text:
Harmony Gold reduces losses, vows to put miner safety first
Gold mining company Harmony reduced its losses by over 40% for the 2019 financial year.
Harmony on Tuesday released its financial and operating results for the year ended June 30, 2019. Net losses came to -R2.6bn, 41% less compared to -R4.47bn reported in 2018. Losses per share decreased 50% to -498c. While headline earnings per share increased 19% to 204c.
Other key features for the period show gold production increased 17% which translated in a 23% increase in production profit. Production was boosted by the first full year financial inclusion of the Moab Khotsong mine which was acquired in 2018, as well as improved production from Hidden Valley mine following capital investments in the mine.
Harmony's revenue increased 32% to R26.9bn. No dividend was declared this year, nor was one declared the year before.
Commenting on the financial year, Chief Executive Officer Peter Steenkamp extended condolences for the lost lives in mining accidents and reiterated goals to ensure a safe work environment. The lives of 11 employees were lost during the year.
"I wish to extend my personal, heartfelt condolences to the families, colleagues and friends of the employees who lost their lives in mining accidents in FY19.
"Together with each and every employee, my aim is to ensure safe production, by preventing fatalities and embedding a proactive safety culture. It is important that every employee returns home each day - both safe and healthy," he said.
For the year ahead, Harmony intends to focus on "safe, profitable production," he added. "Value - rather than volume - will translate to shareholder returns in the long term," Steenkamp said.
Everything you need to know about the R5bn silicosis settlement as mining companies prepare to pay out
Silicosis class action
Further to the results announcement, harmony commented on a historic settlement reached with workers suffering from silicosis or tuberculosis after working in Gold Working Group companies' mines (of which Harmony is part) between 1965 to date. The settlement came following three years of negotiations and will provide compensation to affected workers.
"The Tshiamiso Trust will track and trace class members and administer claims and payments to eligible claimants following the completion of the legal opt out period as set out by the Court," Harmony said.
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assures a future smoother than the sleepster's face each day.
our understanding penetrates this mystic sea.
where freedom's been swindled and swallowed by Persona's lies.
bestow it's balm on all, except who stir the pot and dramatize.
She has a chill surprize, for all who falsely claim her name.
to Earth to resurrect just rots away, while you prance and play.
The road is grim, and gray's the gate, to gain Life's rainbow ray.


Looking for some advice! Liam called into the show because he has been with his girlfriend for a few months now and things have been going great but he feels like she has been trying to train him into her habits. From the way he sleeps to the type of alarm he sets on his phone.
Should he be worried for the future? Listen here and let us know what you think in the comments below!


text:
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So far 3m44e5s0onl0udldyb1i3rrd2ol6 has created 121 blog entries.
3m44e5s0onl0udldyb1i3rrd2ol62021-03-22T14:38:11+00:00March 22nd, 2021|
The team at Emmerson Critchley Ltd has just completed a new limecrete floor at a charming thatched period property in Cambridgeshire.
3m44e5s0onl0udldyb1i3rrd2ol62021-02-16T09:54:18+00:00February 16th, 2021|
This opulent Victorian inspired bathroom is perfectly fitting within its traditional Suffolk country house setting. Its creation has been made possible thanks to a two-storey extension project undertaken by Emmerson Critchley Ltd's specialist traditional building team.
3m44e5s0onl0udldyb1i3rrd2ol62021-01-11T16:45:38+00:00January 11th, 2021|
A once dilapidated barn, formerly on the Buildings at Risk register, is now a stunning three-bedroom dwelling. It offers a quality, modern finish, and showcases the very best traditional building skills from an award-winning traditional building firm.
Come rain, shine or lockdown, the team at our award-winning building firm Emmerson Critchley Ltd continues to work at full capacity. So please feel free to contact us as normal. We are here to support you with your building project. We specialise in traditional building techniques. These are not only for period properties. We also advise on how best to use traditional building methods for modern and new build projects with stunning results. Contact us today for a quote or further advice.
Emmerson Critchley Ltd is proud to use Bulb as its energy supplier and, in so doing, has lowered the firm's carbon impact "by 731 tonnes of CO2 every year".
Pargeting masterclass
Pargeting is a traditional English craft that is particularly prevalent throughout East Anglia. Sadly, it's perhaps a less common craft than it once was. Pargeting is the provision of decorative designs to a façade using lime plaster and was first introduced by Henry VIII. The brief for the Emmerson Critchley Ltd team in this case was to showcase the story of the property and the results are wonderful.
Restored to good health
Another recent project completed by the Emmerson Critchley Ltd team: restoring this lovely timber framed period house. The project included: timber frame repairs, applying lime render, changing the fascias, soffits and guttering and solving a problem with water ingress.
Underfloor heated limecrete floor for GI Listed church
The team at Emmerson Critchley Ltd, which specialises in traditional building techniques and materials, is delighted to have successfully installed a limecrete floor with underfloor heating for this stunning Grade I Listed church. This forms part of a huge renovation project at the historic church.
Featured in Professional Builder Magazine
3m44e5s0onl0udldyb1i3rrd2ol62019-07-18T14:51:34+01:00July 18th, 2019|
The team at Emmerson Critchley Ltd is proud to have had its work featured in an article on the benefits of lime plastering, which has been published in Professional Builder Magazine.
Here's a little snap shot of our flagship project, a house that we are building using traditional building techniques. The team at Emmerson Critchley Ltd is working tirelessly to compete the project within the next few weeks, exciting times!

