.
interested in watching their brethren, and for this reason are constantly weak. They will bear testimony in meeting, and because they have not Jesus in their hearts to confess, they will try to impress upon their brethren their duty. These poor souls do not know their own duty, and yet they take the responsibility of enlightening others in regard to their duty. If such would attend to their own work, and obtain the grace of God in their hearts, there would be a power in the church which is now lacking.
Brother J, you can do good. You possess good judgment, and God is leading you out of darkness into the light. Use your talents to the glory of God. Put them out to the exchangers, that when the Master comes He may receive His own with usury. Break your tendrils from the valueless things of earth, and elevate them to entwine about God. The salvation of souls is of greater consequence than the whole world. One soul saved, to live throughout the ages of eternity, to praise God and the Lamb, is of more value than millions in money. Wealth sinks into insignificance when compared with the worth of souls for whom Christ died. You are a cautious man and will not move rashly. Sacrifice for the truth, and become rich toward God. May the Lord help you to move as fast as you should and place the right estimate upon eternal things.
Your children need a deeper work of grace in their hearts. They need to encourage sobriety and solidity of character. If consecrated to God, they can do good and exert an influence which will be saving upon their companions.
influence if they will cease their gossiping and devote their time to watchfulness and prayer. They can honor God. They can let their light so shine that others, by seeing their good works, will be led to glorify our Father which is in heaven.
As an illustration of the failure on your part to come up to the work of God, as was your privilege, I was referred to these words: "Curse ye Meroz, said the angel of the Lord, curse ye bitterly the inhabitants thereof; because they came not to the help of the Lord, to the help of the Lord against the mighty." Judges 5:23. What had Meroz done? Nothing. And this was their sin. They came not up to the help of the Lord against the mighty.


Google is letting parents snoop on their kids' school work with a new feature for Google Classroom.
When a teacher invites a parent to Classroom, they can see daily and weekly summaries of what their child has accomplished, and view any class announcements. Now parents won't be taken by surprise when it comes time to have that annual parent-teacher conference.
The Classroom app is also allowing annotations, making lessons more interactive and (probably) fun. Google likens it to a portable whiteboard, and notes it's useful for those times a student may be out of the classroom.
Similarly, teachers can annotate homework with notes and examples rather than static text.
Rounding it all out, Google is adding new experiences to its Expeditions app which allows kids to go on a digital field trip of sorts. Rather than just places on a map, experiences like a journey through the human vascular system are now available — which sounds gross, but is probably more memorable than pictures in a textbook.


text:
Greg Stanton
Mayor, Phoenix
(David Kidd)
In 2011, a sociologist at New York University wrote a book that called Phoenix "the world's least sustainable city." The next year, Greg Stanton became mayor. He treated the book not as an insult but as the template for an urban agenda.
Phoenix was the kind of city it had been for decades: a sprawling, car-oriented metropolis economically dependent on the real estate industry. It prospered during the housing boom and suffered worse than most places when real estate values plummeted and construction slowed in the Great Recession. The city was also poised to experience some of the worst possible effects of climate change -- temperatures even hotter than usual, more frequent droughts and parched soil. The city's water came from a distant and dwindling source: the Colorado River.
The most brilliant political leader in the world couldn't make Phoenix as green as Boston or Seattle. But under Stanton, the city has taken significant steps in the direction of sustainability. It sought to cut its greenhouse gas emissions 15 percent by 2015, and achieved that goal by replacing 90,000 energy-wasting streetlights with LED bulbs, making municipal buildings more energy efficient and converting more of the methane released from city landfills into electricity. Stanton now wants to reduce emissions 40 percent by 2025. Earlier this year, when President Trump announced that the federal government would withdraw from the Paris Climate Agreement, Stanton was one of the first mayors in the country to announce that his city would keep its commitments to cutting back on energy use and air pollution.
Two years ago, while campaigning for a second term, Stanton also campaigned for a 35-year transportation package that would add 42 miles of light rail, more than 1,000 miles of bike lanes, 135 miles of sidewalks and expanded hours of bus service, at a projected price tag of $31.5 billion. It's not typical for politicians to push for a sales tax increase as they seek re-election. "My political consultants were not happy about that," Stanton says, "but it was the right thing to do." Voters said yes to both Stanton and his transportation agenda by comfortable margins.
Stanton frames his environmental policies as part of a broader goal of diversifying Phoenix's economy. Perhaps the clearest illustration of this green market-based philosophy is a business incubator supported by the city and Arizona State University. The school's campus houses burgeoning public-private partnerships that aim to help the city recycle materials that would otherwise go to a landfill. So far, firms have found ways to create new, profitable products from discarded mattresses, food waste and palm fronds. In five years, the city has doubled its waste diversion rate from 15 percent to 30 percent.
The 47-year-old Stanton, who has announced he will step down as mayor to run for Congress next year, likes to point out that his environmental policies have coincided with a booming local economy. Last year, Phoenix had the largest numerical increase in residents of any city in the country. Not only has the city unemployment rate steadily declined, but in the past year the Phoenix metro area saw the highest year-over-year wage growth in the nation. Tech jobs increased more than 18 percent and the number of tech companies downtown has quadrupled.
-- By J.B. Wogan
See the rest of the 2017 public officials here.
Content provided by Comcast: Robert Traynham's Newsmaker interview with Mayor Greg Stanton - Phoenix – A Sense of Place.


