text:
\section{Introduction}
The past decade has seen growing interest in identifying new phases of entangled, out-of-equilibrium quantum matter. A sufficiently generic, isolated quantum system is expected to approach thermal equilibrium under its unitary dynamics, and develop an extensive amount of entanglement entropy~\cite{Deutsch_PRA_1991, Srednicki_Entropy_and_area_1993, Srednicki_ETH_1994}. The eigenstates of such systems feature entanglement entropy scaling as a volume law. On the other hand, the presence of disorder or a quasiperiodic potential is capable of drastically changing the dynamical properties of the system, leading to many-body localization (MBL). MBL systems represent a different dynamical phase of matter, in particular characterized by area-law entangled eigenstates. The existence of distinct dynamical phases characterized by qualitatively different scaling of entanglement entropy naturally raises the question of the nature of the so-called MBL phase transition separating the ergodic and MBL phases. While the MBL transition received significant attention~\cite{Nandkishore_2015_review,colloquium_mbl_2019},  it was later realized to be a particular example of an \emph{entanglement transition}, which separates phases with different entanglement scalings.

Beyond MBL,  examples of an entanglement transition are provided by measurement-induced entanglement transitions in random unitary circuits under random local measurements~\cite{Li_PRB_2018, Chan_PRB_2019, Skinner_PRX_2019, Bao_PRB_2020, Jian_PRB_2020, Gullans_PRX_2020, Zabalo_PRB_2020, Gullans_PRL_2020, Tang_PRR_2020, Choi_PRL_2020, Ippoliti_2021, PhysRevB.100.134306, Cao_2019, Nahum_2020_PRR, PhysRevX.11.011030, Lavasani_2021_Nature, sang2020measurement, li2020conformal, PhysRevB.102.014315, PhysRevLett.126.170602, Fuji_2020, PhysRevResearch.2.043072, Szyniszewski_2020, vijay2020measurementdriven, PhysRevB.103.104306, Fidkowski_2021, PRXQuantum.2.010352,lu2021entanglement,buchhold2021effective,bentsen2021measurementinduced,PhysRevLett.126.170503}, random tensor networks~\cite{Hayden:2016aa,Vasseur_2019_ET_RTN,2020arXiv201204666J,Lopez_Piqueres_2020,PRXQuantum.2.010352}, and Rokshar-Kivelson~\cite{RK_PRL_1988} (RK) inspired wave functions~\cite{Fradkin_2015_RK_and_EntanglementT}.
While all these phase transitions feature different tuning parameters and phenomenology, they often can be mapped  onto classical ordering (spontaneous symmetry-breaking) phase transitions. For instance, the measurement-induced transition, resulting from a competition between local random unitary dynamics and the rate of local projective measurements at random points in space and time, was shown~\cite{Jian_PRB_2020, Bao_PRB_2020} to be related to a classical ordering transition in a replicated two-dimensional statistical model. Changing the measurement rate tunes the effective temperature of the classical model, driving it from an ordered phase at small measurement rate~(corresponding to volume-law entanglement) to a disordered phase at large measurement frequency~(area-law). Similar entanglement transitions and mappings also were reported in random tensor networks~\cite{Hayden:2016aa,Vasseur_2019_ET_RTN}.

 A different approach to entanglement transitions was considered in~\cite{Fradkin_2015_RK_and_EntanglementT}. There, the authors considered a variational Ansatz state inspired by the Rokhsar-Kivelson wave function~\cite{RK_PRL_1988}, in which the weights for the configurations are chosen from the Gibbs weights of a classical spin-glass model. Since states with positive weights can only sustain an area-law worth of entanglement~\cite{Grover_2015}, an additional random sign structure was also considered. The entanglement transition in this scenario was proven to be related to the geometric localization of the wave function due to the classical spin glass transition.

Thus, on the one hand, both random tensor networks and measurement-induced entanglement transitions can be understood as an ordering transition in a two-dimensional statistical mechanical model, with the transition being induced by changing the tensor network bond dimension or the measurement rate. On the other hand, the transition observed in the RK-inspired wave function is closely related to a spin glass transition in an all-to-all spin-glass model. This motivates the question if entanglement transitions can be driven by physics beyond classical ordering transitions. The MBL transition as mentioned above could be one example of this. However, investigating the MBL transition is particularly challenging, see~\cite{colloquium_mbl_2019} and references therein for recent progress.

In this work, we focus on the variational wave function approach. Specifically, in this paper, we consider a neural-network inspired variational Ansatz for the quantum wave function~\cite{Carleo_2017}. Machine learning techniques have been proved fruitful to the field of many-body quantum physics~\cite{Carleo_2017, Gao_NatureC_2017, arsenault2015machine, machine_learning_phases_of_matter, Wang_PRB_2016, Broecker_SR_2017, Kelvin_PRX_2017, Hibat_PRR_2020, Vieijra_2020,Levine_2019_QuantumEnt_and_DeepL_arch, Jia2019EntanglementAL, morawetz2020u1}. Specifically, exciting progress has been made in identifying quantum phases and transitions among them, either symmetry-broken phases~\cite{machine_learning_phases_of_matter, van_Nieu_NatureP_2017, Wang_PRB_2016, Broecker_SR_2017, Kelvin_PRX_2017} or topological phases~\cite{Deng_PRB_2017}, establishing connections to renormalization group techniques~\cite{beny2013deep, mehta2014exact} and perturbation theory~\cite{Borin}. In addition, machine learning ideas have also been used in measuring quantum entanglement and wave function tomography~\cite{tubman2016measuring, Palmieri_NPJ, morawetz2020u1}. We focus on a particular neural network variational state, referred to as restricted Boltzmann machines (RBM) quantum states which have been proven~\cite{DasSarma_2017, Jia2019EntanglementAL} to capture both an area-law as well as volume-law worth of entanglement depending on the locality of the neural network. In addition, recent work~\cite{Vieijra_2020} showed that RBM states can also be used to parametrize quantum wave functions with non-Abelian symmetries. Having in mind the representability power of neural network Ans\"atze, and in particular, of the simple RBM Ansatz, we ask under what conditions it is capable of capturing an entanglement transition while continuously varying some parameters used to define the state.

Since our motivation lies in entanglement transitions not driven by classical phase transitions, we consider RBM quantum states where the real part of the wave function is a local function of the spin degrees of freedom. Since no classical phase transition can exist in local one-dimensional statistical models, in this way we exclude any possible entanglement phase transition driven by a classical phase transition in the wave function weights. Our main results and structure of this paper are as follows: After introducing short-range RBM quantum states and discussing their entanglement capabilities in  Sec.~\ref{sec:Section2}, we proceed with the study of short-range RMB states with uncorrelated random phases in Sec.~\ref{sec:Section3}. There we demonstrate the volume-law entanglement scaling for all values of the variational parameter $\beta$ that plays a role of inverse effective temperature, indicating the absence of an entanglement transition. Next, in Sec.~\ref{sec:Section4}  we study the phase diagram for short-range RBM quantum states but with power-law correlated phases as a function of inverse temperature $\beta$ and power-law exponent $\alpha$.  We numerically show the existence of three different scaling regimes of the entanglement entropy and discuss the existence of a possible entanglement transition in the two dimensional phase diagram characterized by $\alpha$ and~$\beta$.  We conclude in Sec.~\ref{sec:Section5} with brief discussions of our results and comments on directions for future work.

\section{Restricted Boltzmann Machines}\label{sec:Section2}
In this section, we introduce restricted Boltzmann machines in the context of their usage as a variational state for many-body quantum physics. Moreover, we discuss the entanglement properties of the resulting wave function which depends on the locality of the RBM~Ansatz.

\subsection{RMB as a wave function Ansatz}
A restriction from a Boltzmann machine~\cite{Ackley1985-ACKALA-2}, the so-called restricted Boltzmann machine (RBM) is one of the simplest cases of an artificial neural network that can learn a distribution over the set of their input. In the context of quantum many-body physics~\cite{Carleo_2017}, RBMs are often used to approximate the wave function that is interpreted as a (complex) marginal probability distribution. Assuming that the wave function is defined on the many-body Hilbert space of spin-1/2 degrees of freedom, the spin configurations $\sigma\in \{-1,1\}$ represent an input referred to as ``physical spins''.

