text:
\section{\label{sec:introduction}introduction}

Characterizing an unknown quantum state is of central importance in developing quantum technologies. Standard quantum state tomography (QST) reconstructs a generic quantum state by performing projective measurements on an informationally complete basis~\cite{white_nonmaximally_1999, JamesWhite2001}. The number of projective measurements required grows exponentially with the system size. In the meanwhile, current quantum technologies have pushed the number of qubits to close to one hundred~\cite{arute_quantum_2019, WuPan2021, ZhuPan2022}, and scalable quantum state tomography schemes are in great need. With additional assumptions on the underlying quantum state, more efficient schemes than the standard QST have been proposed. For example, QST for a sparse quantum state by compressive sensing~\cite{gross_quantum_2010,liu_experimental_2012, Smith_continuous_2013, Riofrio2017}, QST for quantum states which are permutationally invariant [\onlinecite{toth_permutationally_2010}, \onlinecite{moroder_permutationally_2012}], and QST for quantum states which can be efficiently represented with a low-depth parametric quantum circuit[\onlinecite{liu_variational_2020}]. In particular, QST methods based on tensor network representation \cite{cramer_efficient_2010,lanyon_efficient_2017} as well as neural network ansatz~\cite{torlai_neural-network_2018, torlai_latent_2018, carrasquilla_reconstructing_2019, ahmed_quantum_2021,smith_efficient_2021} are promising to extend QST to a much larger scale, and both approaches have been demonstrated on several tens of qubits based on synthetic data.

For an unknown $L$-qubit pure state that can be well approximated by a matrix product state (MPS), it is proved that a set of $O(L)$ local $n$-body reduced density matrices suffices to reconstruct the unknown state, where $n$ is a constant and independent of $L$ if the underlying state has bounded entanglement. Thus, only $O(\operatorname{poly}(L))$ number of measurements are required~[\onlinecite{cramer_efficient_2010}, \onlinecite{lanyon_efficient_2017}]. It has also been shown that a similar approach can be applied to reconstructing an unknown mixed state, with an additional assumption of its \emph{invertibility}~[\onlinecite{baumgratz_scalable_2013}]. However, such methods based on local density matrices are not easy to implement in practice, since (1) exact tomography of a series of local density matrices may be already hard, and (2) we can only reconstruct an approximation of each local density matrix from tomography using a finite number of measurements, and the approximation errors could accumulate and affect the overall tomography performance of the entire state. Another method based on an MPS ansatz is proposed using an unsupervised machine learning algorithm, where only global measurement data on a randomly prepared basis are required~\cite{wang_scalable_2020}. Such method however only considers the reconstruction of pure states. Neural network state based algorithms constitute another important class of heuristic approaches for QST with excellent precision and scalability in practice. Specifically, neural network states are used to model the pure states~\cite{torlai_neural-network_2018,rocchetto_learning_2018} and the density matrices~\cite{torlai_latent_2018} as classical neural networks; alternatively, they are used to model the output probability distributions~\cite{carrasquilla_reconstructing_2019} as classical neural networks. In the latter approach, it will generally be exponentially hard to further reconstruct the state as a vector or a density matrix from the probability distribution. In the former approach, one could efficiently compute amplitudes based on the trained neural network state, but for other tasks such as computing expectation values one still needs to perform a sampling process based on the trained neural network state, which may not be as convenient or efficient, if the underlying quantum state could be well represented as an MPS. Another possible drawback of the QST methods based on neural network states is, a priori, it is not clear which neural network representation is suitable for a given unknown state.

\begin{figure*}[htp]
    \centering
    \includegraphics[width=0.85\linewidth]{scheme.png}

\caption{A flowchart of our nonnegative tensor train state tomography algorithm. Given an unknown $L$-qubit quantum state $\hat{\rho}_s$, an IC-POVM is performed to obtain a sample of bitstrings $\{\bm{a}^j\}$, each of which is then encoded into a \emph{one hot} MPS $S^j$. Based on these $S^j$, an optimal MPS $P(\bm{a})$ with a fixed bond dimension is found through optimization, satisfying that it is the closest to the superposition of all state $S^j$. Then an MPO $\hat{\rho}$ is reconstructed, with the same bond dimension as $P(\bm{a})$, by applying the inverse of the IC-POVM locally on each site of $P(\bm{a})$. Simulations in this work are based on synthetic data.}

\label{fig:scheme}
\end{figure*}

Inspired by the fact that the MPS has been adapted to represent the multivariate probability distribution function, often referred to as the tensor train representation [\onlinecite{oseledets_tt-cross_2010}], we propose a QST scheme that combines the advantages of both the tensor network approach and the neural network approach. Specifically, in the first stage, a tensor train representation of the multivariate distribution function is constructed based on the quantum measurement data, instead of a neural network representation, and a density matrix renormalization group (DMRG)-like algorithm is used to find the optimal tensor train representation. After that, the tensor train is transformed back into a matrix product operator (MPO) representation of the unknown density matrix. Compared to the established QST methods based on tensor network states, our scheme directly uses a tensor train representation for the multivariate probability distribution function, instead of the unknown density matrix; compared to the established QST methods based on neural network states, our scheme constructs the unknown density matrix as an MPO, which usually allows more convenient and efficient evaluations of observables. The flowchart of our algorithm is summarized in Fig.~\ref{fig:scheme}. This work is organized as follows: we show the details of our QST scheme in Sec.~\ref{sec:method}, and then numerically demonstrate our algorithm for the ground state of the XXZ chain perturbed by depolarizing noise in Sec.~\ref{sec:results}, ended with a concluding discussion in Sec.~\ref{sec:conclusion}.

\section{\label{sec:method}Method}
For QST, we use quantum measurements given by informationally complete positive operator-valued measures (POVMs)~\cite{garcia-perez_learning_2021, Flammia_2006, Sosa_Experimental_2017}, which describes the most general quantum measurements allowed by quantum theory [\onlinecite{nielsen_quantum_2002}]. We denote the single qubit POVM as $\{M^s\}$, where $M^s$ is positive semi-definite satisfying $\sum_{s}M^s =\hat{I}$, where $\hat{I}$ is the identity matrix. For a single qubit, a minimal informationally complete POVM can be chosen as $M^s = \frac{1}{2}\ket{\psi^s}\bra{\psi^s}$ with
\begin{equation}
\label{equ:POVM}
	\begin{split}
\ket{\psi^0} &= \ket{0}, \\
\ket{\psi^1} &= \sqrt{\frac{1}{3}}\ket{0}+\sqrt{\frac{2}{3}}\ket{1}, \\
\ket{\psi^2} &= \sqrt{\frac{1}{3}}\ket{0}+\sqrt{\frac{2}{3}}e^{i\frac{2\pi}{3}}\ket{1}, \\
\ket{\psi^3} &= \sqrt{\frac{1}{3}}\ket{0}+\sqrt{\frac{2}{3}}e^{i\frac{4\pi}{3}}\ket{1},
\end{split}
\end{equation}
which form the vertices of a regular tetrahedron in the Bloch sphere [\onlinecite{renes_symmetric_2004}]. Such a single-qubit POVM, $\bm M=\{M^s\}_{s=0,1,2,3}$ can be viewed as a 3-dimensional tensor written as $M^{s}_{\sigma,\sigma'}$ with two physical indices $\sigma,\sigma'$ of dimension 2 and another index $s$ of dimension 4 corresponding to different measurement outcomes. If we reshape the single-qubit density matrix into a vector of size 4, then $\bm M$ becomes a $4\times4$ invertible matrix, representing a one-to-one mapping between the density matrix and the single-qubit probability distribution.

As in [\onlinecite{carrasquilla_reconstructing_2019}], for an $L$-qubit quantum system, we consider the quantum measurement defined by
\begin{equation}
    M^{\otimes \bm{a}}\equiv M^{a_1}\otimes M^{a_2} \otimes \dots \otimes M^{a_L} ,
\end{equation}
where $\bm{a}=(a_1,\ldots,a_L)$ represents a string of integers specifying the local projectors, and each integer $a_l \in \{0, 1, 2, 3\}$. The probability distribution $P(\bm{a})$ forms an $L$-variable distribution function in which each local dimension $d$ is equal to $4$, satisfying $P(\bm{a}) \ge 0$ and $\sum_{\bm{a}}P(\bm{a})=1$. Interestingly, if we assume that the unknown quantum state can be efficiently represented as an MPO
\begin{equation}
    \hat{\rho}=\sum_{b_1,b_2,...,b_{L+1}}W^{\sigma_{1},\sigma_{1}'}_{b_1,b_2}W^{\sigma_2,\sigma_{2}'}_{b_2,b_3} \dots W^{\sigma_L,\sigma_{L}'}_{b_L,b_{L+1}} ,
\end{equation}
where $b_l$ denotes the auxiliary index, then $P(\bm{a})$ can be written as an MPS
\begin{equation}\label{equ:pa}
    P(\bm{a})=\sum_{b_1,b_2,...,b_{L+1}}X^{s_1}_{b_1,b_2}X^{s_2}_{b_2,b_3} \dots X^{s_L}_{b_L,b_{L+1}} ,
\end{equation}
with each tensor $X^{s_l}_{b_l,b_{l+1}}=\sum_{\sigma_l,\sigma_{l}'}W^{\sigma_l,\sigma_{l}'}_{b_l,b_{l+1}}M^{s_l}_{\sigma_l,\sigma_l '}$. Therefore the bond dimensions of $P(\bm{a})$, which are defined as the dimensions of the auxiliary indices $D_l = \operatorname{dim}(b_l)$, are exactly the same as the bond dimensions of $\hat{\rho}$. Since $\bm{M}$ is invertible, we can efficiently transform back and forth between the density matrix $\hat{\rho}$ and the probability distribution $P(\bm{a})$. Here we choose to first construct $P(\bm{a})$ as an MPS, and then transform it back into a density matrix. One advantage of this approach is that as long as the constructed $P(\bm{a})$ is a proper probability distribution, then the density matrix $\hat{\rho}$ from this approach will automatically be Hermitian (which however may not be positive if there are not enough measurement data).

Thus the problem reduces to reconstructing an approximate probability distribution $P_s(\bm{a})$, based on a set of $N$ samples $\bm{a}^1, \bm{a}^2, \dots , \bm{a}^N$ collected from experiment. Assuming among those samples there are only $N_s$ different ones, which are denoted as $\bm{a}^1, \bm{a}^2, \dots , \bm{a}^{N_s}$, where each distinct sample $\bm{a}^j$ has multiplicity $n_j$, and each $\bm{a}^j$ appears with a probability $P_s(\bm{a}^j)=\frac{n_j}{N}$, $j=1,\cdots,N_s$. $P_s(\bm{a}^j)$ will eventually converge to the exact distribution $P(\bm{a})$ as $N$ increases. For a limited number of samples, the entries of $P_s(\bm{a})$ are approximately equal to the corresponding entries of $P(\bm{a})$. Therefore the original QST is reduced to the following mathematical problem: given some approximated values of the nonzero elements of an unknown $P(\bm{a})$, how can we construct a tensor train approximation of $P(\bm{a})$ with a minimum bond dimension $D$?