redpajama_set_name: RedPajamaCommonCrawl


Earlier Wednesday, Canada's USA envoy David MacNaughton, who has taken part in the Washington talks alongside Foreign Affairs Minister Chrystia Freeland, pegged the likelihood of a new trade deal by Sunday's congressional deadline at a "five" on a scale of one to 10.
Lighthizer said the USA wants to see the three-way pact stay intact and remains committed to keeping Canada in the deal now or to let it join later. This will also mean that the United States can impose 25 percent tariffs on Canada's auto and dairy imports and exports.
Speaking at the United Nations General Assembly on Tuesday, Trump touted the success of his trade policy, citing the renegotiated bilateral trade deal with South Korea, as well as a partial rework of NAFTA agreed to with Mexico.
Lighthizer said the timetable for the new deal was set up so Pena Nieto can approve it before he leaves office on November 30 - an arrangement that's acceptable to Lopez Obrador.
The US made a deal with Mexico in August, but stakeholders on both sides of the border have urged for the US to make it a three-way deal and include Canada.
It is possible that Congress, which strongly prefers an agreement involving Canada, would allow Canada to be added to the U.S. -Mexico text at a later date. "We will keep working as long as it takes to get to the right deal for Canada", he said.
But Freeland's spokesman, Adam Austen, said Canada would only sign a good deal. A spokesman for the U.S. Trade Representative's Office declined to comment.
"I suspect that they will be motivated to do so", Mr. Bollyky said, referring to the Senate Majority Leader and the Speaker, respectively.
"I don't think there's anything to read into it", Mr. Trudeau said of the tepid greeting, adding he was just making the rounds of the table.
Trump has used an obscure "national security" provision of US trade law to impose tariffs on imports of Canadian steel and aluminum. "It was an interaction like so many are in the United Nations - quick but cordial".
Trump is serious about renaming NAFTA, possibly to the U.S. -Mexico-Canada pact, or USMC, said Lighthizer.
Oh, and there's also the report that Butler and Irving had an interest in teaming up somewhere within the East . That's why Brooklyn, New York, and Los Angeles were listed as the frontrunner to obtain his services.
Liverpool manager Jurgen Klopp has hailed Mohamed Salah's defensive contribution for the team this season. I would never do that and the players should never do that - only the supporters are allowed to do that.
And he criticized Democrats, who he said should have "done this a lot sooner because they had this information for many months". When she testified before the Judiciary Committee, senators on both sides of the all-male panel questioned her credibility.
Gerst pleaded with people living in the area to heed evacuation orders, warning them there is a "nightmare coming for you". Florence is forecast to make landfall near Cape Fear, North Carolina, as a Category 2 or Category 1 storm Friday morning.


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Empathy encounter
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text:
\section{\label{sec:level1}First-level heading}

\section{Introduction \label{sec:intro}}
In recent years, the study of twisted bilayer systems, or moiré materials, has become one of the most active fields in materials science \cite{cao2018correlated,cao2018unconventional,po2018origin,yankowitz2019tuning,sharpe2019emergent,jiang2019charge,polshyn2019large,lu2019superconductors,kerelsky2019maximized,choi2019electronic,xie2019spectroscopic,cao2020strange,serlin2020intrinsic,stepanov2020untying,saito2020independent,hunt2013massive,dean2013hofstadter,koshino2018maximally,moon2012energy,brihuega2012unraveling,wang2021moire,cano2021moire,carr2020electronic,kennes2021moire,tong2017topological,fujimoto2020topological,fujimoto2022perfect,kariyado2022twisted}. As in the magic-angle twisted bilayer graphene \cite{cao2018correlated,cao2018unconventional}, moiré materials have attracted much attention as a platform for realizing various quantum phases with high tunability in parameters such as the twist angle and the filling factor. The search for topological flat bands is one direction of the study of moiré materials as a foothold to obtain a correlated topological phase, such as a fractional Chern insulator without external field \cite{repellin2020chern,ledwith2020fractional,nuckolls2020strongly,xie2021fractional,wu2021chern,san2013helical,koshino2019band}. A prime example is a fragile topology of the flat band of the magic-angle twisted bilayer graphene \cite{po2019faithful,ahn2019failure,Song2019all}. In many other materials, flat moiré bands with various non-trivial topology, such as the Chern number and valley Chern number, have been proposed \cite{lian2020flat,wu2019topological,claassen2022ultra}. In these studies, the topology of the bands is evaluated with Wilson loop spectra.
\begin{figure}
    \centering
    \includegraphics[width=0.45\textwidth]{fig1.pdf}
    \caption{Schematic pictures of moiré materials with large and small moiré modulations compared with their original band gap. (a) Case where the original band gap (blue arrow in the right end) in the untwisted bilayer is larger than the amplitude of the moiré modulation (red arrow). The left is a band dispersion when the moiré modulation is neglected, and the right is when it is turned on. (b) Case where the original band gap in the untwisted bilayer is smaller than or comparable with the amplitude of the moiré modulation. In this case, a gap-closing may occur when the moiré modulation is gradually turned on.}
    \label{fig:Moiretopotrans}
\end{figure}