The RBM is defined on a bipartite graph, whose vertices are grouped into two classes: the hidden spins and the physical (visible) spins, see Fig.~\ref{Fig:cartoon}.
Suppose there are $N$ visible spins and $M$ hidden spins, and we
associate the $N$ variables $\sigma\in\{-1,1\}$ and $M$ variables $h\in\{-1,1\}$ to the physical and hidden spins respectively. The spins in the hidden layer are connected to those in the physical layer, but there is no connection among spins in the same layer (see Fig.~\ref{Fig:cartoon} for an illustration). The RBM representation of the amplitudes of a quantum many-body wave function is obtained by tracing out the hidden spins:
\begin{equation}\label{Eq:amplitudes_RBM}
\Psi_{\Omega}(\sigma) = \sum_{h_j = \pm 1} e^{\sum^{N}_{i=1} a_i \sigma_i + \sum^M_{j=1} b_j h_j + \sum_{ij}\sigma_i W_{ij} h_j },
\end{equation}
and is fully specified by a set of variational parameters denoted as $\Omega = \{W, a, b\}$ that can assume complex values. Here non-zero interactions between hidden and physical spins $W_{ij}$ induce correlations between physical spins, whereas constants $a_i$ renormalize the wave function amplitudes depending on the state of individual spins and do not induce correlations. The presence of either non-zero $a_i$ or $b_i$ leads to a breaking of the ${\mathbb Z}_2$ symmetry associated with flipping all physical spins. The summation over hidden spins in Eq.~\eqref{Eq:amplitudes_RBM} can be performed analytically, resulting in
\begin{equation}\label{Eq:Psi-RBM}
\Psi_{\Omega}(\sigma)=e^{\sum_{i=1}^{N}a_{i}\sigma_{i}}\prod_{j=1}^{M}2 \cosh \left(b_{j}+\sum_{i=1}^N W_{ij}\sigma_{i} \right).
\end{equation}
Since the quantum many-body wave function typically contains complex parameters, we rewrite each term in the sum in its polar form $\Psi_{\Omega}(\sigma)=e^{i\phi_\sigma} e^{-E_{\Omega}(\sigma)/2}$, where both $\phi_\sigma$  and $E_{\Omega}(\sigma)$ are real, with the latter playing an analogue of an energy in the partition function that determines the norm of the state. More specifically, we introduce the partition function  $Z=\left. \langle \psi_{\Omega} \right| \psi_{\Omega} \rangle =\sum_\sigma e^{-E_\Omega(\sigma)}$, thus corresponding to a statistical model characterized by the energy function $E_\Omega(\sigma)$. In the remaining of the paper, we will explore the structure of entanglement in this wave function, depending on the different choices of the variational parameters $\Omega$.

\subsection{Entanglement of RBM states}
As supported by representability theorems~\cite{LeRoux_2008}, RBM can approximate any many-body quantum state. However, such approximation may require an exponential in system size number of hidden spins and parameters, thus rendering the representation impractical. The interest lies then in finding types of many-body quantum states that can be \emph{efficiently} described by RBM Ansatz with a number of hidden spins and parameters scaling \emph{polynomially} in the number of physical spins $N$. Throughout this work, we restrict to Ans\"atze that have the same number of physical and hidden spins, $N=M$.

\begin{figure}[tb]
\begin{center}
\includegraphics[width=0.95\columnwidth]{cartoon.pdf}\\
\caption{\label{Fig:cartoon}
{\bf{General and local RBM.}} (a) Most generic connectivity of RBM with a dense interaction $W_{ij}$ matrix. (b) Example of ``local'' RBM network. Only nearest neighbour interactions between physical and hidden spins are considered.}
\end{center}
\end{figure}

Entanglement is a crucial feature of the quantum wave function. Hence, to understand the representability power of Ans\"atze that are polynomial in system size, a study of the entanglement structure of such quantum states is required. The entanglement properties of RBM were first studied in~\cite{DasSarma_2017}, where it was demonstrated that RBM states with short-range interactions between hidden and visible spins feature an
area law of entanglement in any dimension and for arbitrary network geometry. More precisely, it was proven (see Theorem 1 of \cite{DasSarma_2017}) that when wave function~(\ref{Eq:Psi-RBM}) has $W_{ij}=0$ if $|i-j|>\mathcal{R}$,  Renyi entropies with an index $n$ of a region $A$ are bounded as $S_{n}(A)\leq (2 \mathcal{R}  \log 2)  \partial A$ for all values of $n$. Here $\partial A$ denotes the surface area of subsystem $A$ and the Renyi entropy with index $n$ is defined as
$$
S_n(\rho_A) = \frac{1}{1-n}\ln \mathop{\rm{Tr}} \rho_A^n,
$$
where $\rho_A$ is a density matrix of the region $A$, obtained by tracing out all complementary degrees of freedom. This bound on all Renyi entropies indicates interesting connections between short-range RBM states and quantum states represented by a matrix-product state~(MPS)~\cite{Werner_1992, Cirac_2007, SCHOLLWOCK201196}. In particular, it was shown that all 1D short-range RBM~\cite{DasSarma_2017, Cirac_RBMs_2018}, as well as sufficiently sparse~\cite{Chen_RBM_and_TNS_2018} RBM can be efficiently described in terms of MPS. It is interesting to note that the validity of the inverse statement is to the best of our knowledge unknown, that is, given a generic MPS with a small bond dimension it is unknown whether there exists a representation in terms of a short-range RBM.

Moreover, Ref.~\cite{DasSarma_2017} demonstrated via an explicit example that long-range RBM states can exhibit volume-law entanglement. This further implies that the corresponding MPS representation of such a state would require an exponential scaling of the bond dimension with the system size.

As we discussed above, RBM Ans\"atze are capable of representing quantum states with both area- and volume-law entanglement. This suggests the natural hypothesis that RBM may provide a potential Ansatz for a variational wave function that exhibits an entanglement transition. Inspired by this hypothesis, in the remainder of this work we explore entanglement structure of the RBM quantum states and its dependence on the variational parameters.

\section{Uncorrelated random phases}\label{sec:Section3}
\begin{figure*}[t]
	\begin{center}
		\includegraphics[width=1.98\columnwidth]{fig2_new.pdf}
		\caption{ \label{fig:constant_E_urandph} {\bf{Absence of entanglement transition in model with uncorrelated random phases.}}
	(a) The apparent finite-size crossing in the plot $s_2 = \langle S_{2}\rangle/S_{A}$ vs $\beta$, for the RBM state with constant energy function and i.i.d random phases, {that could be attributed to a possible} entanglement transition. Points correspond to the quenched average computed numerically, and they nearly perfectly agree with the lower bound (lines) calculated analytically. {The inset shows the drift of the crossing point for analytic curves for different system sizes.}
(b) Difference of the 2nd-Renyi entropy density for system sizes $N$ and $N+2$, showing that the crossing points shift to higher values of $\beta$ with system size $N$, indicating the absence of a transition. (c) At large system sizes we observe a slow, logarithmic dependence of $\beta_{{\rm cross}}$ with system size, i.e., $\beta_{{\rm cross}}(\delta,N)\sim\ln N$ in the $N\gg1$ limit, indicating the absence of a transition. Here we considered system size spacings $\delta =2, 4$ and $6$.
	}
	\end{center}
\end{figure*}

In this section we motivate and introduce the first family of variational RBM Ans\"atze with random uncorrelated phases. After that we discuss results for the annealed average of the second Renyi entropy which shows the absence of an entanglement transition in this family of wave functions.

\subsection{RBM ansatz wave function}
In this work, we only consider ansatzes that do not allow for a description of the entanglement transition in terms of a classical phase transition in the wave function weights. Is it then natural to restrict to local RBM quantum states. However, such construction cannot encode volume law entanglement due to result of Ref.~\cite{DasSarma_2017} discussed above. Thus we introduce a minimal extension to the short-range RBM ansatz and include an additional contribution coming from independent and identically distributed (i.i.d) random phases. In this aspect, our construction is similar to that of Ref.~\cite{Fradkin_2015_RK_and_EntanglementT} that extended the variational wave function of the Rokshar-Kivelson type with random phases. Crucially, here we keep the interactions between spins strictly local.

Specifically, we consider the following ansatz state as our starting point:
\begin{align}
|\psi_\Omega(\beta)\rangle & =\frac{1}{\sqrt{Z}}\sum_{\sigma}e^{i\phi_{\sigma}}\Psi_\Omega(\sigma,\beta)|\sigma\rangle,
\label{eq:sRBM}
\end{align}
where each phase $\phi_{\sigma}$ is i.i.d and drawn from a uniform distribution in the $[-\pi, \pi]$ interval. This wave function is parametrized by the parameter $\beta$ that plays the role of effective inverse temperature in the RBM-type state $\Psi_\Omega(\sigma,\beta)$,
$$
\Psi_\Omega(\sigma,\beta)=\prod_{j}^{N}\cosh\big(\beta(\lambda+\sigma_{j}+\sigma_{j+1})\big).
$$
This state is a particular example of RBM wave function from Eq.~(\ref{Eq:Psi-RBM}),
where the network geometry includes only nearest neighbor interactions between physical and hidden spins, see Fig.~\ref{Fig:cartoon}(b). We note that $\Psi_\Omega(\sigma,\beta)>0$ for all states $|\sigma\rangle$ in the computational basis, and hence it can be written as $\Psi_\Omega(\sigma,\beta) =e^{-E_{\Omega}(\beta)/2}$,
where
\begin{equation}\label{eq:energy_srbm}
E_\Omega(\beta)=-2\sum_{j}\ln\cosh\big(\beta(\lambda+\sigma_{j}+\sigma_{j+1})\big),
\end{equation}
 can be interpreted as the energy of some underlying statistical mechanical model. In what follows we fix the value of lambda such that $\lambda=0.1$.

\subsection{Bounding Renyi entropies}
We are interested in studying average Renyi entropies,
\begin{equation}
\langle S_{n}(\rho_{A})\rangle=\frac{1}{1-n}\big(\langle\ln{\rm Tr}\big(\bar{\rho}_{A}\big)^{n}\rangle-n\langle\ln Z\rangle\big),\label{eq:quenched_ent}
\end{equation}
where $\rho_A=\frac{1}{Z}\bar{\rho}_A$ represent the normalized quantum state of the subsystem $A$. The averaging is performed over the random phases $\phi_\sigma$ in Eq.~(\ref{eq:sRBM}). However, in general calculating $\langle\ln\bar{\rho}_{A}^{n}\rangle$ is analytically intractable and hence we resort to computing a lower bound. The lower bound, $\langle S_{n}(\rho_{A})\rangle
\geq\langle S_{n}(\rho_{A})\rangle_{{\rm ann}}$, uses the so-called annealed average of the same Renyi entropy
\begin{equation}
\langle S_{n}(\rho_{A})\rangle_{{\rm ann}}=\frac{1}{1-n}\big(\ln\langle{\rm Tr}\big(\bar{\rho}_{A}\big)^{n}\rangle-n\ln \langle Z\rangle\big),
\label{eq:anneal_ent}
\end{equation}
where the disorder-averaged density matrix and partition function enter the logarithm.