To this end, we note that each sample $\bm{a}^j$ can be encoded as a \emph{one hot} MPS:
\begin{equation}\label{equ:mapatoA}
    \bm{a}^j \mapsto S^j = \sum_{c_1, c_2, \dots , c_{L+1}}A^{s_1}_{j,c_1,c_2}A^{s_2}_{j,c_2,c_3} \dots A^{s_L}_{j,c_L,c_{L+1}} ,
\end{equation}
such that $\operatorname{dim}(c_l)=1$ and $\operatorname{dim}(s_l)=4$ for all $1\leq l\leq L$, and each tensor $A^{s_l}_{j,c_l,c_{l+1}}$ satisfies $A^{s_l}_{j,0,0} = 1$ iff $s_l$ equals to $a_l$, and $0$ otherwise. For a specific $\bm{a}^j$, if $a_l$ in $\bm{a}^j$ is 3 then $A^{s_l}_{j,c_l,c_{l+1}}$ satisfies $A^{0}_{j,0,0} = 0$, $A^{1}_{j,0,0} = 0$, $A^{2}_{j,0,0} = 0$ and $A^{3}_{j,0,0} = 1$.
With Eq.~(\ref{equ:mapatoA}) we can rewrite the probability distribution formed by $N$ samples as
\begin{equation}\label{equ:psa}
    P_s(\bm{a}) = \sum^{N_s}_{j=1}\frac{n_j}{N}S^j,
\end{equation}
where $P_s(\bm{a})$ can be viewed as a superposition of all one hot states $S^j$, weighted by the multiplicities. $P_s(\bm{a})$ can be directly taken as the best approximation of $P(\bm{a})$, that is, setting $P(\bm{a})=P_s(\bm{a})$, $P_s(\bm{a})$ can be directly evaluated from Eq.~(\ref{equ:psa}) using simple MPS arithmetics. However, given a limited set of samples, the bond dimension of the resulting MPS could be much larger than that of the target distribution. Moreover, this might result in an over-fitting problem, since $P_s(\bm{a})$ will be perfect for known samples but will be $0$ for unknown samples. For better efficiency and generalizability, one can search for $P(\bm{a})$ which is approximately equal to $P_s(\bm{a})$ under the condition that the bond dimension is bounded by a fixed value $D$. This could be done in two approaches [\onlinecite{schollwock_density-matrix_2011}]: (1) evaluating Eq.~(\ref{equ:psa}) exactly and then compressing the resulting MPS using SVD, and (2) iteratively searching for the solution to the following optimization problem
\begin{equation}\label{equ:fpa}
    \operatorname{Loss}(P(\bm{a})) \equiv \sum^{N_s}_{j=1} \left \| P(\bm{a}) - P_s(\bm{a}) \right \|^2 ,
\end{equation}
with a maximal bond dimension $D$, where $ \|P \|$ denotes the Frobenius norm of the tensor $P$. We will follow the latter approach which is more precise in practice. One complication here is that if one directly uses the approaches in [\onlinecite{schollwock_density-matrix_2011}], the MPS ansatz will be kept in a canonical form by iteratively using either singular value decomposition (SVD) or QR decomposition, and the solution generally contains negative values, which is undesirable for a probability distribution. To ensure the nonnegativity of $P(\bm{a})$, one could represent $P(\bm{a})$ as a nonnegative MPS instead, that is, each tensor $X$ in Eq.~(\ref{equ:pa}) is non-negative. Several algorithms have been proposed to approximate a target probability distribution using a non-negative MPS with a fixed bond dimension [\onlinecite{lee_nonnegative_2016},\onlinecite{shcherbakova_nonnegative_2019},\onlinecite{shcherbakova_nonnegative_Large-Scale_2019}]. Here we use a refined approach based on [\onlinecite{shcherbakova_nonnegative_Large-Scale_2019}], the central idea of which is to use a non-negative matrix decomposition instead of SVD or QR decomposition.

Specifically, we first define the following tensors $X^{>k}_{b_{k+1};s_{k+1}, \dots ,s_L}$ and $X^{<k}_{s_{1}, \dots ,s_{k-1};b_k}$:
\begin{subequations}
\begin{align}
&X^{>k} = \sum_{b_{k+2}, \dots , b_{L+1}}X^{s_{k+1}}_{b_{k+1},b_{k+2}} \dots X^{s_{L}}_{b_{L},b_{L+1}},\label{equ:xgk}\\
&X^{<k} = \sum_{b_1, \dots , b_{k-1}}X^{s_{1}}_{b_{1},b_{2}} \dots X^{s_{k-1}}_{b_{k-1},b_{k}},\label{equ:xlk}
\end{align}
\end{subequations}
and $G^{>k}_{b_{k+1},b_{k+1} '}$ and $G^{<k}_{b_{k},b_{k} '}$:
\begin{subequations}
\begin{align}
    &G^{>k}=\sum_{s_{k+1}, \dots ,s_L} X^{>k}_{b_{k+1};s_{k+1}, \dots ,s_L}X^{>k}_{b_{k+1} ';s_{k+1}, \dots ,s_L}, \\
    &G^{<k}=\sum_{s_1, \dots ,s_{k-1}} X^{<k}_{s_1, \dots ,s_{k-1} ; b_k}X^{<k}_{s_1, \dots ,s_{k-1};b_k '}.
\end{align}
\end{subequations}
With Eq.(\ref{equ:xgk}) and (\ref{equ:xlk}) we can rewrite $P(\bm{a})$ as
\begin{equation}\label{equ:newpa}
    P(\bm{a}) = \sum_{b_k,b_{k+1}}X^{s_k}_{b_k,b_{k+1}} X^{<k}_{ \dots ,s_{k-1};b_k} X^{>k}_{b_{k+1};s_{k+1}, \dots },
\end{equation}
for each $1\leq k\leq L$. Substituting Eq.~(\ref{equ:newpa}) into Eq.~(\ref{equ:fpa}), the loss function becomes $\left\| V-WH \right\|^2$, with $V = P_s(\bm{a})$, $W = X^{s_k}_{b_k,b_{k+1}}$ and $H = X^{<k}_{ \dots ,s_{k-1};b_k}X^{>k}_{b_{k+1};s_{k+1}, \dots}$. Thus the goal is to find the best non-negative factorization of $V$. One of the most well known approaches for solving this problem is the following updating rule
\begin{subequations}
\begin{align}
    W\leftarrow W \circ \frac{[VH^t]}{[WHH^t]} , \label{equ:W}\\
    H\leftarrow H \circ \frac{[W^tV]}{[W^TWH]} , \label{equ:H}
\end{align}
\end{subequations}
where $\circ$ means Hadmard (element-wise) product and $\frac{[A]}{[B]}$ denotes the element-wise division of the matrices $A$ and $B$~\cite{lee_learning_1999}. With Eqs.(\ref{equ:W}) and (\ref{equ:H}) the loss function is guaranteed to decrease monotonically. From Eq.~(\ref{equ:W}), one can update the tensor $X^{s_k}_{b_k,b_{k+1}}$ as
\begin{equation}\label{equ:X}
    X^{s_k}_{b_k,b_{k+1}} \leftarrow X^{s_k}_{b_k,b_{k+1}} \circ \frac{[\sum_{s_{l\neq k}}P_s(\bm{a})X^{<k}X^{>k}]}{[\sum_{b_k',b_{k+1}'}X^{s_k}_{b_k',b_{k+1}'}G^{>k}_{b_{k+1},b_{k+1} '} G^{<k}_{b_{k},b_{k} '}]}
\end{equation}
The denominator on the right hand side of Eq.~(\ref{equ:X}) can be efficiently evaluated without computing the summation in Eq.~(\ref{equ:psa}), for which we define two tensors $\widetilde{G}^{>k}_{j,b_{k+1},c_{k+1}}$ and $\widetilde{G}^{<k}_{j,b_{k},c_{k}}$:
\begin{subequations}
\begin{align}
    &\widetilde{G}^{>k}_{j} = \sum_{s_{k+1}, \dots ,s_L} X^{>k}_{b_{k+1};s_{k+1}, \dots ,s_L}A^{>k}_{j,c_{k+1};s_{k+1}, \dots ,s_L}, \\
    &\widetilde{G}^{<k}_{j} = \sum_{s_1, \dots ,s_{k-1}} X^{<k}_{s_1, \dots ,s_{k-1}; b_k}A^{<k}_{j,s_1, \dots ,s_{k-1};c_k} ,
\end{align}
\end{subequations}
where $A^{>k}$ and $A^{<k}$ are defined similarly as $X^{>k}$ and $X^{<k}$ in Eq.~(\ref{equ:xgk}) and (\ref{equ:xlk}). Then we have
\begin{equation}
\begin{split}
    &\sum_{s_{l\neq k}}P_s(\bm{a})X^{<k}X^{>k} \\
    &=\sum_{j}\frac{n_j}{N}\sum_{b_k',b_{k+1}'}A^{s_k}_{j,c_k,c_{k+1}}\widetilde{G}^{>k}_{j,b_{k+1},c_{k+1}}\widetilde{G}^{<k}_{j,b_{k},c_{k}} .
\end{split}
\end{equation}
The complete algorithm to find the optimal $P(\bm{a})$ that minimizes $\operatorname{Loss}(P(\bm{a}))$ in Eq.~(\ref{equ:fpa}) is summarized in Algorithm~\ref{alg:Framwork}. Once $P(\bm{a})$ is found, the best MPO $\hat{\rho}$ can be reconstructed by applying the inverse of the IC-POVM locally on each site of $P(\bm{a})$, as illustrated in Fig.~\ref{fig:scheme}.

\begin{breakablealgorithm}
\caption{Nonnegative Tensor Train State Tomography}
\label{alg:Framwork}
  \begin{algorithmic}[1]
    \Require
      the set of samples from POVM measurement;
    \Ensure
      near-optimal non-negative MPS form of $P(\bm a)$;
    \State Encode each $\bm{a}^j$ into $A^{j}$ according to Eq.~(\ref{equ:mapatoA});
    \State Randomly initialize $P(\bm a)$ as in [\onlinecite{holtz_alternating_2012}];
    \label{code:RandomPa}
    \State $\widetilde{G}^{<1}_{j,b_{1},c_{1}}=1$,$\widetilde{G}^{>L}_{j,b_{L+1},c_{L+1}}=1$
    \State $G^{<1}_{b_{1},b_{1}'}=1$,$G^{>L}_{b_{L+1},b_{L+1}'}=1$