Matthew Leon White of Little Rock Arizona a broker formerly employed by MML Investors Services LLC has been fined $5,000.00 by Arkansas based upon consenting to the Arkansas Securities Department's findings that White sold away from his firm. Case No. S-18-0105 (Oct. 17, 2018).
According to the Order, prior to White having become registered with MML Investors Services, he established at least two real estate ventures. Those ventures were reportedly disclosed by White as outside business activities; however, he mischaracterized them as simple rental positions. Then, after joining MML Investors Services, White set up three additional real estate ventures. White evidently also mischaracterized those activities. The Order revealed that White's conduct was discovered after leaving the firm and attempting to register an investment advisory.
The Order indicated that White had actually engaged in private securities transactions. Particularly, White reportedly established and promoted the real estate ventures, involving the firm's customers as investors in the ventures. Apparently, White neither registered the ventures with SEC or sought an exemption from registration. Arkansas Securities Commissioner found that White's failure to disclose the private securities transactions in a matter which complied with FINRA Rule 3280 was violative of Rule 308.01(x) of the Rules of the Arkansas Securities Commissioner.
White was discharged by MassMutual on May 30, 2018 founded on allegations that his outside business activities had not been property disclosed by him to the firm.


This great mind power has been used for centuries because of its success in altering thought processes, causing events to happen, attracting money, and changing habits to improve one's health and life. In fact, visualization and meditation are techniques used often by elite athletes. For example, a major league baseball pitcher uses visualization exercises before a game by seeing himself on the pitchers mound throwing the ball, where it goes over the plate resulting in a perfect strike. The pitcher practices visualizing this scene in his minds eye over and over again. The day of the game, the pitcher throws a perfect pitch one after the other.
What do you do if you can't visualize? Easy all you have to do is use your other senses–feel, touch, smell and sense. For instance, if you are looking to take a vacation to Hawaii feel yourself relaxed with sand touching your toes and the wind blowing across your face. If you still are having trouble using your other senses, there is another way to accomplish the same objective–use affirmations and create visuals!
For instance, if you'd like to purchase a vacation home in Florida, find images of scenes from Florida in magazines, newspapers, and brochures. Cut the images out and paste them onto a calendar or a goal notebook. If you don't have the time to create your dream collage, you can also write-out affirmations that state exactly what you desire—"It is the year 2010, and I am sitting by my pool in West Palm Beach, Florida sipping on a nice cold Pina Colada." By doing these simple exercises, within a matter of days to weeks, you will find that you are a magnet for attracting friends and even strangers who are planning a trip to Florida, have just recently visited Florida, or are living in Florida. The more positive and focused you are the closer you will be to purchasing your vacation home. The key in fulfilling your dream is to not give up! Believe that you have the ability to manifest everything and anything you want.
You may want to check out Jack Canfield Visualize and Affirm Your Desired Outcomes: A Step-by-Step Guide too!
Like everything in life, it takes time. The more you practice the better you'll become with creating the life you desire with fewer trials and error.


text:
package net.glowstone.util;

import org.bukkit.NamespacedKey;
import org.junit.jupiter.api.Test;

import static org.hamcrest.core.IsEqual.equalTo;
import static org.junit.Assert.assertThat;

public class NamespacedKeyTest {

    @Test
    public void testFromStringWithKey() {
        String keyRaw = "minecraft:abc";
        NamespacedKey key = new NamespacedKey(keyRaw.substring(0, keyRaw.indexOf(':')),
            keyRaw.substring(keyRaw.indexOf(':') + 1, keyRaw.length()));
        assertThat(key.toString(), equalTo(keyRaw));
    }