It is possible to show that for any state of the form of Eq.~\eqref{eq:sRBM} all annealed Renyi entropies can expressed via modified partition functions depending on the Renyi index $n$. In particular, focusing on the second  Renyi entropy we obtain
\begin{equation}
\langle S_{2}(\rho_{A})\rangle_{{\rm ann}}=-\ln\left(\frac{{\rm Tr}_{A}Z^2_A+{\rm Tr}_{B}Z^2_B}{Z^{2}(\beta)}-Y(\beta)\right),\label{eq:lower_sRBM}
\end{equation}
where $Z_{A,B} = {\rm Tr}_{A,B} e^{- E_\Omega(\beta)}$ are the partition function on region $A$ and its complement $B$, and $Y= Z(2\beta)/Z^2(\beta)$ corresponds to the inverse participation ratio. Such representation of the second Renyi entropy opens the door to analytical calculations of Eq.~\eqref{eq:lower_sRBM}. The final results is then an  analytical function of the system size $N$ and the variational parameter $\beta$. This allows us to obtain the value of $\langle S_{2}(\beta)\rangle_{{\rm ann}}$ for an arbitrary system sizes $N$. We relegate the detailed derivation to Appendix~\ref{App:A} and instead discuss results below.

\subsection{Absence of entanglement transition}
In Fig.~\ref{fig:constant_E_urandph}(a) we compare the numerical results for the average bipartite second Renyi entropy with the corresponding lower bound. We observe a good agreement between the average second Renyi entropy and its lower bound throughout the full range of considered values of $\beta$. At low $\beta$ the bipartite second Renyi entropy scales extensively with system size, $S_2 \sim N$ which further implies the same scaling for the entanglement entropy. At larger values of $\beta$ we observe an apparent crossing for curves corresponding to different system sizes. While this may suggest the existence of an entanglement transition tuned by $\beta$, below we will argue that this crossing originates from strong finite size effects.

To explore the fate of the crossing between normalized second Renyi entropy curves as the number of spins is increased, we first compute the difference between the annealed second Renyi entropy for systems consisting of $N$ and $N-2$ spins. Figure~\ref{fig:constant_E_urandph}(b) shows that the crossing point shifts toward larger values of $\beta$ when the number of spins $N$ is increased, suggesting the absence of an entanglement transition in the present case. The absence of transition is further supported by Fig.~\ref{fig:constant_E_urandph}(c), that shows a logarithmic increase of the value of $\beta_\text{cross}^{(\delta,N)}$ defined as the point where crossing occurs between normalized second Renyi entropy for $N$ and $N+\delta$ spins. The logarithmic increase with $N$ holds for $\beta_\text{cross}^{(\delta,N)}$ irrespective of the separation $\delta$ between the system sizes considered, giving a strong indication that the crossing shifts to $\beta=\infty$ in the thermodynamic limit.

Summarizing, the above results imply that short-range RBM quantum states with uncorrelated random phases, Eq.~\eqref{eq:sRBM}, always display a volume-law entanglement at arbitrary large but finite values of $\beta$. Therefore this ansatz does not have an entanglement transition as a function of $\beta$. While the result here was obtained for a simple class of RBM states with only nearest neighbor interactions, we also numerically confirmed it for longer-range local RBM states. Thus we believe that arbitrary local (finite-range) RBM states feature volume-law entanglement for any finite values of $\beta$, and thus do not have an entanglement transition.

\section{Correlated random phases}\label{sec:Section4}

\begin{figure*}
\includegraphics[width=1.9\columnwidth]{phase_diag.pdf}
\caption{{\bf{Phase diagram:}} (a) The phase diagram derived from the implications of the analytical bound, which implies $S\sim N^{2-\alpha}$ for $\alpha<2$  and $S\sim \text{const}$ for $\alpha>2$ for large values of $\beta$. For smaller $\beta$ we use the finite size scaling of the numerical data, which lead to the tentative critical line $\beta_c=\beta(\alpha)$ (grey and black).  Here the arrows refer to the different finite size behaviors of the tentative critical line $\beta_c$, and could be consistent with its disappearance in the thermodynamic limit.  The use of different colours in the critical line for $\alpha<1$ (grey) and $\alpha>1$ (black) is to signal that the former corresponds to a crossover, and hence is it a finite size effect.
(b-e) Illustration of finite size scaling of $\langle S_2 \rangle/S_A$ for different fixed values of $\beta$ and number of physical spins ranging between $N=12$ and $N=20$.
(b-c) For values of $\alpha<1.5$ the presence of crossings is observed suggesting the existence of a critical line separating two regions with different scaling for the entanglement entropy. However, the stability of this observation in the thermodynamic limit cannot be fully established within the current reach of our numerics; see the main text for a further discussion.
(d) For $1.5 < \alpha < 2$ numerics suggest the entropy to scale sub-extensively with system size $N$ in agreement with the analytical bounds predicting the entanglement entropy to be, at large values of $\beta$, upper bounded by $N^{2-\alpha}$.
(e) For $\alpha>2$ numerical results show the entropy becomes independent of system size $N$ hence satisfying an area-law of entanglement.
}
\label{fig:phase_diag}
\end{figure*}

As we discussed in Sec.~\ref{sec:Section3}, the presence of uncorrelated random phases does not allow for an entanglement transition in the local RBM variational Ansatz. Two natural directions towards an entanglement transition consist in relaxing either the locality of the energy function $E_{\Omega}(\beta)$ or introducing correlations between random phases in Ansatz~(\ref{eq:sRBM}). In order to avoid a spin-glass transition in the classical Hamiltonian, leading to the geometric localization of the wave function, we keep the local structure of RBM and relax the condition of uncorrelated random phases. In particular, below we consider a short-range RBM ansatz with power-law correlated random phases, controlled by a power-law exponent $\alpha$.
\subsection{RBM Ansatz wave function}
We introduce correlations between random phases using the RBM description of the wave function with complex parameters. Specifically, we consider the Ansatz Eq.~(\ref{Eq:Psi-RBM}) with $a_i=0$ and complex values of $W_{ij}$ written as $W_{ij} =  W^{(1)}_{ij}+ i W^{(2)}_{ij}$. The real part of the couplings is taken to be local with constant nearest neighbors interaction, that is, $W^{(1)}_{ij}$ is the same as in Eq.~\eqref{eq:sRBM}. The imaginary part of couplings,  $W^{(2)}_{ij}$, is a random number that is suppressed with distance between points $i$ and $j$,
\begin{equation}\label{Eq:}
W_{ij}^{(2)} = \frac{w_{ij}}{|i-j|^{\alpha}}, \text{ with $w_{ij} \in [-\pi, \pi]$.}
\end{equation}
 Here the power-law exponent $\alpha>0$ controls the decay of correlations in real space. In addition, we consider a longitudinal magnetic field of the form $b_j=\lambda + i b_j^{(2)}$, with $b_j^{(2)} \in [-\pi, \pi] $.

 Translating the above choice of complex $W_{ij}$ into the wave function and keeping only the local part of the energy function we obtain the following expression:
\begin{equation}\label{eq:cRBM_state}
|\psi_\Omega(\beta)\rangle=\frac{1}{\sqrt{Z}}\sum_{\sigma}e^{i\sum_{j=1}^N\arg(z_{j}(\beta))}\prod_{j=1}^N\cosh(\beta X^{(1)}_{j})
|\sigma\rangle.
\end{equation}
where $z_j$ depends on the  complex parameters of the RBM under consideration,
\begin{equation*}
z_j = \cosh (\beta X^{(1)}_{j}) \cos X^{(2)}_{j}+i\sinh (\beta X^{(1)}_{j}) \sin X^{(2)}_{j},
\end{equation*}
with $X^{(1,2)}_j = b_{j}^{(1,2)}+\sum_{i=1}^N\sigma_{i}W_{ij}^{(1,2)}$. From this representation we see that the presence of non-zero imaginary part of the RBM parameters translates into correlated phases entering in the expression for the RBM wave function, Eq.~(\ref{eq:cRBM_state}).

The presence of non-local random phases in this model makes it impossible to find an exact expression for the lower bound of $\langle S_2(\beta) \rangle$ as done in Section.~\ref{sec:Section3}. Hence, we resort to perturbative expansions in the the high-$\beta$ regime of the state in Eq.~\eqref{eq:cRBM_state}.