    \For{$k=1, 2, \dots ,L-1$}
        \State $G^{<k+1}_{b_{k+1},b_{k+1}'}=
        \sum_{s_k,b_k,b_k'} G^{<k}_{b_k,b_k'} X^{s_k}_{b_k,b_{k+1}} X^{s_k}_{b_k',b_{k+1}'} $;
        \For{$j = 1,2,\dots,N_s$}
            \State $\widetilde{G}^{<k+1}_{j,b_{k+1},c_{k+1}}= $
            \Statex \qquad \qquad \qquad \qquad $\sum_{s_k,b_k,c_k} \widetilde{G}^{<k}_{j,b_k,c_k} X^{s_k}_{b_k,b_{k+1}} A^{s_k}_{j,c_k,c_{k+1}} $;
        \EndFor
    \EndFor

    \For{$k=L-1,L-2,\dots, 1$}
        \State $G^{>k}_{b_{k+1},b_{k+1}'}= $
        \Statex \qquad $\sum_{s_{k+1},b_{k+2},b_{k+2}'}
        G^{>k+1}_{b_{k+2},b_{k+2}'} X^{s_{k+1}}_{b_{k+1},b_{k+2}} X^{s_{k+1}}_{b_{k+1}',b_{k+2}'} $;
        \For{$j = 1,2,\dots,N_s$}
            \State $\widetilde{G}^{>k}_{j,b_{k+1},c_{k+1}}= $
            \Statex \qquad $\sum_{s_{k+1},b_{k+2},c_{k+2}} \widetilde{G}^{>k+1}_{j,b_{k+2},c_{k+2}} X^{s_{k+1}}_{b_{k+1},b_{k+2}} A^{s_{k+1}}_{j,c_{k+1},c_{k+2}} $;
        \EndFor
    \EndFor

    \label{code:fram:GandGtilde}
    \While{$true$}
        \For{$k=1, 2, \dots ,L-1$}
            \State update $X^{s_k}_{b_k,b_{k+1}}$ using Eq.~(\ref{equ:X});
            \State $G^{<k+1}_{b_{k+1},b_{k+1}'}=
            \sum_{s_k,b_k,b_k'} G^{<k}_{b_k,b_k'} X^{s_k}_{b_k,b_{k+1}} X^{s_k}_{b_k',b_{k+1}'} $;
            \For{$j = 1,2,\dots,N_s$}
                \State $\widetilde{G}^{<k+1}_{j,b_{k+1},c_{k+1}}= $
                \Statex \qquad \qquad \qquad \qquad $\sum_{s_k,b_k,c_k} \widetilde{G}^{<k}_{j,b_k,c_k} X^{s_k}_{b_k,b_{k+1}} A^{s_k}_{j,c_k,c_{k+1}} $;
            \EndFor
        \EndFor

        \For{$k = L-1, L-2,\dots , 1$}
            \State update $X^{s_{k+1}}_{b_{k+1},b_{k+2}}$ using Eq.~(\ref{equ:X});
            \State $G^{>k}_{b_{k+1},b_{k+1}'}=$
            \Statex \qquad \quad $\sum_{s_{k+1},b_{k+2},b_{k+2}'} G^{>k+1}_{b_{k+2},b_{k+2}'} X^{s_{k+1}}_{b_{k+1},b_{k+2}} X^{s_{k+1}}_{b_{k+1}',b_{k+2}'} $;
            \For{$j = 1,2,\dots,N_s$}
                \State $\widetilde{G}^{>k}_{j,b_{k+1},c_{k+1}}= $
                \Statex \qquad \quad$\sum_{s_{k+1},b_{k+2},c_{k+2}} \widetilde{G}^{>k+1}_{j,b_{k+2},c_{k+2}} X^{s_{k+1}}_{b_{k+1},b_{k+2}} A^{s_{k+1}}_{j,c_{k+1},c_{k+2}} $;
            \EndFor
        \EndFor

        \If {\emph{stopping criterion is meet}}
            \State break;
        \EndIf
    \EndWhile
    \State \Return $P(\bm{a})$ \label{code:recentEnd}
  \end{algorithmic}
\end{breakablealgorithm}

\begin{figure}[htp]
    \centering
    \includegraphics[width=0.95\columnwidth]{fig3.pdf}
\caption{(a) $\mathcal{I}_q$ (red dashed line with squares) and $\mathcal{I}_c$ (blue solid line with circles) as functions of system size $L$ for fixed $p=0.6$. The inset shows $\mathcal{I}_c$ as a function of system size for larger system size ($\mathcal{I}_q$ for $L>6$ is not shown since it is too expensive to compute). (b) $\mathcal{I}_q$ and $\mathcal{I}_c$ as functions of depolarized noise intensity $p$ for fixed $L=4$. (c) The minimum number of required training data $N$ as a function of $L$ such that $\mathcal{I}_c \leq 1\%$, with $p=0.6$. (d) The minimum number of required training data $N$ as a function of $p$ such that $\mathcal{I}_c \leq 1\%$, with $L=4$. All simulations are done with a bond dimension $D=10$.  }
\label{fig:fig1}
\end{figure}

\section{results}\label{sec:results}
We demonstrate our algorithm by reconstructing the density matrix corresponding to the ground state of the XXZ chain subjecting to depolarizing noise. The Hamiltonian of the XXZ chain can be written as
\begin{equation}\label{eq:ham}
    \hat{H} = \sum_{l=1}^{L-1}J(\hat{\sigma}^x_l\hat{\sigma}^x_{l+1} + \hat{\sigma}^y_l\hat{\sigma}^y_{l+1} + \gamma\hat{\sigma}^z_l\hat{\sigma}^z_{l+1}) + h\sum_{l=1}^{L}\hat{\sigma}^z,
\end{equation}
where $L$ is the number of the spins, $J$ is the tunneling strength which we fix to $1$, $h$ is the magnetization strength, and $\gamma$ is the interaction strength. We choose $h=1$ to break the degeneracy of the ground state due to the spin flip symmetry. The depolarizing noise is described by the CPTP map:
\begin{equation}\label{eq:noise}
    \hat{\rho} \rightarrow \mathcal{E} (\hat{\rho}) = \frac{p\hat{I}}{d} + (1 - p)\hat{\rho},
\end{equation}
with $d=2^L$ as the dimension of the Hilbert space, $\hat{\rho}$ the density matrix corresponding to the exact ground state, and $p$ the strength of the noise. We note that for $p=0$, namely for pure states, there already exists efficient MPS-based tomography algorithm which directly use MPS as the ansatz to represent an unknown pure state~\cite{cramer_efficient_2010}.

\begin{figure}[htp]
\centering
\includegraphics[width=0.95\columnwidth]{fig1.pdf}

\caption{\label{fig:fideity} (a, c) $\mathcal{I}_q$ (a) and $\mathcal{I}_c$ (c) as functions of the number of sweeps for different $\gamma$s with $p=0.4$. (b, d) $\mathcal{I}_q$ (b) and $\mathcal{I}_c$ (d) as functions of the number of sweeps for different $\gamma$s with $p=0.6$. The inset in (d) shows the tail of the convergence of $\mathcal{I}_c$. In (a, b, c, d) we have chosen $5$ best results according to their loss values out of $100$ trials and plotted the mean values of them (The standard deviations are shown as error bars). (e) The left and right axis show the final $\mathcal{I}_q$ and $\mathcal{I}_c$ as functions of $\gamma$ with $p=0.4$. (f) The left and right axis show the final $\mathcal{I}_q$ and $\mathcal{I}_c$ as functions of $\gamma$ with $p=0.6$. Here we have chosen $L=6$ and used $N_{\operatorname{train}}=30000000$.
}
\label{fig:fig2}
\end{figure}

Similar to~\cite{carrasquilla_reconstructing_2019}, we use both the quantum fidelity and the classical fidelity to measure the learning accuracy. Specifically, the quantum fidelity is defined as
\begin{align}\label{eq:fq}
\mathcal{F}_q = {\rm tr}^2\left(\sqrt{\sqrt{\hat{\rho}_1}\hat{\rho}_2 \sqrt{\hat{\rho}_1}}\right),
\end{align}
for two density matrices $\hat{\rho}_1$ and $\hat{\rho}_2$, and the classical fidelity is defined as
\begin{align}\label{eq:fc}
\mathcal{F}_c = \mathbb{E}_{\bm{a}\sim P_i}[\sqrt{P_m(\bm{a})/P_i(\bm{a})}],
\end{align}
where $P_m(\bm{a})$ is the measured probability distribution, and $P_i(\bm{a})$ is the ideal probability distribution. We also define the quantum and the classical infidelities as $\mathcal{I}_q = 1 - \mathcal{F}_q $ and $\mathcal{I}_c = 1 - \mathcal{F}_c$ respectively. In our numerical simulations, we have generated two independent synthetic datasets for each parameter setting we have considered, each with $30,000,000$ samples. One dataset is used for training and the other is used for testing. For the quantum fidelity, we directly compute $\mathcal{F}_q$ between the reconstructed density matrix and the target density matrix. For the classical fidelity, we use a test dataset to evaluate Eq.~(\ref{eq:fc}).

\begin{figure}[htp]
    \centering
    \includegraphics[width=0.9\columnwidth]{fig6.pdf}

\caption{$\mathcal{I}_q$ (red dashed line with squares) and $\mathcal{I}_c$ (blue solid line with circles) as functions of the bond dimension $D$. Here we have used $L=4$, $p=0.6$ and $N_{\operatorname{train}}=30000000$. }
\label{fig:fig3}
\end{figure}
We first study the final reconstruction quality as a function of the system size $L$ and the noise strength $p$. We show $\mathcal{I}_q$ and $\mathcal{I}_c$ as functions of $L$ in Fig.~\ref{fig:fig1}(a) and of $p$ in Fig.~\ref{fig:fig1}(b) respectively. We can see that the final fidelity (both the quantum and the classical) decreases as $L$ increases and increases as $p$ increases. We can also see that it is much easier for a near-perfect reconstruction of the probability distribution than the construction of the underlying quantum state, as in the numerical simulations $\mathcal{I}_c$ is always at least one order of magnitude smaller than $\mathcal{I}_q$. In Fig.(\ref{fig:fig1})(c, d) we show the minimum number $N$ of required training data for $\mathcal{I}_c \leq 1\%$ as a function of $L$ and $p$ respectively. We can see that $N$ increases as $L$ increases and decreases as $p$ increases, as shown in  Fig.~\ref{fig:fig1}(a, b).