    @Test
    public void testFromStringWithoutKey() {
        String keyRaw = "abc";
        NamespacedKey key = new NamespacedKey(NamespacedKey.MINECRAFT, keyRaw);
        assertThat(key.toString(), equalTo("minecraft:" + keyRaw));
    }
}

redpajama_set_name: RedPajamaGithub


The UN humanitarian chief says 1.25 million people in war-torn South Sudan are one step away from famine — twice as many as the same time last year.
Mark Lowcock told the UN Security Council that 7 million people in the world's newest nation — almost two-thirds of the population — need humanitarian aid.
And he warned that in early 2018, half of the country's population will be reliant on emergency food.
"The next lean season beginning in March is likely to see famine conditions in several locations across the country," Lowcock said.
UN peacekeeping chief Jean-Pierre Lacroix called the security situation in South Sudan "precarious."
He warned of escalating military conflict as the dry season sets in and urged the council to take action to stop the violence.


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Posted by Hrēodbēorht Bātweard in Uncategorized
Þyrs, Cerne, God, Goddess, Legend, Myth
The people of Cerne were a hardy folk, well used to surviving amongst the chalk hills of the Cerne valley that rose up from the river of the same name. They grazed their cattle and sheep upon the land and they showed their gratitude to the gods with their sacrifices and offerings in keeping with tradition. There rose, within Cerne, a well-spring from deep under the chalk hills, known to the locals as the Seolfor Cwylla and it carried with it fresh water that it was said could cure the ills of the local folk and could be depended upon to water the fields and provide sufficient refreshment for the cattle so that the people of Cerne would continue to thrive when the skies ran dry during the Summer months.
There lived nearby a crone, bent and twisted with age and she took a copse of trees for her home high in the hills above Cerne. She was said to be a gyden who had lived in the hills for longer than man could remember, tending to the wild places and keeping them free from maleficent wihta and outlaws. She was said to be very wise and knowledgeable in the ways of healing worts and their applications. The folk of Cerne named her as Helið and took her for a goddess of their own. They would leave their offerings to her at the site of where the Seolfor Cwylla reached the surface, and merchants would throw pieces of silver downstream to pay their respects to Helið as their wares were pulled from one marketplace to another throughout the Frome Valley of Dorset and beyond.
Cerne was a place of peace and plenty for many a year until the coming of a mighty Hyll Þyrs one night following a mighty thunderstorm. The Þyrs appeared from out of the trees, carrying an enormous club hewn from the trunk of an oak. He was naked and proudly so, staking his claim to a new home on one of the hills above the village. From his lofty perch he demanded the villagers present him with sacrifices from their finest stock, and when at first they refused, he slew their strongest warriors with a single sweep of his mighty club. The villagers succumbed to his demands and despaired, their flocks of sheep and oxen rapidly diminishing as the Þyrs gorged itself on their carcasses. At night its heavy footsteps could be heard and felt around the village as it helped itself to more livestock.
It became known that whilst the Þyrs was in possession of its club, the Þyrs could not be defeated. Warriors came from near and far to take on the Þyrs and each were summarily beaten, slain and consumed by the Þyrs of Cerne, as it became known. The villagers knew not where to turn. Then one night the Þyrs discovered the Seolfor Cwylla, pushing aside the underbrush and attempts by the villagers to disguise their pure water source and, having developed a terrible thirst from the consumption of so many of the beasts of burden belonging to the villagers, he then gorged himself on the pure waters of the Seolfor Cwylla and drained it dry in a single sitting.
And thus did he anger Helið, as he drank the waters that fed the copse of trees within which she dwelt. Her anger was terrible to behold and it was said that the beasts and birds of the Ūtangeard did fall silent as she smouldered with fury within the dying trees of her home. Yet it was from here that she plotted her revenge. From stiðe she wove a net, strong and durable; lacing it with a deadly poison. Waiting until the moon was full, she strode down from her home, casting a glamour all about her such that she shone with the radiance of the full moon, her hair appearing as pure as the silver waters from the Cwylla and her countenance was said to be as fair as Frīg herself.
The Þyrs was stood high on its hill, looking down at the village as he intended again to help himself to the cattle and livestock, his hunger once again upon him. Helið approached from the mouth of the wellspring, striding with apparent swiftness towards the Þyrs. It beheld her as she approached and was struck dumb by her intense beauty. Such was its arousal at her countenance that it lowered its mighty club, leaving itself open to her approach. Helið did not falter. She did not delay but cast the net she had created wide, throwing it upon the Þyrs as it stood enraptured, the bonds tightening about it and the poison setting to its task with startling rapidity. The Þyrs bellowed in pain and surprise, its legs giving way beneath it such that it fell against the hillside with a mighty crash, its head striking the chalky earth so hard that its skull did break. Helið stood watching in silence, gathering in the net she had woven and stowing it safely away. The Cerne Þyrs was dead, and from its broken head did pour the waters of the Seolfor Cwylla, leaking back into the chalk hill.
The folk of Cerne rejoiced in the death of the Þyrs and Helið strode back through the village, her glamour now failing as the moon's rays dissipated behind clouds, returning her countenance once again to that of the crone that she truly was. As she passed by the Seolfor Cwylla, the waters it had previously provided once again burst forth and with it returned the life and purity of the surrounding area. Helið returned to the hills to tend to the wild places once again, and the people of Cerne never again faced the threat of a Þyrs, marking the site of the dead creature by grinding its bones into the chalk beneath the grass of the hill which serving as a warning to others that here was one that met its end.
And the folk of Cerne created their idols to Helið in recognition of her deeds, and from that day until the coming of Augustine, they lived in harmony with one another and paid tribute to their goddess at the Seolfor Cwylla. Many now do not recall the deeds of Helið, but there are some that do and will always honour her. Should you pass through the village of Cerne in your travels, ensure you pay tribute to her at the Seolfor Cwylla, the Silver Well, which still runs to this very day through the heart of the village whilst the image of the defeated Þyrs remains imprinted for all time on the hill above it. On a moonlit night you may see her still, watching over the village and the hills above Cerne, bent and haggard with age and care, but determination burning from eyes of the purest silver.