\subsection{High-$\beta$ limit}
In the limit of large $\beta$ we expand Eq.~(\ref{eq:cRBM_state}) to first non-trivial order in $\beta|X^{(1)}_{j}|$, which gives following expression
\begin{equation}
\label{eq:high_beta_state_approx}
|\psi_\Omega(\beta\gg1)\rangle\approx \frac{1}{\sqrt{Z(\beta)}}\sum_{\sigma}e^{i\phi_{\sigma}}e^{-E_\Omega(\beta)/2}|\sigma\rangle,
\end{equation}
where $\phi_{\sigma}= \sum_{j=1}^{N}\mathop{\rm sign}[X^{(1)}_{j}]X^{(2)}_{j}$ and $E_\Omega(\beta)$ is given by Eq.~\eqref{eq:energy_srbm}.
We can think of the state Eq.~\eqref{eq:high_beta_state_approx} as the result of time evolving the state
$
|\Phi\rangle=\frac{1}{\sqrt{Z}}\sum_{\sigma}e^{-E_\Omega(\beta)/2}|\sigma\rangle
$ that has no phases with a Hamiltonian $H_{Z}$ that is diagonal in the computational basis and has eigenvalues
$\phi_{\sigma}$. Since the state $|\Phi\rangle$ features an area-law entanglement~\cite{DasSarma_2017}, the structure of entanglement of the state $|\psi_\Omega(\beta\gg1)\rangle$ is determined by the phases encoded in $H_Z$. Below we will consider the structure of $H_Z$ and use it to understand the entanglement of the resulting state.

The explicit form of $H_{Z}$  depends on the range $\mathcal{R}$ of the real part of RBM couplings $W^{(1)}_{ij}$. However, for any finite $\cal R$ it features long-range power-law interactions between spins determined by the parameter $\alpha$. As an example, it is possible to show that for the present ansatz
\begin{equation}
H_Z =\sum_{ij}\frac{J_{ij}}{|i-j|^\alpha}  \sigma^z_i\sigma^z_j + \sum_i h_i \sigma^z_i,
\end{equation}
where $J_{ij} \propto w^2_{ij}$ and $h_i$ is a random number uniformly distributed in the $[1/2, 1/2+\pi]$ interval. In order to understand the entanglement created by $H_Z$, we use results of Ref.~\cite{Gorshkov_2017_Entanglement_area_laws}. This work obtained an upper bound on the rate of production of entanglement entropy, $\Gamma = dS_A/dt$. The entanglement rate scales as the area of the boundary's subregion when $\alpha>2$ ($\alpha>D+1$ in arbitrary dimensions). Since the initial state $|\Phi\rangle$ is an area-law state, the aforementioned result guarantees that the state $|\psi_\Omega(\beta\gg1)$ has an area-law entanglement if $\alpha>2$. In contrast, for $\alpha<2$ the results of Ref.~\cite{Gorshkov_2017_Entanglement_area_laws} imply that the entangling rate that scales as $\Gamma \sim N_A^{2-\alpha},$ where $N_A$ is the size of the subregion $A$ which here we always take as $N_A=N/2$ since we focus on the bipartite entanglement. Note that when $\alpha\in(1,2)$ we get that $2-\alpha<1$ and hence, the entangling rate scaling is sub-extensive in the system size $N$.

The application of the upper bound from Ref.~\cite{Gorshkov_2017_Entanglement_area_laws} results in the high-$\beta$ phase diagram boundaries shown at the top part of Fig.~\ref{fig:phase_diag}(a). For $\alpha>2$ the bound implies area-law scaling of entanglement. For the intermediate values of $1<\alpha<2$ we expect at most a subextensive amount of entanglement, $S\propto N_A^{2-\alpha}$. Finally, for the values of $\alpha<1$ the upper bound has volume-law entanglement and thus is not very useful.

\subsection{Phase diagram}

Although the bound discussed above provides expectations for the phase diagram at high values of $\beta$, the expansion breaks down at small values of $\beta$. Therefore, we resort to numerical simulations to determine the phase boundaries at intermediate and small values of $\beta$. To be consistent with our previous approach, we focus on the second Renyi entropy and perform numerical simulations for systems with up to $N=20$ physical spins. The results of these simulations are summarized in Fig.~\ref{fig:phase_diag}.

To begin with, let us explore the region determined by $\alpha<1$, where according to summary shown in Fig.~\ref{fig:phase_diag}(a) we expect the volume law entanglement. In this region, the analytical bound does not provide any useful information. We compare the numerical results for average second Renyi entropy $\langle S_2(\alpha, \beta) \rangle$ with fixed $\alpha<1$ to the analytical result from Eq.~\eqref{eq:lower_sRBM} for the annealed average obtained under assumption of i.i.d random phases and the same non-random energy function. Remarkably, we observe a good agreement between both quantities at all values of $\beta \in [0, 1.5]$ considered in the numerical simulations, see an example in Fig.~\ref{fig:phase_diag}(b). In particular, we find that for every $\beta$ in the considered range the difference between the analytical expression and numerically averaged second Renyi entropy is on average $\sim 10^{-7}$ and assumes the maximal value of $\sim 10^{-4}$ in the worst case, achieved for small values of $\beta$. This result suggests that, in this regime, the average second Renyi entropy in the presence of long-range phase correlations nearly coincides to its annealed average value in the case of uncorrelated random phases. This case was considered in Section~\ref{sec:Section3}, where we demonstrated an absence of entanglement transition.

Therefore, although the finite size scaling reveals a crossing in  Fig.~\ref{fig:phase_diag}(b), we expect this crossing to shift to larger values of $\beta$ with increasing system size.
This is further supported by Fig.~\ref{fig:betac_vs_alpha_Rhalf}, that shows the increase of the point $\beta_{\rm cross}$,  defined at the point where curves corresponding to different system sizes cross, for $\alpha<1$. This result is along the line with our expectations of a volume law entanglement at all finite $\beta$.  However, the available range of $N$ is insufficient to check if $\beta_\text{c}$ grows logarithmically with $N$ as we demonstrated in Sec.~\ref{sec:Section3}.

Next, we continue with the region $1 < \alpha <2$. Here the bound suggests the existence of a sub-extensive scaling of the entropy at large $\beta$, as indicated at the top of Fig.~\ref{fig:phase_diag}(a). Numerical simulations in Fig.~\ref{fig:phase_diag}(c) show the presence of crossings for values of $\alpha$ that are sufficiently close to one, for example $\alpha=1.15$. For larger values of $\alpha$, for instance $\alpha = 1.66$ no crossing is observed and instead we find a good agreement with a sub-extensive $N^{2-\alpha}$ scaling of the entropy shown in Fig.~\ref{fig:phase_diag}(d).
This result suggests the existence of a critical region separating the volume-law and sub-extensive scaling regimes, as is illustrated by the black line in Fig.~\ref{fig:phase_diag}(a) that shows the position of the crossing. The inset of Fig.~\ref{fig:betac_vs_alpha_Rhalf} shows the scaling collapse for $\alpha=1.15$ with critical exponents $(\beta_c, \nu) = (0.42, 0.5)$.

We observe the crossing and performed scaling collapse for the region of $1<\alpha<1.53$ that is suggestive of entanglement transition. However, as observed in Fig.~\ref{fig:betac_vs_alpha_Rhalf},  finite size scaling of data shows that in the region $\alpha>1$ the critical line shifts toward smaller $\alpha$ when considering larger system sizes. Such finite size drift may again suggest this region might be associate with a crossover rather than an actual entanglement transition, but due to our limited system size points, we cannot rule out any of the two possibilities.

Finally, for  $\alpha>2$, numerical simulations in Fig.~\ref{fig:phase_diag}(e) show the entanglement entropy to be independent of system size for all finite values of $\beta$, signaling the existence of area-law scaling for the entanglement entropy. This is reflected in Fig.~\ref{fig:phase_diag}(a) by the shaded region for $\alpha>2$.

In summary, the phase diagram proposed in Fig.~\ref{fig:phase_diag}(a) agrees with our numerical findings for the existence of three different scaling regimes for the entanglement entropy. The possible entanglement transition tuned by parameter $\beta$ could be realized in this phase diagram for an intermediate range of $\alpha$, $1 <  \alpha \lesssim 1.53$. However, the example of strong finite-size effects and eventual absence of transition for $\alpha < 1$ suggests that one has to interpret these findings with care, and additional studies maybe needed to rule out the possibility of this being a crossover rather than a true entanglement transition.

\begin{figure}[t]
\includegraphics[width=\columnwidth]{fig4.pdf}
\caption{{\bf Finite size scaling for the critical curve:} Clearly distinct behavior in the finite size scaling results for the critical $\beta(\alpha)$ ($\alpha(\beta)$) is observed for regions $\alpha \lessgtr 1$. For $\alpha<1$ with increasing system size the crossing point shifts towards larger $\beta$, which is in agreement with our previous expectations. Moreover, for $\alpha>1$ with increasing $N$ the crossing point shifts towards smaller $\alpha$. Circles (triangles) correspond to cuts at constant $\beta$ ($\alpha$). \emph{Inset}: Example of scaling collapse of numerical data at fixed $\alpha=1.15$. We find the critical exponets to be $(\beta_c, \nu) =(0.42, 0.5)$. Scaling collapses of data were performed using the \texttt{pyfssa}~\cite{pyfssa, autoscalepy} package.}
\label{fig:betac_vs_alpha_Rhalf}
\end{figure}

\section{Discussions}\label{sec:Section5}
Motivated by recent studies of entanglement transitions, we considered a neural-network inspired variational Ansatz for the quantum wave function. We used RBM quantum states, which have been proven capable of representing ground states of many-body Hamiltonians with polynomial-size gap and quantum states generated by any polynomial-size quantum circuits~\cite{Gao_NatureC_2017,  Huang_2017}. We studied whether such variational states can capture an entanglement transition while continuously varying some parameters used to define the underlying neural network.