Then we fix $L=6$ and investigate the variations of $\mathcal{I}_q$ and $\mathcal{I}_c$ as functions of the number of sweeps, which is shown in Fig.~\ref{fig:fig2}. In Fig.~\ref{fig:fig2}(a, c), we show $\mathcal{I}_q$ and $\mathcal{I}_c$ as functions of the number of sweeps when $p=0.4$ for different values of $\gamma$, while in Fig.~\ref{fig:fig2}(b, d) we show $\mathcal{I}_q$ and $\mathcal{I}_c$ as functions of the number of sweeps when $p=0.6$ for different values of $\gamma$. We can see that for both noise strengths, $\mathcal{I}_c$ converges in about $1000$ sweeps and $\mathcal{I}_q$ does not fully converge after $4000$ sweeps. The final values of $\mathcal{I}_q$ and $\mathcal{I}_c$ after $4000$ sweeps are also shown in Fig.~\ref{fig:fig2}(e) for $p=0.4$ and in Fig.~\ref{fig:fig2}(f) for $p=0.6$. We can see that in both cases $\mathcal{I}_c$ is about two orders of magnitude smaller than the corresponding $\mathcal{I}_q$ and that $\mathcal{I}_q$ and $\mathcal{I}_c$ for $p=0.6$ is smaller than those for $p=0.4$. %
\begin{figure}[htp]
    \centering
    \includegraphics[width=0.9\columnwidth]{fig2.pdf}
    \caption{\label{fig:loss} The $x$ axis denotes different labels of the $100$ numerical experiments, labelled $1$ to $100$, sorted by their final loss values from large to small. In our simulation, we have used $P^2(\bm{a}) - 2P(\bm{a})P_s(\bm{a})$ as the loss value, which simply shifts the original loss value in Eq.~(\ref{equ:fpa}) by a constant. Here the results are taken from the reconstruction of $P(\bm{a})$ for $L=6$, $\gamma=2.0$ and $p=0.6$. }
    \label{fig:fig4}
    \end{figure}

Next we explore the learning accuracy as a function of the bond dimension $D$ used in our ansatz. The bond dimension of the MPS corresponds to the number of singular values retained in the process of restoring the original density matrix after matrix SVD. In our case the ground state can be represented as an MPS with a certain bond dimension $D_0$. For a perfect training, we need to have $D \geq D_0$ since otherwise our ansatz is not expressive enough to represent the target quantum state. If $D$ is too large and we do not have enough training data, we might have the problem of overfitting which would also result in bad learning accuracy. The dependence of the quantum and the classical infidelities as functions of $D$ are shown in Fig.~\ref{fig:fig3}, where we can see that both $\mathcal{I}_q$ and $\mathcal{I}_c$ decrease as $D$ increases until saturation.

Due to the variational feature of our algorithm similar to DMRG, it could be trapped in local minima (also because the initial MPS $P(\bm{a})$ is randomly initialized) [\onlinecite{LiuDeng2021}]. Therefore in our numerical results, the same reconstruction algorithm is run for many trials with random initialization of $P(\bm{a})$, and the one with the lowest loss value is chosen as the final result. Ideally one would likely to directly choose the trials with the highest fidelity. However in real experiment the target state is unknown and it is not possible to compute the fidelities. As a result it is important that the trials with lower loss values will correspond to those with higher fidelities. Such correspondence between loss values and fidelities is shown in Fig.~\ref{fig:loss}, where we have repeated the reconstruction algorithm for $100$ times. We can see that indeed the loss value has the desired correspondence with the fidelity.

\section{Conclusion}\label{sec:conclusion}
We have presented an algorithm based on the non-negative matrix product state for quantum state tomography. Given a number of experimental measurement outcomes, our algorithm iteratively finds the optimal non-negative MPS representation which best approximates the probability distribution of these outcomes. Applying simple local transformations, the reconstructed non-negative MPS can be converted into a density matrix for the unknown quantum state. This is in comparison with the QST methods based on neural network states, for which one generally can not directly write down the quantum state but only has indirect access to it via sampling from the trained neural networks. As applications, the effectiveness of our algorithm is demonstrated to reconstruct the ground state of the XXZ chain with depolarizing noise.

\begin{acknowledgments}
CG acknowledges support from National Natural Science Foundation of China under Grants No. 11805279. DH and XW gratefully acknowledge the grant from the National Key R\&D Program of China, Grant No. 2018YFA0306703.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Home>Ras Al Khaimah
Ras Al Khaimah has earned its reputation as a pre-eminent commercial center with an innovative, dynamic and entrepreneurial business culture. The city of Ras Al Khaimah, the capital of the Emirate, is divided into two parts by a creek. The western part, known as "old Ras Al Khaimah", comprises government departments, educational institutions, shopping malls, hotels as well as residential areas and new construction projects. The eastern part, known as Al Nakheel, houses the Emiri Court, some government departments, markets, Ras Al Khaimah Exhibition Center, hospitals and residential areas housing the majority of the city's population. A bridge and a network of modern roads link the two parts of the city.
Ras Al Khaimah consists of sandy desert, coastal strips with parts of salt flats, mangroves and mountains. All these areas have different ecosystems, which makes the Emirate a fascinating place.
Apart from cultivated plants, there are three categories of flora in Ras Al Khaimah – the salt loving vegetation, mountains and desert plants which are plentiful after rainfall. The Emirate is also home to a number of mammals, mainly foxes, jerboas or wildcats as well as hundreds of bird species.
Attaction

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Normalizing in Mongo simply to reduce file size/increase performance? Working with MongoDB, I'm fairly aware of when normalization makes sense, but I'm trying to understand if it makes sense from a data-size or query-performance sense.
As an example, let's say I have a list of 2,000 retail stores. For the example, I do not care about anything else so I only have the store name. At least a few characters but never longer than a hundred.
I have 20 million records of people who took a trip to a store. I'd record some info about the trip, along with this store name.
In MySQL, the file size of the table/records can impact the query performance quite heavily. Normalizing the store names so that I can store the string once, and then write the key (an int) instead saves on a lot of disk space. That turns into performance gains.
In MongoDB, this type of data is small and unimportant enough that it should simply be embedded. However, I'm concerned that after 20 million records, queries and/or file size will suffer performance problems because of how much redundant data is there.
If 5 million people all went to a single store, there's going to be 5 million embedded copies of that string in mongo documents. That will take up a lot more disk space and seems like it may eat up performance over an integer.
I suppose if I did normalize the data, Mongo would still have some performance overhead to query that additional data.

A:
If 5 million people all went to a single store, there's going to be 5 million embedded copies of that string in mongo documents.

Yeah, and much worse, should the name ever change, you'd have to update 5M entries

That will take up a lot more disk space and seems like it may eat up performance over an integer.

I'd abstain from integers as keys. Integers create bottlenecks if sequenced (the sequencer becoming the bottleneck) and non-monotonous if using algorithms like HiLo. Use ObjectId or something else that is non-sequential, but monotonic.
Monotony often improves data locality (if creation time is a locality criterion, which it often is), and helps utilize the BTree more efficiently.

I have 20 million records of people who took a trip to a store. I'd record some info about the trip, along with this store name.

That's a typical graph problem. People and Stores are nodes, trips are the edges. MongoDB handles normalized graphs better than one might think.
Directly comparing the performance of the two approaches is tricky - the additional roundtrip will make the normalized query slower, but you could choose to additionally store the store's name with each trip. The performance overhead won't be huge, but it will add RAM pressure.
Summing up, adjusting the data structure for less queries has certainly merit, but for sheer size reduction from, say, 80 bytes on average to 24 bytes I wouldn't do it. The normalized structure is much easier to keep consistent (or eventually consistent, when storing both), easy enough to query and can be efficiently 'joined' using $in. The upside is clear data ownership and more flexibility (e.g. reversing the query to 'who ever took a trip to place x') is much easier.

A: the question of normalizing depends how you are accessing the data 95% of the time.
e.g. if you have a site or app that lists the stores first and
then based on a request shows the trips to the store then definitely Normalize
adding a index to the Store attribute in your collection would enhance the performance of your searches whether or not its a int
assuming you have done that, from what I have read the document size does not affect search of the document as it would use the index to find the rows with the referenced Store

redpajama_set_name: RedPajamaStackExchange


From Wikipedia, the free encyclopedia. Shahada Salah Sawm Zakat Hajj. The Sufi Path of Love: Mevlana Museum Mevlevi Order.
The Masnavi masnavi manavi started by the Rumi during the final years of his life. Early Contemporary Eschatology Theological. Works by Rumi Persian poems. In other projects Wikimedia Commons Wikisource.
For the type of poem, masnavi manavi Masnavi poetic form. It incorporates a variety of Islamic wisdom but primarily focuses on emphasizing inward personal Sufi interpretation. Wikisource has original text related to this article: The Masnavior Masnavi-i Ma'navi Masnavi manavi State University of New York, Some scholars suggest that in addition to the incomplete Book 6, there might have been a seventh volume.
The title Masnavi-i Ma'navi Persian: The Masnavi is a poetic collection of masnavi manavi and stories derived from the Masnavi manavihadith sources, and everyday tales. Stories are told to illustrate a point mnaavi each moral is discussed in detail. The Masnavi is a series of six books of poetry that together amount to around 25, verses or 50, lines.
In contrast to Rumi's Diwan, the Masnavi is a relatively "sober" text. Quran Sunnah Hadith Tafsir Seerah. Views Read Edit View history. The sixth and final masnavi manavi would remain incomplete.
Archived from the original on This article is about the Sufi poem by Rumi. Wikimedia Commons has media related to Masnavi. The six books of the Masnavi can be divided into three groups masnavi manavi two because each pair is linked by a common theme: These men are said to have met regularly in meetings where Rumi would deliver the masnavi manavi and Chalabi would write them down and recite them back to him.
Although there is no masnavi manavi frame, style, or plot, Rumi generally follows a certain writing pattern that flows in the following order: This page was last edited on 2 Mayat Schools Sunni Ash'ari Maturidi Traditionalism.
He began dictating the first book around the age of 54 around the year and continued composing verses until his death in It is one of the best known and most influential works of Sufism.