text:
Announcement | March 23, 2020
Council for a Strong America Urges Congress to Address the Needs of Child Care in COVID-19 Response
The child care sector is a critical component of the economy and a crucial support for working families
Champions for America's Future
Council for a Strong America Applauds Bold Congressional Action in Response to COVID-19
Statement from Barry Ford on Organizational Response to COVID-19
Letter to USDA: Retired Admirals and Generals Urge Preservation of Healthy School Meals
Letters to Lawmakers
Council for a Strong America (CSA) urges Congress to continue to seek timely, bipartisan measures that address the COVID-19 health emergency that poses such a significant threat to our nation.
We applaud Congress for the action it has taken so far in working to mitigate this pressing health crisis. However, we implore Congress to continue to move forward with further action, and, in doing so, to prioritize addressing the urgent and potentially devastating effects COVID-19 will have, and is having, on child care.
Already in the midst of a child care crisis, our nation now faces the reality that child care providers, about 70 percent of which are small businesses, will suffer badly if not supported by Congressional action that will help them weather the economic challenges ahead.
The impacts of that grim possibility can't be overstated, not only for the providers themselves, but for the working families that contribute so much to our economy, including first responders and healthcare professionals. That's why it's critical for Congress to ensure that all remedies for small businesses and workers take into account the unique characteristics of child care providers.
Because most providers are small businesses, Congress should make sure that child care providers are eligible for any type of small-business assistance offered. For instance, Congress should clarify that charitable nonprofits are able to participate in the emergency Small Business Loan Program.
And, although most providers are small businesses, they're often early childhood educators first, and businesspeople second. That means that they'll need technical assistance and guidance to help them access any resources made available to them.
Finally, Congress should be sure to consider the other unique challenges of the child care industry, such as self-employed / independent contractors who aren't covered by unemployment insurance.
Congress could also give HHS the ability to re-allocate already appropriated CCDBG funds that have been returned to HHS by the states, as opposed to sending the funds to the Treasury Department. Such a measure would, again, direct funds to the areas of greatest need, while also not requiring new appropriations by Congress.
For these reasons and many others, Congress must ensure that child care providers continue to be able to serve working families and the communities in which they live. Any proposals must acknowledge the pivotal role that the child care industry will necessarily play in our collective societal and economic strength today and tomorrow.
As Congress endeavors to meet the ever-changing challenges associated with this public health emergency, we strongly urge lawmakers to remember to address the pressing, unique challenges associated with the child care industry. The steps that Congress takes now can and should maintain capacity for when our nation's working parents are able to return to work.
Council for a Strong America is a national, bipartisan nonprofit that unites five organizations comprised of law enforcement leaders, retired admirals and generals, business executives, pastors, and prominent coaches and athletes who promote evidence-based solutions that ensure our next generation of Americans will be successful, productive members of society.