First, we considered a short-range RBM state with independent random phases parametrized by $\beta$  that plays the role of an inverse temperature. For this Ansatz we analytically calculated a lower bound on the second Renyi entropy.  We found numerically that the averaged second Renyi entropy is very close to the analytic lower bound for all numerically accessible number of spins (up to $N=20$). Although both the analytical lower bound and the numerically averaged Renyi entropy display finite size crossings, we demonstrate that they are associated with a crossover rather than an actual entanglement transition. Using the analytical lower bound we observe that the crossing point $\beta_{\rm{cross}}$ scales very slowly, as $\ln N$ for large $N$, a scaling that would be extremely hard to recognize from numerical simulations due to the limited range of accessible number of spins. We conclude that the short-range RBM Ansatz with random phases features a volume law entanglement at all finite values of $\beta$, thus ruling out the possibility of an entanglement transition.

As a more general example, we relaxed the assumption of uncorrelated random phases, and considered random power-law correlated phases controlled by the exponent $\alpha$. The presence of long-range correlated phases did not allow to apply the analytic approach and we instead resorted to numerical simulations of the second Renyi entropy. Using known bounds on the entangling rate for systems with power-law interactions, we derived a hypothetical phase diagram with three regions of different scaling of entanglement entropy for large values of $\beta$. For small and intermediate values of $\beta$, our numerical simulations suggest the existence of a critical curve in the $(\beta, \alpha)$ plane. However, the limited range of number of spins we can access does not allow us to exclude the presence of a crossover rather than an actual phase transition.

As a future research direction, it would be interesting to go beyond RBM states. In particular, a recent work~\cite{Levine_2019_QuantumEnt_and_DeepL_arch} suggested  that contemporary deep learning architectures, in the form of deep convolutional and recurrent networks, can also efficiently represent highly entangled quantum systems. Moreover, it was shown that such architectures can support volume-law entanglement scaling, polynomially more efficiently $\mathcal{O}(N)$ than presently employed RBM, $\mathcal{O}(N^2)$. Hence, it would then be interesting to carry out the same study we pursued in this work but using these state-of-the-art neural-network base wave functions.

\section*{Acknowledgments}
We would like to thank to S. De Nicola and P. Brighi for fruitful discussions and valuable feedback on the manuscript. R.M. and M.S. acknowledge support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No.~850899). R.V. acknowledges support from the US Department of Energy, Office of Science, Basic Energy Sciences, under Early Career Award No. DE-SC0019168, and the Alfred P. Sloan Foundation through a Sloan Research Fellowship.

redpajama_set_name: RedPajamaArXiv


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The Emotional Recovery After a Heart Attack Is a Life-Long Process, Says Bob Harper
"I had to build that trust — that relationship with my heart — again."
It's been over two years since fitness trainer Bob Harper went into cardiac arrest at a New York City gym. The then-51-year-old was revived by a stranger (who happened to be a doctor), and paramedics before being taken to the hospital where he was induced into a coma for two days. The former Biggest Loser host had what's known as a "widow-maker" heart attack — complete blockage in the left anterior descending artery (LAD) of the heart — which is about four times more deadly than other types. Since then, Harper has shared countless health tips to help people lower their risk of heart disease, but now he's focused on something new: the emotional recovery post-heart attack that often goes unnoticed when discussing heart disease.
Harper has teamed up with AstraZeneca to spread the message behind Survivors Have Heart, a national support group-type program that celebrates survivorship and provides emotional help for heart attack survivors and their loved ones. The first event kicks off this summer in Tampa, Florida on June 5, 2019.
For Harper, the road to recovery first began with forgiving his body for "failing." In an exclusive interview with DoctorOz.com, Harper shares what he's learned about balancing the emotional fears and stress that come with surviving a heart attack and shares his tips on how you can move forward with balancing your mental health.
Lean On Your Doctors
"There's such a mental aspect in recovery that people aren't even aware of," Harper says. "As a survivor you'll think, 'My body is better, but why is there a constant voice in the back of my head that's saying, 'What's my heart rate? My heart is pounding—is that okay?' The inner dialogue happens all the time." As a result, Harper battled depression for months. "Imagine if you've been in a relationship where someone broke your heart and now they're back," he explains. "My heart got broken. I kept thinking, 'You stopped on me and now you're back? How do I know you aren't going to stop on me again?' I had to build that trust — that relationship with my heart — again."
The 53-year-old couldn't be more thankful that his medical team has been addressing mental health. "It's been very much in the forefront," he says. "At first when I'm sitting in my cardiologist's office, they're being very pragmatic, but I'm not; I'm emotional." Harper encourages fellow survivors to open up to their physicians about their thoughts and feelings. "You've got to have trust in your healthcare providers — you're not just a name on a chart," he stresses. "I'm sure this has to be hard on doctors, but we need it. I need it."
Take Advantage of Cardiac Rehabilitation
"For me, a huge, huge, part of rebuilding that trust came from [going to] cardiac rehab [a customized, out-patient exercise and counseling program that is medically supervised]," states Harper. "Being strapped up to heart monitors, watching my heart rate — just seeing my heart working was really helpful." He adds that his early sessions, which included moderately peddling on a stationary bike and strolling on a treadmill, were very humbling. "Privately, I would have said humiliating, but I got over that quickly." He credits the physical therapists for talking him "off the ledge" on the days he feared going home after rehab and having another heart attack. "I was there three days a week for months, and speaking with the therapists and other heart attack survivors slowly helped me feel more confident."
Even though some of the health data is alarming, one statistic that's posted on SurvivorsHaveHeart.com is inspiring: There are approximately 7.9 million heart attack survivors in the U.S. "Look at the survival rate and maybe it can somehow let you to start to exhale," he says. "You're not alone."
Control What You Can
Once Harper "graduated" from cardiac rehab and got the okay from his MD to head back to his regular gym, he suffered from panic attacks. "All of a sudden, I wasn't going to be in a confined area with other doctors," he explains. To overcome this fear, he makes sure he's in a gym where the fitness instructors are CPR (cardio-pulmonary resuscitation) certified and that there is an AED (automated external defibrillator) on site. "It's about having the practical things in place in order to give you peace of mind," he continues. "I wouldn't be here right now if I didn't have someone around me at the time when I needed them the most."
Find Ways to Quiet Your Mind
While he learned that reducing stress levels would be beneficial for both his emotional and physical health, Harper found himself in a catch-22 situation. After all, hardcore workouts had been his go-to coping mechanism. "Then all of a sudden that shifted, which is why those panic attacks were very real for me." These days, the television personality achieves inner calmness by meditating ("I've been doing Bikram yoga that they call an open-eye meditation"), along with tapping into creative interests, such as cooking ("Rachael Ray has me cooking a lot and I love it!"), photography ("It's very challenging, very fulfilling"), and reading ("I didn't go to college, so now I'm getting acquainted with the Bronte Sisters, John Steinbeck, and F. Scott Fitzgerald"). "These are great hobbies because they take your mind someplace else," he adds.
Harper says it took him nearly one year after his life-altering event to stop focusing on the "what-ifs" and to start living in the moment. "None of us know what is out there waiting for us, so I choose to be optimistic," he states. "As for me, I do what I'm told and I try not to sweat the big and the small things." Repeating mantras, such as "It's going to be okay," remind him to appreciate that he's been given a second chance at life. "You're going to have the sh*ttest days ever and that's okay because there will be better days ahead," he continues. "It's a journey I'm still on. It takes time."
For more Dr. Oz wellness tips, recipes, and exclusive sneak peeks from The Dr. Oz Show, subscribe to the Dr. Oz newsletter.
Bob Harper Meets the Man Who Saved His Life
The Genetic Condition Behind Bob Harper's Heart Attack
Bob Harper's New Post-Heart Attack Diet
This website is for informational and entertainment purposed only and is not a substitute for medical advice, diagnosis, or treatment.
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Hilario Durán (born 1953, Havana) is a Cuban-Canadian jazz pianist.

Durán studied at Conservatorio "Amadeo Roldán" Amadeo Roldan Music Institute in Havana, studying tumbao with Evaristo Aparicio, composition and conducting from German Pifferrer, and orchestration from Guillermo Barreto. He formed a group in the 1970s called Los D'Siempre, which melded traditional Cuban elements with those of modern jazz. He joined Arturo Sandoval's band from 1981 to 1990. He also worked with Dizzy Gillespie's United Nation Orchestra and Michel Legrand. He formed a new group, Perspectiva, in 1990, and toured Central America and Europe. From 1995 he worked as a solo artist in Toronto, Canada, and has collaborated over the course of his career with Tata Güines, Changuito, Horacio "El Negro" Hernandez, Jorge Reyes, Roberto Occhipinti, Larry Cramer, John Patitucci, Michael Brecker, Regina Carter, Dave Valentin, Juan Pablo Torres, John Benitez, Dafnis Prieto, Hugh Marsh, Carlos "Patato" Valdés, Lenny Andrade, Quartetto Gelato, Jane Bunnett and the Gryphon Trio. Duran was nominated for Juno Awards in 2002, 2005, 2006, and 2007, winning in 2005 for New Danzon, and 2007:From The Heart", this album also was Grammy nominated.