text:
Daily Briefings Newsletter - DHS (WNB – DHS Today)Daily Briefings Newsletter – Emergency Preparedness and WMDDaily Briefings Newsletter – Public Health Preparedness (WNB – Responders Today)
FEMA Ended $156 Million Contract With One-Woman Company for Puerto Rico Meals
FEMA Corps members provide food in the aftermath of Hurricane Maria. (FEMA)
The Federal Emergency Management Agency terminated on Oct. 19 its contract for 30 million emergency meals with Tribute Contracting LLC, whose owner and only employee is Tiffany Brown, The New York Times reported Feb. 6. FEMA awarded the Tribute contract on Oct. 3, 2017, for ready-to-eat meals at $5.10 apiece to be delivered to Puerto Rico after Hurricane Maria devastated the island.
By the time 18.5 million meals were to have been delivered, Brown had provided 50,000, without the heating pouches required by FEMA's solicitation for "self-heating meals," prompting cancellation of the deal. FEMA paid Tribute $255,000 for 50,000, CNBC reported.
The Times report prompted Rep. Elijah Cummings (D-Md.) and Del. Stacey Plaskett (D-V.I.) to ask the House Oversight and Government Reform Committee Chairman Trey Gowdy (R-S.C.) to subpoena FEMA for documents related to the meals contract. Cummings is minority leader and Plaskett is a member of the committee. They seek to know how and why FEMA "inexplicably" awarded the meals contract to "a tiny, one-person company with a history of struggling with much smaller contracts," according to their Feb. 6 letter.
"FEMA's decision is even more incomprehensible given the company's inability to fulfill previous government contracts that were only a fraction of the size," the legislators wrote. The Federal Prison System and the Government Publishing Office (GPO) canceled five contracts valued at less than $100,000 each with Tribute in 2013 and 2014, according to the letter. GPO ruled Tribute ineligible for contracts larger than $30,000 from 2016 through 2019. It is unclear whether FEMA was aware of Tribute's previous problems or disregarded them, the lawmakers wrote.
Brown has appealed the contract termination. FEMA said it would be inappropriate to comment on a contract under appeal.
"At the time of the contract termination there were ample commodity supplies in the pipeline, and distribution was not affected," FEMA spokesman William Booher told the NYT.
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Photo shoots for couples are becoming increasingly popular; often presenting a different side of your relationship to your wedding album – they are relaxed, intimate, and set in a favourite place that's packed full of your special memories. Maybe that's the place you got engaged, where you first met or just where you love to spend time together.
A pre-wedding photo shoot provides an opportunity not only to add even more gorgeous photos to your album, but to develop a relationship with me – your wedding photographer. The thought of entrusting your wedding day photography to a stranger is pretty daunting, so let's grasp an opportunity for me to get to know what makes you laugh and smile. You'll also get to know how I work, relax in front of the lens and feel assured that the photography of your one very special and sacred day is in safe hands.
In the comfort of my studio or on location; sessions are for up to 1hour. For location shoots 5 miles outside of the studio, an additional cost will be charged to cover time and travel.
"Sarah is absolutely incredible! From the run up to the big day Sarah has been a friend checking everythings going ok. She put so much effort in and was such a big help!
The photos she produces are amazing and top quality, I really wouldn't use anyone else ever! She spent all our wedding day running around making sure she had the perfect photos making everyone laugh and feel comfortable, she really gives it her all.


Drive to Tavertet, and take the road leaving Tavertet near the Church heading East and signposted to Rupit. It is paved and narrow and has potholes which add to the charm. You will know you are on the right road because after 50 metres a sign warns to look out and respect walkers, cyclists and animals with the words PRECAUCIÓ, CAMÍ ESTRET. The speed limit is 30 km/hour. At the entrance of the village at weekends there is a barrier next to the parking, but ignore it and say you are going to l'Avenc if stopped and continue.
After 3 km. you will see the entrance (by road) to l'Avenc to your left, this takes you to the reception and service area of the new wing. Don't turn here. 50 metres further on is the main garage entrance where you can leave your car out of the sun or rain and take the lift up to the reception passing throw the main hall.
Coming from Barcelona, take the C-17 that goes around Vic and heads north. Don't go into Vic. Carry on until you are signposted to Girona on C-25 (also called the Eix Transversal from Lleida to Girona). Take the Girona direction and come off at the second exit to Roda de Ter and C-153. This road takes you past Roda de Ter and would end up in Olot but after 10 kms you'll need to turn off at L'Esquirol, go through the village and up a 13km narrow winding newly tarred road Tavertet. The views are spectacular. The whole journey takes approximately: 2 hours.
Coming from Girona and the airport, you'll no doubt be on the Eix C25 and heading for Vic. Don't exit at Vic but at the next exit to Roda de Ter. This road takes you past Roda de Ter and ends up in Olot but after 10 kms you'll need to turn off at L'Esquirol, go through the village and up a 13km narrow winding newly tarred road to Tavertet. The views are spectacular. The whole journey takes approximately: 1h 45m.
From France and Figueres head for Besalú and Olot. From Olot head for Les Preses on the C-154 towards Vic and Santa Coloma de Farners but don't take the new tunneled road to Vic, Torelló/Manlleu (avoid turning off at the big roundabout after Les Preses. Carry on for 300 metres and turn right on the old road C153 to Rupit and Vic. You'll know you are right because after a dead straight road it starts to wind. At km. 28.5 (counting backwards on the road) turn left up towards Rajols, l'Avenc and Tavertet, this is a farm road and about 1km past the turnoff to Rupit. L'Avenc is 5 kms along this road. Approximate journey from Figueres: 1h 30m.
From Barcelona, you can get to Vic by train or coach. See RENFE (trains) and SAGALÉS (Barcelona-Rupit). Public transport is very reasonable in Catalunya.
From Vic the Sagalés Coach Company goes to Rupit. Check timetables as there are only a few buses a day. Then you need to get a taxi to l'Avenc.
From Vic, you can also get a taxi to l'Avenc for about 55€. The taxi driver who we work with is Manel (0034 629708077).


text:
COVID-19 Publications
New Job-Protected Leave Announced for British Columbia Employees to Get Vaccinated
Dianne Rideout*
Michelle McKinnon
New Job-Protected Leave Announced for British Columbia Employees...
April 6, 2021 Employment and Labour Bulletin < 1 minute read
Dianne Rideout*, Michelle McKinnon
A new job-protected leave has been announced for British Columbia employees to get vaccinated. This new leave allows employees to take time off work to receive the Covid-19 vaccine, and also extends to employees who need time off to take dependent family members to get vaccinated. The BC government has also announced plans to consult industry stakeholders on the feasibility of making this job-protected leave paid, which we will continue to monitor.
Changes have also been made to the existing job-protected leave in s. 52(12) of the Employment Standards Act, that allows employees time off work for reasons relating to Covid-19. This leave has been extended to now include unpaid leave to care for family members because of Covid-19 (and not only children and dependents), as well as allowing employees who are receiving medical treatment for underlying medical conditions, or who have contracted another illness that make them more susceptible to Covid-19, to take unpaid leave.
We will continue to monitor further developments and will provide further updates as they become available!
by Dianne Rideout and Michelle McKinnon


text:
Mechanism of the 1975 Kalapana, Hawaii, earthquake inferred from tsunami data
Ma, Kuo-Fong and Kanamori, Hiroo and Satake, Kenji (1999) Mechanism of the 1975 Kalapana, Hawaii, earthquake inferred from tsunami data. Journal of Geophysical Research B, 104 (B6). pp. 13153-13167. ISSN 2169-9313. doi:10.1029/1999JB900073. https://resolver.caltech.edu/CaltechAUTHORS:20141111-145056810
We investigated the source mechanism of the 1975 Kalapana, Hawaii, earthquake (M_S= 7.2) by modeling the tsunamis observed at three tide-gauge stations, Hilo, Kahului, and Honolulu. We computed synthetic tsunamis for various fault models. The arrival times and the amplitudes of the synthetic tsunamis computed for Ando's fault model (fault length = 40 km, fault width = 20 km, strike = N70°E, dip = 20°SE, rake = −90°, fault depth = 10 km, and slip = 5.6 m) are ∼10 min earlier and 5 times smaller than those of the observed, respectively. We tested fault models with different dip angles and depths. Models with a northwest dip direction yield larger tsunami amplitudes than those with a southeast dip direction. Models with shallower fault depths produce later first arrivals than deeper models. We also considered the effects of the Hilina fault system, but its contribution to tsunami excitation is insignificant. This suggests that another mechanism is required to explain the tsunamis. One plausible model is a propagating slump model with a 1 m subsidence along the coast and a l m uplift offshore. This model can explain the arrival times and the amplitudes of the observed tsunamis satisfactorily. An alternative model is a wider fault model that dips 10°NW, with its fault plane extending 25 km offshore, well beyond the aftershock area of the Kalapana earthquake. These two models produce a similar uplift pattern offshore and, kinematically, are indistinguishable as far as tsunami excitation is concerned. The total volume of displaced water is estimated to be ∼2.5 km^3. From the comparison of slump model and the single-force model suggested earlier from seismological data we prefer a combination of faulting and large-scale slumping on the south flank of Kilauea volcano as the most appropriate model for the 1975 Kalapana earthquake. Two basic mechanisms have been presented for explaining the deformation of the south flank of Kilauea: (1) pressure and density variation along the rift zone caused by magma injection and (2) gravitational instability due to the steep topography of the south flank of Kilauea. In either mechanism, large displacements on the south flank are involved that are responsible for the observed large tsunamis.
http://dx.doi.org/10.1029/1999JB900073 DOI Article
http://onlinelibrary.wiley.com/doi/10.1029/1999JB900073/abstract Publisher Article
Kanamori, Hiroo 0000-0001-8219-9428
Satake, Kenji 0000-0002-3368-3085
© 1999 The American Geophysical Union. Paper number 1999JB900073. Received September 9, 1997; Revised February 16, 1999; Accepted March 1, 1999. We thank the reviewers R. Denlinger and R. Crosson for critical reading of the manuscript, valuable comments, and suggestions that helped us to improve the manuscript. This work was supported by the National Science Foundation grants EAR-9303804 and EAR-9316528 and National Science Council, Taiwan, contract NSC83-0202-M-008-050T. Contribution 8487 of the Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California.
NSF EAR-9303804
National Science Council (Taiwan) NSC83-0202-M-008-050T
Other Numbering System:
Other Numbering System Name
Other Numbering System ID
Caltech Division of Geological and Planetary Sciences 8487
Ma, K.-F., Kanamori, H., & Satake, K. (1999). Mechanism of the 1975 Kalapana, Hawaii, earthquake inferred from tsunami data. Journal of Geophysical Research: Solid Earth, 104(B6), 13153-13167. doi: 10.1029/1999jb900073