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OG Latina Rapper From The West Coast
By Flakiss
The West Coast Queen returns stronger than ever
LOS ANGELES, Brizz Productions presents "24/7" the much anticipated new album from Latin Hip Hop sensation Flakiss. 24/7 will be her forth album, scheduled to be released to retail stores in March 2009. Her previous three records "Liberate", "Asi Soy" and "En Las Calles" were released on Univision Records.
Raised in the hard streets of South Central Los Angeles, Flakiss made her triumphant debut in 2004 with Liberate (Free Yourself) which placed her on the map as the first Latina Rapper out of the west coast. Flakiss is considered a voice for Latina empowerment and an advocate for women's equality, something that is needed in this community. She has recorded songs that brought to light topics that are considered taboo and too contriversal to talk about. Her songs resonate with the youth as they offer deep and meaningful narravites of life in the barriors of America. Due to this, she has become a house hold name and a "favorite" daughter of the Latino community in the United States.
In the competative world of Hip Hop which is widley dominited by male artists, Flakiss has held her own by performing and recording along side such heavywieghts as Down aka Kilo, Butch Cassidy, Kokane, Jae-P and David Rolas. She has helped promote the Urban Regional movement through out the world and has hosted her own morning radio show for "KOKO 94" FM in Fresno, California to the delight of many.
"Before I started writing this record I took some time to reflect on my life and made sure I searched really deep and wrote from the heart" says Flakiss "with this album, I want to give people hope, love and inspiration through my music. I got personal and wrote about my fame and family and about my deepest desire to have peace in the streets and to make this world a better tommorow for our childern." Flakiss adds, "I know the power music has on people and I want to contribute positively to society through my songs, I hope I can change the heart of someone that wants to commit a negative action, I want to touch them so deeply they can think about it twice."
Produced by platinum record producer and music impresario Byron Brizuela, 24/7 counts with 11 songs 7 of which Flakiss pen herself. This record is her best to date, containing a variety of contemporary urban beats; club bangers, regional urbano and songs that will thrill her long time fans and capture the admiration of new ones.
The album takes off with the up tempo cut "Girls Nite Out"(two versions) a song intended for her female fans and their party crews. The spirit felt "Always There" which is her most reflective work talks about her struggles with life and how she seeks forgiveness. "I Wanna Make It Better" is a ballad that focuses on a better world through peace and love. "Take it Easy" and "Lift Yo Head Up" are songs of hope and inspiration over phat 808 beats and sick synth stabs. "Ese Lo Que Es" and "24/7" boost her Hip Hop bravado in her native tongue Spanish, as only she can. The album also counts with three gems from the past "Friday Nite", "Ya Quisieras" and "Party Time" all redux for your listening and dancing pleasure.
"The aim of this record is to bring forth great songs, tight beats and a positive message" says Byron Brizuela "I believe she out did herself on this record I am very excited and thankful to be a part of it." Flakiss will be touring and promoting her album nation wide starting in February 2009.
"24/7" is due out in March 2009 in the United States. Under Rize High Records, distributed nationwide by Select-O-Hits.
Flakiss, first Westcoast Latina rapper to establish herself as a commercial success. The central theme around her albums "Liberate," "Asi Soy", "En Las Calles" and "24/7" focused on abuse, teenage pregnancy, machismo and girl power. Recently she had a leading role as Lala in the movie "End of Watch" which debut #1 at the U.S. box office.


Fellow blogger, hiker, lover-of-mountains-and-wild-places, portland-er, and fabulous writer Kim has had a weekly post focused on thanking life for all of it's greatness.
you can read my response to her here – and while you're there, you should read her stuff anyway, because she's really great.
and besides she and I having a mutual Portland friend and besides us being meant to be friends – her husband is a Sasquatch believer aficionado. Which makes both of them even cooler too.
So – thank you Kim. And of course…. thank you life (but you'll have to check out her blog to see my post!).
Thanks lady!!! I love your letter.