Discography
Habana 9 P.M. (Areito, 1978)
Francisco's Song (Justin Time, 1996)
Killer Tumbao (Justin Time, 1997)
Havana Flute Summit (Naxos Jazz, 1997)
Habana Nocturna (Justin Time, 1999)
Havana Remembered (Avalon Music, 2002)
New Danzon (Alma Records, 2005)
Encuentro en La Habana (Alma, 2006)
From the Heart (Alma, 2006)
Motion (Alma, 2010)
Cuban Rhapsody (Alma, 2011) with Jane Bunnett
Christmas Salsa (Avalon, 2013)
Contumbao (Alma, 2017)
The Cuban (Alma, 2019)

References
[ Hilario Durán] at Allmusic

1953 births
Living people
Cuban jazz pianists
Cuban emigrants to Canada
Afro-Cuban jazz pianists
Post-bop pianists
People from Havana
Canadian jazz pianists
Juno Award for Contemporary Jazz Album of the Year winners
21st-century Canadian pianists
Justin Time Records artists

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Soccer Wing product design is derived from the United States. Industrial-grade aluminium alloy materials are selected for the products, and all components are detachably assembled and connected. The product surface is disposed by electrostatic powder spraying. The product has some features as rust and corrosion resistance, high-safety and environmental protection, easy assembly and a high-end and beautiful appearance. The product life lasts more than 20 years.


text:
To see All uses of "malicious" in Oliver Twist, please enable javascript.
wanting to see others suffer; or threatening evil
That he had, from his birth, displayed no better qualities than treachery, ingratitude, and malice.
Chapter 17 — Oliver's Destiny Continuing Unpropitious, Brings a Great.... (84% in)
Intent upon this innocent amusement, Noah put his feet on the table-cloth; and pulled Oliver's hair; and twitched his ears; and expressed his opinion that he was a 'sneak'; and furthermore announced his intention of coming to see him hanged, whenever that desirable event should take place; and entered upon various topics of petty annoyance, like a malicious and ill-conditioned charity-boy as he was.
Chapter 6 — Oliver, Being Goaded by the Taunts of Noah, Rouses into Action.... (39% in)
'That's very likely,' returned Sikes with a malicious grin.
Chapter 13 — Some New Acquaintances Are Introduced to the Intelligent.... (38% in)
Every member of the respectable coterie appeared plunged in his own reflections; not excepting the dog, who by a certain malicious licking of his lips seemed to be meditating an attack upon the legs of the first gentleman or lady he might encounter in the streets when he went out.
When Mr. Brownlow admitted that on no one point of inquiry could he yet return a satisfactory answer; and that he had postponed any investigation into Oliver's previous history until he thought the boy was strong enough to hear it; Mr. Grimwig chuckled maliciously.
Chapter 14 — Comprising Further Particulars of Oliver's Stay at Mr.... (73% in)
The old gentleman was just going to say that Oliver should not go out on any account; when a most malicious cough from Mr. Grimwig determined him that he should; and that, by his prompt discharge of the commission, he should prove to him the injustice of his suspicions: on this head at least: at once.
He talked of miseries which his wife had brought upon him; of the rebellious disposition, vice, malice, and premature bad passions of you his only son, who had been trained to hate him; and left you, and your mother, each an annuity of eight hundred pounds.
Chapter 51 — Affording an Explanation of More Mysteries than One.... (37% in)
As the villain folded his arms tight together, and muttered curses on himself in the impotence of baffled malice, Mr. Brownlow turned to the terrified group beside him, and explained that the Jew, who had been his old accomplice and confidant, had a large reward for keeping Oliver ensnared: of which some part was to be given up, in the event of his being rescued: and that a dispute on this head had led to their visit to the country house for the purpose of identifying him.
I offer you, now, no distinction among a bustling crowd; no mingling with a world of malice and detraction, where the blood is called into honest cheeks by aught but real disgrace and shame; but a home—a heart and home—yes, dearest Rose, and those, and those alone, are all I have to offer.'
There are no more uses of "malicious" in Oliver Twist.


Meg here, sharing a little creative inspiration for your office. I just can't get enough of post-it notes. They can be used for so many things, from organization and note keeping to decorating. My favorite post-it notes are these adorable Marseille Collection notes. The colors are so cheery that I just can't help but smile when I see them. These are just a few cute ideas for using post-it notes in your space!
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Ornaments- Christmas may have passed but I think these adorable ornaments can be hung up all year around. They look just like spring to me!
Goal List- This daily goal board is so cute. The tutorial is a little big for a desk, but you can easily create a little goal board that fits right in your office. It's such a nice way to keep your daily and weekly goals up to date and easily visible.
I hope these Post-It Note ideas got you inspired to make a post-it note project of your own. Send me your favorite ways to use post-it notes!
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At home in both contemporary and traditional decor, this kettle boasts a fresh take on classic design. The elastic and supple appeal of tea is brought to life by the artist through the use of lacquer. The processes of moulding and casting translate the fluidity of the medium in metal and wood. The elaborate, whimsical silhouette of this kettle makes it a work of art.


Do You Have a Surgical Error Claim?
Every surgery carries with it an expected benefit, as well as the possibility of recognized side effects or complications, which vary according to the specific procedure and are accepted as part of the risk of surgery. If you or a loved one has suffered due to serious complications either caused or exacerbated by surgical error, however, you deserve compensation for the suffering that was never part of the bargain.
At the Law Offices of Steven I. Kastner, we are known for our successful record of recovering compensation for victims of medical negligence. To schedule a free consultation with a San Diego surgical errors attorney, contact us today.
When you have experienced this kind of trauma, you may require additional medical treatment and possibly even ongoing health care. You may also need to take more time away from your job, leading to a larger wage loss than was originally expected.
You may be entitled to compensation for medical costs, wage loss, pain and suffering, and other related damages suffered due to surgical errors. Contact us online or for a free consultation call 619-232-8822 to speak with a Chula Vista surgeon negligence lawyer.


text:
Q: Analogue of Schur indicator for reps in p-adic fields Suppose we have a finite group $G$, a division algebra $X$ over $\Bbb Q_p$ with (some) maximal subfield $L$ and an irrep $V$ of $G$ over $L$ (one may assume that everything is separable to make life easier). We can compute invariants $$\nu_s := \frac{1}{|G|} \sum_{g \in G} \chi_{V}(g^s).$$
Can we tell whether $V$ is induced from some $L' \subset L$, or admits an $X$-structure looking at those numbers?
P. S. I tried to prove easy part of Frobenius-Schur theorem (i. e. that those numbers can only be roots of unity or zero) but failed to do so; it's just false for $s \neq [L:\Bbb Q_p]$, if my computations are correct, but I may have failed at checking irreducibility. If it holds in case they are equal, or in general, I'd be happy to know why.

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The Woodlands Where self-sufficiency is the master plan It used to be, they say, that anytime anybody in The Woodlands ever needed anything, they had to fire up the SUV for the minute trek to Houston: Now, 39 years on, it appears the original master planned community really did have a master plan, so much so that residents these days find it difficult to leave at all.
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Wealthy dating by kalyani10 The largest city in the US state of Texas, Houston is also the fourth biggest city in the entire country. The fact that the city is also the economic hub of the Houston-Sugar Land-Baytown Metropolitan area, the sixth largest such metropolitan area in United States, is an indication of the financial prosperity that many of its residents enjoy. Thus if you are looking to meet and date rich successful guys from the Lone Star state, Houston is one of the best places to begin your search.
The two main segments of the energy industry here are oil and natural gas even though renewable energy resources like wind and solar power now have growing economic bases in the city. Thus if you are eager to meet the oil barons or millionaires who have made their money in the lucrative energy sector, Houston offers ample opportunities to do so, especially in the many upscale cafes and pubs along the Energy Corridor.
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The Houstonian offers couples a romantic getaway just outside Houston's downtown area in a secluded acre wooded property. The resort's room accommodations feature floor-to-ceiling windows, premium bedding, plush robes and spacious bathrooms with deep tubs.
Zora Hughes – Updated July 30, Romantic restaurants, date spots and ambiance are not hard to find in a city as large and cosmopolitan as Houston, Texas. But in the middle of the city, it's hard to find a true resort getaway experience for you and your special someone. The Greater Houston area, however, has number of couple-friendly resorts where you can focus on romance in a relaxing, luxurious environment — all within 30 minutes to an hour from downtown Houston.
Step outside the city for romance in the Greater Houston area. Meet Singles in your Area! The Houstonian Club, Resort and Spa The Houstonian offers couples a romantic getaway just outside Houston's downtown area in a secluded acre wooded property. The resort's room accommodations feature floor-to-ceiling windows, premium bedding, plush robes and spacious bathrooms with deep tubs.
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The company purchased 1, acres 7. When Houston Heights was founded, it was a streetcar suburb of Houston which attracted people who did not wish to live in the dense city. It had its own municipality until the City of Houston annexed the Heights in
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Landmarks[ edit ] Houston's mercat cross , used as a symbol of the village. Houston's historic village centre, located at the north-west edge of the village, is a designated conservation area. The area is home to the main village pubs, small shops and the village's Post Office. North Street and South Street are dominated by traditional white cottages, some dating to the 17th century.
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The steeple is obscured.
Houston Press January 6, 2011 : Page 1
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Denver Area Gluten Free Christmas Pie Sale | Gluten Free Things, Inc.
If you're planning to make your own gluten-free or vegan fruit pies, pumpkin pies and goodies for the Christmas holiday gathering, then we salute you. Unfortunately not everyone has the time nor inclination.
Our Gluten Free Things Pie and Goodie Sale is now available for online pre-orders.
Visit this link to cut to the chase and get er done.
Of course baking during the holidays is a totally different animal than the routine dinner every night schtick. You know, the age old "What's for dinner tonight" question that comes floating in from members of the family to the main cook. Because he occasionally rattles off the statement "I know you hate to cook", I consistently reply to my husband the same statement: "thats not true, I don't hate cooking" (not really getting WHY he didn't process the last time I said the same thing). I gently launch into the same explanation. "It's the "ROUTINE" of dinner every night, every night, that gets old", I repeat for the umpteenth time.
I digress. Back to the real topic of this blog article. We're announcing that our Christmas Pie and Goodie Sale is now on, and since baking your own gluten-free anything can be quite the project, John Irvin, Master Baker and owner of Gluten Free Things, enjoys helping his customers opt for an alternative when it comes to your Gluten Free Christmas. "We can help you with the gluten-free vegan fruit pies, gluten free pumpkin pie, and gluten-free vegan breads like a dozen dinner rolls, French Loaf, Croissants, and Hoagie Rolls", John states to the person who called the bakery.
Gluten Free Things hope the Early Bird Sale Prices will help your ease the demands on your wallet and also help you streamline your holiday preparations.
Early Bird Pricing on Pre-Orders for Arvada and Denver Metro customers is available online until Saturday, December 16th.
Visit Shop.GlutenFreeThings.com to pre-order online.
After Saturday, December 16th our pie and goodies will be regular price. We will end ordering at closing time on Tuesday, December 19th. For those of you who just got busy and realize you need a pie or dinner rolls, call John at 303-668-1663 to inquire about extras he may have.
Pickup dates before Christmas are: 7am and 7pm Thursday, December 21st and Friday, December 22nd. Or 7am to noon on Saturday, December 23rd.
As a reminder, all items in our Holiday Pies & Goodies category are for Arvada and Denver Metro area Customer Pickup Only. No Shipping.
In addition to pies (Apple, Blueberry, Cherry, Pumpkin and Peach varieties) we've also got dinner rolls, french loaves, croissants and hoagies available for early bird pricing.