Last Friday we packed our bags and headed to the Yorkshire Dales for a weekend away. We were full of grand plans for our trip - maps were consulted for walking routes, visitor attractions were looked up online and menus were researched for the purpose of indulging in long pub lunches nestled beside roaring fires. And then on Thursday we all caught the cold. One by one we were turned into a family with hacking coughs, permanent runny noses and Lemsip drinkers. Not at all what we had envisaged. Instead of getting out and about we spent many hours on the sofa, kettle on, watching movies and playing board games. On the plus side this gave us plenty of time to properly appreciate all that Burtersett Cottage had to offer.
We were kindly invited to stay by Gorgeous Cottages who offer a hand-picked collection of the finest luxury holiday cottages in Yorkshire. They have beautiful homes on the North Yorkshire Moors, the Yorkshire Coast, the Yorkshire Wolds and the Yorkshire Dales, many which offer family spaces and doggy friendly ones. Gorgeous Cottages offered us a choice of which area we wanted to visit and immediately we knew we wanted to explore the Dales. Our drive up took us through some pretty little villages and beautiful scenery. Pen-y-Ghent was incredible to look at with a little snow still sitting on the top. Having taken the train on the Settle-Carlisle line several times before I have passed over the Ribblehead Viaduct and each time been captivated by how magnificent it is (it is known as one of the great railway journeys). But actually stopping the car and walking up to it was a whole other experience. It's simply breathtaking and we're planning to head up there again soon for a longer walk.
Burtersett is a peaceful hamlet located only a few minutes away in the car from Hawes which is famous for its cracking Wensleydale cheese and a bustling tourist attraction particularly for walkers and cyclists. The scenery around the cottage is spectacular - lots of dry stone walls criss-crossing the fields, the Traditional Farm Buildings nestled on the hillside and of course, many, many sheep. Arriving at the cottage, we parked the car and a beautiful black horse stuck his head over the stone wall to greet us (I think he hoped we had a carrot but as we didn't he had a good lick of my camera instead). Our home for the weekend was a two bedroom, Yorkshire stone built cottage. The front door had the prettiest stained glass window and the entrance was surrounded by terracotta pots of daffodils and violas. As you enter the house you step immediately into the living room, with original stone flooring, an open fire, two super comfy sofas, a sideboard which is stuffed to the rafters with books and dvds as well as a huge wooden chest that was filled with classic board games.
We had brought some dvds with us, but never bothered to watch them as there was a huge choice in the cottage to pick from. The owners had also really thought about the kids too, as there were hundreds of books for all ages (including so many good picture books) as well as another large selection of kids dvds. Book wise, you were spoilt for choice with walking guides, Yorkshire photography books, fiction titles and nature guides. The chest provided us with hours of entertainment by way of Cluedo, chess and best of all, dominoes. We spent a lot of time in this room, fire blazing away, eating chocolate eggs and watching The Damned United, Skyfall and the Harry Potter movies.
I've always thought the heart of any home is the kitchen. Sadly, in mine, that's not the case as it's tiny. Burtersett Cottage had the kitchen of my dreams. A gorgeous proper farmhouse table and chairs, woodburning stove, a Gorenje fridge freezer (oh my how I want one of these now) and a Smeg range cooker. I photographed this room A LOT. It's fully stocked for all your cooking needs - toaster, microwave, teapot, casserole dish, pizza tray, steamer and cafetieres. There is also a washing machine and an original airer on a pulley to dry your clothes near the woodburner. The back door opens to a cute courtyard that is shared with the next door cottage (also a holiday let). Welcoming us when we arrived was a bottle of white wine in the fridge, grapes, fresh coffee, Yorkshire Tea and cheeses from the Wensleydale Creamery. I was over the moon that there was a piece of Richard the Third Wensleydale which is one of my favourites and I find it difficult to get in Leeds. There were fresh flowers on the table, some beautiful crockery to use in the larder cupboard and tealights on the table too. The decor was perfect for me - rustic touches, vintage charm, the plate rack with the Cable and Cotton lights strung around it and the letterpress print of Yorkshire places above the stove area. I spent a lot of time admiring that rug too (it's in the very top picture, I need to find out where it is from!). We cooked both nights in here, simple meals as we weren't feeling great, but I loved sitting at that table, woodburner on, wine flowing and music playing softly in the background.
Upstairs the main bedroom makes for a calming retreat and offers a super comfy double bed, wardrobe and two bedside cabinets. The windows look out on to the hillside and it was lovely pulling back the curtains in the morning, sipping a coffee in bed and taking in that gorgeous view. The room is full of natural details - a hand picked posy of snowdrops, dried seed heads in the fire grate, a basket of scented pine cones and a pretty touch of fairy lights wrapped around more dried flower heads in a vintage jug. It's a beautiful, calming space to unwind in.
The second bedroom was taken by our twelve year old son. It's a small room so furnished simply with a trunk bed, a country style chest of drawers, a clothes hanging rail and a small Shaker style peg rail. The duvet was warm and added cosiness was provided by thick Yorkshire woollen blankets and at night the pretty table light brightened up the room (it's by Hebden Bridge designer Hannah Nunn whose work I admire greatly). Impressive too was the view from the window, sheep and lambs grazing in the farmer's field and the sun moving across the hills, highlighting little rusty-orange patches.
On the landing there was a narrow window up high and on Sunday morning the light streamed through it, offering shapes and shadows on the walls that begged to be photographed. There is central heating in the cottage too, so we were always warm in all the upstairs rooms. The bathroom was great too with shower, bath and a heated towel rail (and proper giant, thick bath sheets to wrap yourself up in).
Outside the cottage the village is a pretty place to explore. Lots of little paths and farm tracks that lead to the Dales, ramshackle buildings and of course, sheep! It is a hamlet surrounded by working farms, so there are many tractors and farm vehicles going up and down the tracks but it all adds to the charm of the Dales. We did get out and about a little, with visits to Sedbergh, England's Book Town, which had a lovely cafe, The Three Hares. Small but with a pretty, rustic decor, we had coffee and cake (I had the raspberry frangipane - it was so good) and a trawl of the second hand book stores. Our favourite was Westwood Books, a huge shop stuffed to the rafters with vintage titles. There were overflowing cases of vintage Penguin paperbacks and boxes of Observer Books. We could have spent hours in there and I did buy several Agatha Christie novels, The Professor by Charlotte Bronte and the Observer Book of Cacti (which I had been searching for months for, only to find they had about twenty of them!). I'm kicking myself that I didn't buy a copy of the Observer Book of Birds Eggs which someone had made careful notes in of the eggs they had spotted back in 1950! In Hawes we visited the Provisions store which was great for local beers, preserves and fresh Dales eggs which we had for breakfast the following morning.
And even though we were feeling under the weather, we still had an amazing weekend and have plans to return. Burtersett Cottage was an absolute delight, a real home from home. A place to rest, relax and retreat from the world. The owners have created a very special place indeed.
Our adventures in the Dales are also over on Instagram if you want to see a little more.
Thank you to Gorgeous Cottages for providing us with two nights accommodation at Burtersett Cottage for the purposes of this review. All photographs, words and opinions are my own.


Everton's Muhamed Besic is being linked with a move away from the Toffees.
Everton fans don't seem too upset by the speculation that Muhamed Besic could leave.
Sky Sports reported today that Italian side Torino are interested in signing the midfielder.
The 25-year-old joined Everton under Roberto Martinez for £4 million but has managed only 37 appearances since then and it appears as if the Toffees are ready to part ways.
Besic did, at times, show glimpses of his potential, but he's at an age now where he should be playing and performing well every week and it seems unlikely that those chances will be afforded to him under Sam Allardyce.
Idrissa Gueye is ahead of him in the pecking order on Merseyside, but losing Besic will surely mean that the Everton boss plans on recruiting another defensive midfielder at some point this month.
There are much better, much more Premier League proven players around than the Bosnia and Herzegovina ace, and Toffees supporters know this.


Because of the Preakness Stakes, I was thinking today about Leonard Pennario and how he loved horse racing. If Pennario were alive I am sure he would be watching the Preakness. He watched it last year.
But what about this crowd of slugs and schufts at the Preakness? I just found this on the Baltimore Sun's site.
Imagine wanting to be a part of this! Pennario would be aghast at this scene. That is for sure.
It is almost as bad as George Bellows' "I Remembering Being Initiated Into the Frat." Remember that?
But Pennario did love horse racing albeit in a very genteel style I would never be able to glimpse on my own. Pennario would go to California horse races and often he would be asked to crown the winner.
My brother George has a very funny story about how when the great pianist came to Buffalo and we all ended up at the Hyatt, there was a conversation about horse racing going on. Pennario was at another table in a whole different conversation but George said you could tell he was tuned into the horse racing conversation that was going on without him.
This is the funniest part of the story: Someone raised some question about some jockey or other, and you could see Pennario nodding, trying to answer the question while continuing to converse with whoever it was who was monopolizing him at the time.
Which was probably me. Ha, ha!
I am web-logging about the Preakness because that is one of the topics everyone is searching for today. I want people to be searching for Preakness and find themselves on the Leonard Pennario Web log.
You have to learn to use trends like this to your advantage!
For instance everyone is searching for "Wolfram Alpha." I have absolutely no idea what that is. But I am going to go with it anyway.
Say the name Wolfram to me and I think of Wolfram von Eschenbach. He is the troubadour from "Tannhauser." Pennario and I went to see that opera together!
I heard Wolfram sing the "Evening Star" aria while I was sitting next to the Alpha Pianist. That is something I will never forget!
See, we are on top of the trends here at the Leonard Pennario desk.
Welcome, new fans and followers!
That is really cool to hear about Pennario in that conversation, lol! That is great! That is talent!
Other than that, I seem to be off track today. That crowd reminds me of 1969 when I was up your way to the Woodstock festival. The main difference is the hair length.
And why do I think of Wolfman Jack?
I forgot all about the Preakness until I saw your comment on Facebook at about 6:18, ran to the television, and caught most of it without the less than interesting buildup. Great race!
Becky, did you bet? Larry, you were at Woodstock??!? I would never have guessed that!
Well, between you and me, I bet there are a lot more things that you would never have guessed!
But, I am all grown up now!


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Category: October 2014
Massive Protests Lead Guatemala to Reject 'Monsanto Law' in Court
by Oregon PeaceWorks • October 30, 2014 • 0 Comments
TEX DWORKIN – In a landmark decision on September 4, following intense pressure by indigenous people, trade unions, farmer's organizations and others, the Guatemalan judiciary ruled to suspend the controversial Plant Variety Protection Law, commonly referred to as the 'Monsanto Law' because of the multinational biotech company's involvement in it.
The United States is No. 1 — But in What?
LAWRENCE WITTNER – American politicians are fond of telling their audiences that the United States is the greatest country in the world. Is there any evidence for this claim?
New Pentagon Study Confirms Risks of Climate Change
CORAL DAVENPORT – The accelerating rate of climate change poses a severe risk to national security and acts as a catalyst for global political conflict, a report published in May, 2014 by a leading government-funded military research organization concluded.
Paying Respects, Pentagon Revives Vietnam, and War Over Truth
SHERYL GAY STOLBERG – It has been nearly half a century since a young antiwar protester named Tom Hayden traveled to Hanoi to investigate President Lyndon B. Johnson's claims that the United States was not bombing civilians in Vietnam. Mr. Hayden saw destroyed villages and came away, he says, "pretty wounded by the pattern of deception." Now the Pentagon — run by a Vietnam veteran, Defense Secretary Chuck Hagel — is planning a 50th anniversary commemoration of the Vietnam War. The effort, which is expected to cost taxpayers nearly $15 million by the end of this fiscal year, is intended to honor veterans and, its website says, "provide the American public with historically accurate materials" suitable for use in schools. But the extensive website, which has been up for months, largely describes a war of valor and honor that would be unrecognizable to many of the Americans who fought in and against it.
Risen's New Book Exposes the "War on Terror"
NORMAN SOLOMON – No single review or interview can do justice to Pay Any Price — the new book by James Risen that is the antithesis of what routinely passes for journalism about the "war on terror." Instead of evasive tunnel vision, the book offers big-picture acuity: focusing on realities that are pervasive and vastly destructive. Published this week, Pay Any Price throws down an urgent gauntlet. We should pick it up. After 13 years of militarized zealotry and fear-mongering in the name of fighting terrorism, the book — subtitled "Greed, Power, and Endless War" — zeros in on immense horrors being perpetrated in the name of national security.
When Liberals Go to War: As ISIS Slaughters Kurds in Kobani, the U.S. Bombs Syrian Grain Silos
AJAMU BARAKA – The U.S. is conducting a curious humanitarian war against ISIS in Syria. While Kobani, the largely Kurdish district that straddles the border with Turkey is being attacked by ISIS forces and facing the very real possibility of mass civilian killings if it falls, U.S. military spokespersons claimed that they are watching the situation in Kobani and have conducted occasional bombing missions but that they are concentrating their anti-ISIS efforts in other parts of Syria. Those other efforts appear to consist of bombing empty buildings, schools, small oil pumping facilities, an occasional vehicle and grain silos where food is stored to feed the Syrian people. Turkey also seems to be watching as the Kurds of Kobani fight to the death against ISIS.
Why Vote?
STARHAWK – We're getting close to voter registration deadlines here in the US for our November elections, and it's time for my periodic voting rant. Why vote, when politics are vile, the right wing is a pack of intransigent bullies and the politicians who call themselves progressive inevitably go belly-up and give in to them? Obama, the guy who stood for hope, turned out to be just another good-looking guy who let us down, and a true progressive like Bernie Sanders – I'm at an age where I go for older men! – probably doesn't stand a chance. Nonetheless, it is vitally important that you vote, and here's three good reasons why: the practical, the political, and the spiritual.
Building the Movement to End the Latest Expanded U.S. War in the Middle East
JIM LAFFERTY – If the U.S. public gained a fuller and more honest understanding of what U.S. and U.S. backed Arab states have done that has led to the creation of ISIS, what the true nature of the threat is from ISIS, and the futility and negative blow-back from waging such a war, antiwar sentiment would develop much more quickly and deeply than otherwise. And those who already oppose this new war would be more articulate opponents of it if they, too, had a better understanding of the root problem, its origins, why the U.S. has entered the fray, and why this war is not in the best interests of the people of this nation.
Oregon and Washington Continue to Fund Fossil Fuel Infrastructure
ONWARD OREGON – Although Governors Kitzhaber and Inslee are publicly concerned about fossil fuel exports, other branches of our state governments are investing in infrastructure supporting these activities. Thanks to our friends at Sightline Institute, we see that Oregon and Washington have made substantial investments in enhancing fossil fuel export facilities.
Peace is Breaking Out All Over the World
STEVEN YOUNGBLOOD – A friend and colleague recently wrote me and asked if I, an advocate for peace, was discouraged by the avalanche of violence that seems to be engulfing mankind. It's certainly easy to get discouraged, or even to abandon the notion that peace is possible, given the new status quo in Ukraine, the Central African Republic, Iraq, Nigeria, Ferguson, Missouri, Mexico, Syria, Gaza, Somalia and so on. Against this backdrop, the annual commemoration of the International Day of Peace on Sept. 21 seemed futile—like holding a storm awareness seminar in the middle of a category five hurricane. Yes, the big picture seems awful. But it's not the only picture. That's why I choose to look instead at a number of other pictures that show peace breaking out all around the globe.
The New War, the Forever War, and a World Beyond War
WORLD BEYOND WAR ISIS STATEMENT – The following is an assessment of the current ISIS crisis. The statement examines: (1) the social context of the destructive violence in Syria and Iraq — where we are; (2) viable nonviolent alternatives — what should be done; and (3) opportunities for civil society to advocate and push for those alternatives — how we can make it happen. The alternatives and pathways toward achieving those are not only preferable from a perspective of humanity, but proven to be more effective.
People's Climate March Was a "Glimpse of the Movement We Need"
by Oregon PeaceWorks • October 8, 2014 • 0 Comments
NAOMI KLEIN – Once every five or 10 years, Naomi Klein publishes a book that changes the way we see things. With No Logo, published in 1999, she explored corporate power in a globalized world and the movements springing up to resist it. The Shock Doctrine, published in 2007, showed how governments collude with big corporations to take advantage of natural and human-made disasters to push through deeply unpopular change.Her newest book, This Changes Everything: Capitalism vs. the Climate is another transformational book.
What Would a Paradigm for Peace Look Like?
DAVID SWANSON – Raise your hand if you weren't surprised when fancy films of beheadings resulted in bombings? Keep your hand up if you weren't shocked when bombings resulted in more brutality and beheadings? Is it possible we need a radically different way of thinking about how to solve violence?
Global Problems Call for Global Solutions
LAWRENCE WITTNER – Sometimes, amid the heated political debate about what should done by the U.S. government in world affairs, a proposal cuts through the TV babble of the supposed experts with a clear, useful suggestion.
Overcoming Our Inner Dinosaur
WINSLOW MYERS – Is it too much of a stretch to link the alleged police execution of Michael Brown in Missouri with the terrorist execution of journalist James Foley somewhere in Iraq? Setting aside obvious differences, do these tragedies have anything in common?


As one of the best anxiety treatment centers near Seattle, we offer a broad range of treatment options, which allows us to customize the care we offer for each patient's individual needs. We focus on treatment and activities that support patient-centered care.
Generalized Anxiety Disorder is a disorder that can be a debilitating condition for many individuals who are diagnosed with it. GAD is characterized by irrational and overstated anxiety that occurs even when one has no actual reason to worry. While everyone has some amount of anxiety in their lives, those with GAD experience a severe amount of anxiety on a continuous and regular basis. The anxiety associated with this disorder is so bad at times that it begins to impact an individual's ability to complete daily tasks. Individuals with generalized anxiety disorder report that they can't always identify specific triggers that cause the development of their anxiety. A great deal of the time, the anxiety comes out of nowhere and completely overwhelms the individual.
At our anxiety treatment center near Seattle, we know how exhausting it can be to feel trapped in the world, never knowing when the next wave of anxiety will hit. With proper treatment, medication management, and support, anxiety symptoms can be controlled. We want you to know that you can successfully learn how to overcome your anxiety and live a life with less stress and worry.
With the high possibility for generalized anxiety disorder to cause significant negative consequences, it should be treated as soon as possible. If left alone, an individual will continue to worry and stress so much that soon they will no longer be able to properly function in society. In some severe cases, an individual may not be able to leave their house for fear of what may happen if they do. This causes job loss and complete social isolation.
Cascade Behavioral Health Hospital has leading health care experts who offer genuine compassion and have a commitment to treating you as an individual. The innovative programs we have created exist to comfort, educate, and empower our patients and their loved ones. We take a holistic approach to every aspect of care, which also includes the environment. This is why at our hospital you will find homelike, welcoming spaces that are designed to support the healing process. Our nursing stations are always approachable and patient care areas are created to promote a sense of calm.
The staff here at our hospital for anxiety treatment knows that when an illness is present it doesn't just affect an individual physically, but emotionally, mentally, and spiritually as well. This is why we firmly believe in caring for the whole person. We believe that each patient has rights, responsibilities, and choices when it comes to their healthcare. Additionally, we know that each patient has unique physical, emotional, intellectual, spiritual, and cultural needs. This approach to treatment empowers our patients to be involved in their own mental health care and encourages healing partnerships between all those involved in the process.
The treatment offered at Cascade are there to optimize care with minimal disruption to patients' lives. Our care includes treatment to stabilize a patient's condition, lectures for educational purposes, and individual and group therapy sessions. Before treatment can begin, comprehensive assessments are conducted to determine which program is best suited for your needs. We will determine if there are any substances in your system and if you are presenting with any co-occurring disorders.
Most commonly, GAD is treated with a combination of medication and therapeutic modalities. If your treatment plan dictates that you would benefit from medication, you will likely be given anxiety medication to help manage your symptoms. Once you have learned to better control your anxiety, medication dosage may be reduced or eliminated. All medication decisions and management will be determined by you and your treatment team. In addition to any medication that may be used, we also employ a number of other therapeutic techniques.
Our therapeutic techniques are used to treat generalized anxiety disorder and are comprised of different treatment modalities. We know that not everyone experiences anxiety in the same way, so we make sure that we use the treatments that work best for you. Additionally, we consistently reassess your condition throughout your stay so we can alter your plan as necessary.
Individual sessions will be held at our treatment center with you and a counselor, giving you time to process emotions surrounding your anxiety. Additionally, group sessions will be held so that you can work with others who are going through similar troubling times. Groups allow individuals to work together to learn more effective coping strategies and life skills. Through group work individuals can also build a stronger support network. Groups are held daily and cover a wide range of topics.
We understand that every individual we treat is part of a larger family and community. At our hospital, we welcome the involvement of friends and family as care partners. A care partner is an individual chosen by the patient who will be involved in their healthcare experience. The support of a loved one is vital during time of illness. A care partner is there to offer the love, support, and encouragement that make a huge difference in the healing process. Many times all a patient needs is a reassuring touch or encouraging smile.
When the inpatient treatment process is coming to an end we will work with you to ensure that an effective aftercare plan is put into place. At Cascade, we want to ensure that all parts are in place so that you can have a smooth transition into the next phase of your treatment, allowing you to continue making progress toward your recovery goals. Some individuals will be ready to discharge home, while others will step down into a less intense level of care. Cascade offers an outpatient program that gives individuals enough flexibility to still meet their work and school obligations. Our outpatient program uses techniques such as group therapy, family therapy, and informational lectures. Patients are taught skills such as stress management, relapse prevention, and life skills. Both morning and evening group times are available.
Our location in Tukwila near Seattle allows for us to serve residents from all over SeaTac region including Renton, Burien, and Des Moines. Call us today to begin the process of recovering from general anxiety disorder.


Founded in September 2015, in less than two years, badi has become the leader of the room rental market in Spain with a record of 760.000 matches between listers and seekers in only 2017 and 10.000.000 rental requests. Badi fills a gap in the market where there is an increasing need.
A few months back, badi received a Series A funding round. This allowed the company to continue growing and keep up with the overwhelming demand on an international scale. This year, badi is moving into new booming markets such as London, Paris & Amsterdam where there is a significant growth in organic traffic and a lot of evidence that shows the high demand of customers in these cities.
Originally inspired by the word "buddy", he turned this word into badi to make it sound catchy. As his main idea was to connect people who want to live together, he was convinced that "buddy" was the perfect concept to demonstrate the power of building connections.
In a house, the most important thing is not the space but the relationships you have with the people you share. This is like bringing a piece of joy to daily life such as sharing a simple piece of toast with your flatmates. With our first logo, composed of two slices of bread overlapping, which sets them apart from the cliché of a symbol of a house used by almost all real estate agencies, we wanted to put the message across that making a home is about people.
When we looked back, we realized that we needed to update our brand with a fresher look that reflects the values and beliefs of our trustworthy community and also the maturity of our product.
So, our amazing creative team updated in-house the current logo which features a modified and modern version of the slices of bread following three pillars: authenticity, modernity, and recognition to the digital world. We wanted to keep the slices of bread cool and captivating to break the standard vision people have of the real estate market.
To design the new logo, we isolated all the elements in their purest form. The overlapping forms express connectivity, whilst the square forms with rounded corners suggest the "toast" of the old logo. This new logo keeps showing the connections between people with a modern look and completely optimized to the digital world.
The colour fade represents the evolution of the business. Green for our origins, blue for the implementation of trustworthy new features and purple for prosperous worldwide connections. This new look and feel express our identity and community beliefs more profoundly.
We crafted a modern and fresh new brand identity that brings us one step closer to our dream of being the world's best real estate platform.
The new product is more seamless, intuitive & user-friendly. It delivers a better User Experience improving our security & social interactions. During this year, we will reinforce trust, diversity, reliability in an online secure environment with the launch of new exciting features and product updates.
Trust and safety remain the cornerstone of our marketplace. With our room booking system "Book Now", we can more readily establish and maintain user trust and security. "Book Now" allows you to book a room even if you are on the other side of the world. From now on, Seekers and Listers can send booking requests to the roommate they want to live with.
Acting as an escrow agent, badi will withhold the booking amount until 48 hours after the entry date of the seeker into the new room. We actively developed this feature to avoid being scammed on our platform and provide online secure payments for our entire community. At badi, we take your safety seriously and believe this feature has the ability to meaningfully enhance the Badi Experience.