It all started with an angry letter.
Over a year ago, I was watching my boyfriend play an adventurous video game. I noticed that the protagonist was a middle-aged man, greying and wrinkled, and I thought it was interesting and neat that the developers made this decision of age when creating the character.
It got me thinking though… How many middle-aged women are protagonists in video games?
How many middle-aged women do we see adventuring, and showing what great capabilities they still have?
As I started researching, looking up lists of female protagonists in video games and talking with everyone I knew, I became more and more angry about the utter lack of representation of middle-aged and elderly women in video games. Especially in American culture, I see that women over child-bearing age are rarely seen in media (other than advertising anti-aging products). The only middle-aged/elderly women I see in video games are always pigeon-holed into nurturing grandma roles, which of course does exist and is a role that should be represented and honored.
But I feel that we as women have a lot more to offer than just those traditional roles.
I started writing an angry letter, addressing video companies as a whole, verbally trashing and attacking them about the lack of representation of women over child-bearing age.
Once I was done with the letter however, I also realized that an angry letter wouldn't spark the kind of change that I wanted to see in the world.
Over the next few months, the Wise Not Withered project slowly began to inhabit a bigger and bigger space in my mind, and I realized that I had an idea that could be huge and awesome and really connect people.
Instead of writing simply an angry letter, I thought… How great would it be to send an encouraging package to video game companies to invite them to diversify the ages of their female protagonists, but not just with words?
What if I could show them—through pictures, stories, and music—what was possible?
When I started seriously putting more and more thought and concerted effort into this project idea, I knew that I wanted to somehow involve the demographic of women that I am advocating for. If I was going to argue that women over child-bearing age have rich stories to tell, why not reach out to the wise not withered women in my life and listen to their stories?
On Friday, November 30, 2018, the first episode of the Wise Not Withered Podcast will be released. Season 1 will consist of 10 interviews that I have conducted with wise women in my life. Audio recordings will be available through this very website, soundcloud, iTunes, and wherever else I can figure out!
I wanted to make an intro for the podcast that had simple but compelling instrumentation and inspirational words. Here it is!
The longer our lives, the richer our stories.
A woman of strength, integrity, character.
A woman who has seen hardships, struggles, pain, and loss.
A woman who has compassion, love, courage, and power.
A woman who has succeeded, failed, and learned.
A woman who will continue to persevere and thrive.
When I look at you, I see a woman who is WISE NOT WITHERED.
Season 1, Episode 1 Release Date: November 30, 2018! Stay tuned!!


text:
Komitet Centralny Komunistycznej Partii Kuby (Comité Central del Partido Comunista de Cuba) – centralna instancja partii, wykonująca polecenia Biura Politycznego Komunistycznej Partii Kuby, de facto organ zarządzania wszystkimi dziedzinami życia w tym kraju.

Komórki organizacyjne
 Wydział Organizacyjny i Polityki Kadrowej (Departamento de Organización y Política de Cuadros)
 Wydział Ideologiczny (Departamento Ideológico)
 Wydział Stosunków Międzynarodowych (Departamento de Relaciones Internacionales)
 Wydział Edukacji, Sportu i Nauki (Departamento de Educación, Deportes y Ciencia)
 Wydział Nauki (Departamento de Ciencia)
 Wydział Ekonomiczny (Departamento Económico)
 Wydział Transportu, Turystyki, Łączności i Usług (Departamento de Transporte, Turismo, Comunicaciones y Servicios)
 Wydział Orientacji Rewolucyjnej (Departamento de Orientación Revolucionaria)
 Wydział Polityki Socjalnej (Departamento de Atención a la Población)
 Wydział Sektora Rolno-Spożywczego (Departamento de Agroalimentario)
 Wydział Przemysłu i Budownictwa (Departamento de Industria y Construcción)
 Biuro ds Wyznań (Oficina de Atención a los Asuntos Religiosos)
 Wydział Ameryki (Departamento América)
 Archiwum (Archivo)
 Centrum Dokumentacji (Centro de Documentación)

Przy KC funkcjonują:
 Wyższa Szkoła Partyjna im. Nico Lopeza  (Escuela Superior del Partido Ñico López), Havana, 5ta. Ave. y 246 Sta. Fe, Playa
 dziennik Granma, Havana, General Suárez y Territorial
 wydawnictwo literatury politycznej KC KPKuby (Editora Política del CCPCC), Havana, Belascoaín y Desagües No. 864, Centro Habana

Siedziba Komitetu Centralnego
Mieści się w prawym skrzydle Pałacu Rewolucji przy Plaza de la Revolución.

Zobacz też
 Komitet Centralny Komunistycznej Partii Związku Radzieckiego
 Komitet Centralny Socjalistycznej Partii Jedności Niemiec

Bibliografia
 Ministerio de Relaciones Exteriores de la Republica Cuba: Sistema politico y electoral Cubano, Havana 1997
 Estructura del Partido Comunista Cubano, [w:]
 hasła na hiszpańskiej Wiki
 hasła na hiszpańskojęzycznej kubańskiej e-encyklopedii EcuRed

Przypisy

Hawana
Partie komunistyczne
Polityka Kuby


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text:
package org.helenus.commons.lang3;

import java.io.ByteArrayInputStream;
import java.io.ByteArrayOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.Serializable;

import java.util.zip.GZIPInputStream;
import java.util.zip.GZIPOutputStream;

import org.apache.commons.lang3.SerializationException;

/**
 * The SerializationUtils class defines helper methods for
 * serialization.
 *
 * @copyright 2015-2015 The Helenus Driver Project Authors
 *
 * @author  The Helenus Driver Project Authors
 * @version 1 - Jan 15, 2015 - paouelle - Creation
 *
 * @since 1.0
 */
public class SerializationUtils extends org.apache.commons.lang3.SerializationUtils {
  /**
   * Serializes and compresses a given object to the specified stream.
   *

   * The stream will be closed once the object is written.
   * This avoids the need for a finally clause, and maybe also exception
   * handling, in the application code.
   *

   * The stream passed in is not buffered internally within this method.
   * This is the responsibility of your application if desired.
   *
   * @author paouelle
   *
   * @param  obj the object to serialize and compress
   * @param  outputStream the stream to write to
   * @throws SerializationException (runtime) if the serialization fails
   * @throws NullPointerException if outputStream is null
   */
  public static void serializeAndCompress(Serializable obj, OutputStream outputStream) {
    org.apache.commons.lang3.Validate.notNull(outputStream, "invalid null outputStream");
    try {
      final GZIPOutputStream os = new GZIPOutputStream(outputStream);

      org.apache.commons.lang3.SerializationUtils.serialize(obj, os);
    } catch (IOException e) {
      throw new SerializationException(e);
    }
  }

  /**
   * Serializes and compresses a given object.
   *
   * @author paouelle
   *
   * @param  obj the object to serialize and compress
   * @return an array of bytes representing the compressed serialized form of
   *         the object
   * @throws SerializationException (runtime) if the serialization fails
   */
  public static byte[] serializeAndCompress(Serializable obj) {
    final ByteArrayOutputStream baos = new ByteArrayOutputStream(512);

    SerializationUtils.serializeAndCompress(obj, baos);
    return baos.toByteArray();
  }

  /**
   * Decompresses and deserializes an object from the specified stream.
   *

   * The stream will be closed once the object is written. This
   * avoids the need for a finally clause, and maybe also exception
   * handling, in the application code.
   *

   * The stream passed in is not buffered internally within this method.
   * This is the responsibility of your application if desired.
   *
   * @author paouelle
   *
   * @param  inputStream the serialized object input stream
   * @return the corresponding object
   * @throws NullPointerException if outputStream is null
   * @throws SerializationException (runtime) if the serialization fails
   */
  public static Object decompressAndDeserialize(InputStream inputStream) {
    org.apache.commons.lang3.Validate.notNull(inputStream, "invalid null inputStream");
    try {
      final GZIPInputStream is = new GZIPInputStream(inputStream);

      return org.apache.commons.lang3.SerializationUtils.deserialize(is);
    } catch (IOException e) {
      throw new SerializationException(e);
    }
  }