This collection contains newspaper abstracts from Portsmouth, New Hampshire.
This collection may help you sketch a more detailed view of your ancestor's life and struggles. For example, we learn from an advertisement that John Abbot, located at his shop in Portsmouth, offered a reward of 20 shillings for any information regarding the individuals who attempted breaking into his shop. The dates the advert ran are also included.


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Cigna Institutes Quarterly Cash Dividend and Declares First Quarterly Dividend; Announces Investor Day on March 8, 2021 | News
BLOOMFIELD, Conn., Jan. 6, 2021 /PRNewswire/ — Global health services company Cigna Corporation (NYSE: CI) today announced that its Board of Directors has instituted a quarterly cash dividend and declared the first quarterly cash dividend of $1.00 per share of Cigna common stock to be paid on March 25, 2021 to shareholders […]
BLOOMFIELD, Conn., Jan. 6, 2021 /PRNewswire/ — Global health services company Cigna Corporation (NYSE: CI) today announced that its Board of Directors has instituted a quarterly cash dividend and declared the first quarterly cash dividend of $1.00 per share of Cigna common stock to be paid on March 25, 2021 to shareholders of record as of the close of trading on March 10, 2021.
"Cigna has a long track record of effective capital deployment, and our initiation of a quarterly dividend demonstrates our confidence in our ongoing ability to drive growth as we meet the needs of those we serve," said David M. Cordani, president and chief executive officer. "We are excited to share more at our Investor Day on March 8, 2021 about the strategic positioning of our businesses, drivers of ongoing, differentiated growth, and strong operating cash flow generation, which position us to deliver attractive shareholder returns."
"The Board's initiation of a quarterly dividend is part of a balanced capital deployment strategy to maximize shareholder value," said Brian C. Evanko, executive vice president and chief financial officer. "As we complete our intended deleveraging plans, our strong operating cash flows and forward growth path enable us to initiate a quarterly dividend while maintaining strong liquidity and capital flexibility in order to support ongoing investments for growth and expected meaningful share repurchase activity."
Cigna intends to pay regular quarterly dividends, with future declarations subject to approval by its Board of Directors and the Board's determination that the declaration of dividends remains in the best interests of Cigna and its shareholders. The decision of whether to pay future dividends and the amount of any such dividends will be based on the Company's financial position, results of operations, cash flows, capital requirements, the requirements of applicable law and any other factors the Board of Directors may deem relevant.
As of December 31, 2020, Cigna's outstanding share repurchase authority as approved by Cigna's Board of Directors was approximately $3.9 billion. Cigna expects to deploy at least $2 billion to share repurchase during the first quarter of 2021.1 From November 5, 2020, when Cigna reported third quarter 2020 earnings, through December 31, 2020, Cigna repurchased 5.9 million shares of common stock for approximately $1.2 billion.
Cigna will be hosting its virtual Investor Day on Monday, March 8, 2021. A live webcast of the presentation will be available on the Investor Relations page on www.cigna.com. A replay will be available for four weeks after the event at www.cigna.com.
About Cigna
Cigna Corporation is a global health service company dedicated to improving the health, well-being and peace of mind of those we serve. Cigna delivers choice, predictability, affordability and access to quality care through integrated capabilities and connected, personalized solutions that advance whole person health. All products and services are provided exclusively by or through operating subsidiaries of Cigna Corporation, including Cigna Health and Life Insurance Company, Connecticut General Life Insurance Company, Evernorth companies or their affiliates and Express Scripts companies or their affiliates. Such products and services include an integrated suite of health services, such as medical, dental, behavioral health, pharmacy, vision, supplemental benefits and other related products. Cigna maintains sales capability in over 30 countries and jurisdictions, and has more than 170 million customer relationships around the world. To learn more about Cigna®, including links to follow us on Facebook or Twitter, visit www.cigna.com.
1. The timing and actual number of shares repurchased will depend on a variety of factors, including price, general business and market conditions, and alternate uses of capital. The share repurchase program may be effected through open market purchases or privately negotiated transactions in compliance with Rule 10b-18 under the Securities Exchange Act of 1934, as amended, including through Rule 10b5-1 trading plans. The program may be suspended or discontinued at any time.
This press release, and oral statements made in connection with this release, may contain forward-looking statements within the meaning of the Private Securities Litigation Reform Act of 1995. Forward-looking statements are based on Cigna's current expectations and projections about future trends, events and uncertainties. These statements are not historical facts. Forward-looking statements may include, among others, statements concerning future dividends, share repurchases and other capital deployment plans and other statements regarding Cigna's future beliefs, expectations, plans, intentions, liquidity, cash flows, financial condition or performance. You may identify forward-looking statements by the use of words such as "believe," "expect," "plan," "intend," "anticipate," "estimate," "predict," "potential," "may," "should," "will" or other words or expressions of similar meaning, although not all forward-looking statements contain such terms.
Forward-looking statements are subject to risks and uncertainties, both known and unknown, that could cause actual results to differ materially from those expressed or implied in forward-looking statements. Such risks and uncertainties include, but are not limited to: our ability to achieve our financial, strategic and operational plans or initiatives; our ability to predict and manage medical and pharmacy costs and price effectively; our ability to adapt to changes or trends in an evolving and rapidly changing industry; our ability to effectively differentiate our products and services from those of our competitors and maintain or increase market share; our ability to develop and maintain good relationships with physicians, hospitals, other health care providers, producers, consultants, and pharmaceutical manufacturers; changes in the pharmacy provider marketplace or pharmacy networks; changes in drug pricing; the impact of modifications to our operations and processes; our ability to identify potential strategic transactions and realize the expected benefits (including anticipated synergies) of such transactions in full or within the anticipated time frame, as well as our ability to integrate or separate operations, resources and systems; the substantial level of government regulation over our business and the potential effects of new laws or regulations or changes in existing laws or regulations; the outcome of litigation, regulatory audits, investigations, actions or guaranty fund assessments; uncertainties surrounding participation in government-sponsored programs such as Medicare; the effectiveness and security of our information technology and other business systems and those of our key suppliers or other third parties; the impact of our debt service obligations on the availability of funds for other business purposes; unfavorable industry, economic or political conditions, including foreign currency movements; acts of civil unrest, war, terrorism, natural disasters or pandemics; reinsurance credit risk; the scale and scope of the COVID-19 pandemic and its potential impact on our business, operating results, cash flows and financial condition, as well as on our employees, clients, customers, suppliers and partners and on the U.S. and global economies; as well as more specific risks and uncertainties discussed in our most recent report on Form 10-K, as supplemented by our Form 10-Q for the quarter ended March 31, 2020, and subsequent reports on Forms 10-Q and 8-K available through the Investor Relations section of www.cigna.com. You should not place undue reliance on forward-looking statements, which speak only as of the date they are made, are not guarantees of future performance or results, and are subject to risks, uncertainties and assumptions that are difficult to predict or quantify. Cigna undertakes no obligation to update or revise any forward-looking statement, whether as a result of new information, future events or otherwise, except as may be required by law.
Alexis Jones
Jim Cohn
Once lost to addiction, she returns with message of hope
PHILADELPHIA (AP) — Under the weight of a soaked blanket, Megan Cohen inched her way, on foot, along a stretch of Interstate 95 in Philadelphia, the rain beating against her frail body. She wasn't looking to be saved. "I was so broken. I was homeless at that point for quite […]
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Failing to appear within visitors courtroom is really a breach from the created guarantee to appear in court on the provided trip to a particular period. It's possible to end up being punished for any failing to appear even though they're discovered simple from the police arrest or even quotation cost as well as when the situation is actually ignored. Failing to appear might be described as a misdemeanor criminal offense in certain jurisdictions. Whenever courtroom is wearing report your own failing to look, they might concern the table bring about for the police arrest. Failure to appear may also create a courtroom purchase in order to postpone your own permit. In several jurisdictions, to be able to obvious Failure to appear report an individual should spend the initial quantity for that quotation as well as the fee costs for that failing to look.
Failure to appear may also affect infractions associated with court providers needs. Just about all USA people older than 18 are needed legally to satisfy court responsibility providers regularly unless of course the lawful reason may be authorized through the correct government bodies. With respect to the legal system, Failure to appear with regard to court responsibility might at first lead to notices and extra court responsibility task updates. From any kind of stage, Failure to appear with regard to court responsibility providers might create a table bring about becoming released for that police arrest from the individual within disregard associated with courtroom. Failure to appear with regard to court responsibility could also lead to punitive penalties.
Failure to appear inside a municipal situation offers somewhat various outcomes compared to individuals within additional Failure to appear instances. When the plaintiff (the one that submitted the actual lawsuit) does not come in courtroom because needed, the situation might be ignored, therefore forfeiting the opportunity to go after the actual lawful situation later on. When the accused or even respondent inside a municipal situation commits Failure to appear breach, the actual courtroom might instantly assess in support of the actual plaintiff within the lack of an effort. This really is known as the default common sense and also the choices made in this manner tend to be lawfully joining to any or all events.
Whenever one is billed having a criminal offense, there might be large fees and penalties with regard to failing to look. If your individual encounters felony costs you will see numerous required courtroom looks they have to help to make. On police arrest as well as just before discharge, the actual supposed culprit may accept come in courtroom on the particular day time as well as period. Failure to appear can lead to the table bring about released for the police arrest. As soon as apprehended, the actual accused might be asked to publish bail or even end up being refused through discharge before the summary from the test. A lawyer can happen with respect to the accused from a good arraignment listening to, other than within instances associated with household physical violence, DRUNK DRIVING, or even additional crimes. In many additional instances, nevertheless, Failure to appear within felony courtroom because needed can lead to substantial fees and penalties.
If you'd like for more information regarding failure to appear in court, make sure you e mail us in order to consult with an experienced as well as skilled lawyer in your town.
A police friend of mine said 70% of his stops involved someone that had been drinking. He said no matter the time of day, they are more than likely drunk or close to drunk.
These topics are so cnoufisng but this helped me get the job done.
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