  /**
   * Decompresses and deserializes the blob back into the original object.
   *
   * @author paouelle
   *
   * @param  data the blob to decompress and deserialize
   * @return the corresponding object
   * @throws SerializationException (runtime) if the serialization fails
   */
  public static Object decompressAndDeserialize(byte[] data) {
    return SerializationUtils.decompressAndDeserialize(
      new ByteArrayInputStream(data)
    );
  }
}

redpajama_set_name: RedPajamaGithub


text:
Last edited by Maunris
6 edition of The Father of All Things found in the catalog.
The Father of All Things
Tom Bissell
A Marine, His Son, and the Legacy of Vietnam (Vintage Departures)
by Tom Bissell
Published March 11, 2008 by Vintage .
Essays & Travelogues,
Travel / Essays & Travelogues,
Travel - General
(DR) The things of the world were created by God for the proper use of men to achieve their salvation. Yet too often they have been deprecated as hindrances to sanctity. Father Pierre Charles here offers a guide to prayer — meditation, especially — which will be welcomed by all who have found concentration on abstract spiritual concepts exclusively very difficult, frustrating and. For all these things, we should thank God. Most of all, we should thank him for giving us life. If we are really thankful to God, we will do something. What is that?— We will listen to God, and we will do what he tells us in the Bible. In that way we can show that we love the One who made all things.
26 But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you all things and will remind you of everything I have said to you. (Read full chapter. The book is titled after a phrase from the pre-Socratic philosopher Heraclides, who said: War is the father of us all. And what he meant by that was not to glorify war, but to realize that it's in.
"The Signature of All Things" is not, by any means, a seamless novel. There are moments of jarring prose, of nonsensical leaps, of characters going places you doubt they would ever go. Significantly, all three of these reasons why Jesus is the Father can be identified in Abinadi's message: (1) Jesus is the Creator, "the very Eternal Father of heaven and of earth" (Mosiah ); (2) Jesus is the Father of His seed, or posterity, begotten through the Atonement (see Mosiah –13); and (3) Jehovah speaks as Elohim in.
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Immunogenetics in Rheumatology
A question of upbringing
The Foraging Spectrum
Hotline and the LTV Corporation present the almanac of 1988 presidential politics
Peoples Lives
Growing trees in Canadian gardens
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Methods of cell research
The New View of Society and Other Writings
Biological diversity of Gujarat
The Father of All Things by Tom Bissell Download PDF EPUB FB2
Blending history, memoir, and travelogue, The Father of All Things is a portrait of the war's personal, political, and cultural impact from the perspective of the generation that grew up in the wake of the conflict.
It is also a wise and revelatory book about the bond between fathers and sons/5(21). The Father of All Things: A Marine, His Son, and the Legacy of Vietnam. Tom Bissell. Rating details ratings 37 reviews. In Aprilas Saigon fell to the North Vietnamese Army, John Bissell, a former Marine officer living in the Upper Peninsula of Michigan, was glued to his television/5.
The Father of All Things is a riveting, haunting, and often hilarious account of a veteran and his son's journey through Vietnam. As his father recounts his experiences as a soldier, including a near fatal injury, Tom Bissell weaves a larger The Father of All Things book of the war and explores.
The Father of All Things Book Summary. Opening with a gripping account of the chaotic and brutal last month of the war, The Father of All Things BookBrowse Review. The Father of All Things is an angry, heartfelt, deeply personal, sometimes darkly funny book that.
As he did in that book, so too in "The Father of All Things", Tom has written an eminently readable autobiographical/historical work as a result of what seems to be a prodigious amount of research. The historical material in this work, concerning the Vietnam war, and the actions and motivations of key political figures in it, is a synopsis of the views and thoughts of many another writer/5(21).
The Father of All Things; The first of the book's three sections narrates the historical leadup to Saigon's fall inspliced with Bissell's imagined vision of his family on the night Saigon fell (his parents' marriage was rapidly collapsing due to John's postwar trauma and alcoholism).
Next comes an exhaustively researched history of. Tom Bissell (b. ), a travel writer and novelist, is the son and grandson of Marine officers who served in Vietnam. The destruction of South Vietnam was followed by the destruction of his parents' marriage.
Father of All Things is Bissell's attempt to learn more about. THE FATHER OF ALL THINGS A MARINE, HIS SON, AND THE LEGACY OF VIETNAM by Tom Bissell ‧ RELEASE DATE: March 6, A penetrating look back at the Vietnam conflict, with Bissell (Chasing the Sea,etc.) alternately guiding and following his veteran father.
Opening with a gripping account of the chaotic and brutal last month of the war, The Father of All Things is Tom Bissell's powerful reckoning with the Vietnam. A glorious, sweeping novel of desire, ambition, and the thirst for knowledge, from the # 1 New York Times bestselling author of Eat, Pray, Love and Committed.
In The Signature of All Things, Elizabeth Gilbert returns to fiction, inserting her inimitable voice into an enthralling story of love, adventure and discovery/5(K). From award-winning author Tom Bissell comes a riveting book that offers a fresh perspective on the Vietnam War: that of veterans' adult children.
In Tom and his veteran father, John, traveled to Vietnam, reliving John's experiences in the war while familiarizing themselves with.
The Father of All Things is a riveting, haunting, and often hilarious account of a veteran and his son's journey through Vietnam. As his father recounts his experiences as a soldier, including a near fatal injury, Tom Bissell weaves a larger history of the war and explores Brand: Knopf Doubleday Publishing Group.
The Father of All Things is an angry, heartfelt, deeply personal, sometimes darkly funny book that explores the war that shattered Bissell's father and in turn ruptured their family. yet for us there is but one God, the Father, from whom all things came and for whom we exist. And there is but one Lord, Jesus Christ, through whom all things came and through whom we exist.
Ephesians as a plan for the fullness of time, to bring all things in heaven and on earth together in Christ. Ephesians James Context. 14 But every man is tempted, when he is drawn away of his own lust, and enticed. 15 Then when lust hath conceived, it bringeth forth sin: and sin, when it is finished, bringeth forth death.
16 Do not err, my beloved brethren. 17 Every good gift and every perfect gift is from above, and cometh down from the Father of lights, with whom is no variableness, neither shadow of. "Father of All " is a song by American rock band Green Day, released as the lead single from their thirteenth studio album, Father of All Motherfuckers, on Septem Background and composition.
Lead vocalist Billie Joe Armstrong has stated the song is about "making people feel bad." Armstrong added "Rock and roll sometimes has. Bible verses related to God The Father from the King James Version (KJV) by Relevance - Sort By Book Order 1 Corinthians - But to us [there is but] one God, the Father, of whom [are] all things, and we in him; and one Lord Jesus Christ, by whom [are] all things, and we by him.
God the Father is the Supreme Being in whom we believe and whom we worship. He is the ultimate Creator, Ruler, and Preserver of all things. He is perfect, has all power, and knows all things. He "has a body of flesh and bones as tangible as man's" (Doctrine and Covenants ).
Opposition in All Things. By Elder Dallin H. Oaks. Of the Quorum of the Twelve Apostles. Opposition permits us to grow toward what our Heavenly Father would have us become. Central to the gospel of Jesus Christ is the Father's plan of salvation for the eternal progress of His children.
That plan, explained in modern revelation, helps us understand many things we face in mortality. Instructional 4-DVD set for the I Can Do All Things art program.
Features video instruction and demonstration for all lessons. This is a component of the I Can Do All Things Book Set with DVDs that is included with the Adventures in U.S.
History Deluxe Package. But the Advocate, the Holy Spirit, whom the Father will send in My name, will teach you all things and will remind you of everything I have told you. Berean Literal Bible But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things and will bring to your remembrance all things that I have said to you.The Father-Thing" is a science fiction short story by American writer Philip K.
Dick. The story, told through third-person narration but focusing on the child, concerns the replacement of a boy's father with a replicated version.
At first, only the child sees the difference and has to .This book brings you the original version of a book titled THE HISTORY OF THE ORIGIN OF ALL THINGS. It is published here in its un-edited version, which Jesus began dictating in and had published in as a philosophical foundation for understanding the spiritual history of the planet as well as its future.
siyamiozkan.com - The Father of All Things book © 2020


An Irvine man was charged last week with aiding a drunk driver to flee the scene of a deadly crash, then lying to police about the driver's whereabouts, according to a news release from the Orange County district attorney's office.
Jamie Servin, 38 was charged with one felony count of accessory after the fact with knowledge of a person, and one misdemeanor count of resisting and obstructing a peace officer.
Servin also faces a sentencing enhancement for a prior robbery conviction in 1992. If convicted, he faces a maximum sentence of six years in state prison.
Servin is accused of assisting 38-year-old Robert Charles Serrano on Jan. 3. While driving under the influence of alcohol, Serrano ran a red light at the intersection of MacArthur Boulevard and Main Street in Santa Ana.
Four cars, including Serrano's, were involved in the ensuing crash. A female driver of one of the involved vehicles, Corban White, 18, was injured and later died at a nearby hospital.
Servin is accused of picking Serrano up at the scene and later telling police he had not been in contact with and did not know where Serrano had gone, according to the release.
Servin turned himself in to the La Palma Police Department on Thursday. He was released from custody on $100,000 bail.
Serrano pleaded guilty Feb. 22 to one felony count of vehicular manslaughter with gross negligence while intoxicated and multiple sentencing enhancements. He was sentenced to 31 years in state prison.


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