Generally, when a band has a nontrivial topology, a corresponding edge state appears if an edge is truncated \cite{hasan2010colloquium}. Typically, when occupied bands of an insulator have a nontrivial topological invariant, conducting edge states appear in the gap on the Fermi level. The analysis of these edge states is also important for understanding the topological properties of the system. However, the Wilson loop evaluation for a single band cannot determine which gap the edge state appears, above or below a non-trivial band. This issue is solved for normal (non-moiré) materials by evaluating all occupied bands because edge states never appear in the lower end of the occupied bands.
However, for moiré materials, it is not feasible to evaluate all occupied bands due to the huge number of occupied bands. A low-energy approximation used in moiré materials also makes the all-band evaluation impossible because it neglects bands far from the Fermi level. This obstacle in the edge state analysis has not been a problem in previous moiré materials, such as twisted bilayer MoS$_2$ family, because they have a large band gap at the Fermi level \cite{lian2020flat,wu2019topological,claassen2022ultra}\footnote{Or, it may not really matter which gap the edge states appear in because the Fermi level can be easily tuned.} that makes it easy to determine the presence or absence of edge states at the Fermi level. If the band gap at the Fermi level of the untwisted bilayer material is larger than the amplitude of moiré modulation, the presence or absence of edge states at the Fermi level of the moiré material is the same as that of the untwisted bilayer material. The reason is explained in Fig. \ref{fig:Moiretopotrans}(a). If we make a moiré supercell hypothetically neglecting the moiré modulation, the band folding by the moíre superlattice does not change a topological invariant \footnote{This statement is correct if the topological invariant is a strong invariant, such as the $\mathbb{Z}_2$ invariant in the 2D class AII. However, some topological invariants, such as the weak $\mathbb{Z}_2$ index in the 3D class AII, is not invariant against band folding.}. Even if the moiré modulation is turned on, the gap-closing does not occur and the topological invariants are preserved if it is small enough. Although moiré materials are generally capable of large carrier doping, the properties at the Fermi level can be used as a basis to discuss the properties of band gaps around.

However, very recently, twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ has been proposed \cite{tateishi2022quantum}, in which topological insulator (TI) domains and normal insulator (NI) domains coexist in the moiré unit cell (Fig. \ref{fig:sche_tBHZ}(a)). In such materials, the moiré modulation is larger than the band gap of the original untwisted bilayer (Fig. \ref{fig:Moiretopotrans}(b)). Therefore, the moiré modulation can induce a topological phase transition in the local electronic states and multiple domains of different topological phases are formed in the moiré unit cell. The previous study has shown the moiré band dispersions of these materials have a gap at the Fermi level. The question is how to determine the presence or absence of edge states in the gap at the Fermi level in such materials.
In this paper, we study a method to determine the presence or absence of edge states at the Fermi level in a moiré material with multiple topological domains in the moiré unit cell, i.e., a method to evaluate a sum of the topological invariant for all occupied bands. We show a correspondence between the topological invariant of those moiré materials at the Fermi level and the topology of the domain structure in real space by a toy model calculation. We also find a bulk-edge corresponding that is compatible with a continuous change of the truncation condition, which is specific to moiré materials.
Note that, although in a non-moiré material it is usually enough to evaluate a few valence-top bands or conduction-bottom bands to know the topological properties of the gap at the Fermi level, it does not necessarily work well for a moiré material (see Appendix \ref{sec:App_counterexample}).

This paper is organized as follows. Section \ref{sec:model} introduces a model we use to discuss the topological invariant of a moiré system with domains of two different topological phases in the moiré lattice. Section \ref{sec:method_para} presents a parameter space where we calculate a topological phase diagram and a method to determine the topological phases. Section \ref{sec:topo_phase_C3} discusses a topological phase diagram for a case when a $C_3$ symmetric mass term is assumed. Section \ref{sec:topo_phase_C2} discusses a topological phase diagram for a case when a $C_2$ symmetric mass term is assumed. Section \ref{sec:conclusion} concludes this paper. Some supplementary information is in the appendixes.

\begin{figure}
    \centering
    \includegraphics[width=0.45\textwidth]{fig2.pdf}
    \caption{Schematic picture of a moiré material with TI and NI domains in the moiré unit cell. (a) Domain structure and a moiré unit cell in real space. Green regions are TI domains and an orange region is a NI domain. The domain structure is determined by the sign of $M(\bm{r]})$. (b) $M(\bm{r})$ along the line $y/L = 0.5$ (red line in (a)). (c) Reciprocal lattice vectors and a moiré BZ of the moiré system.}
    \label{fig:sche_tBHZ}
\end{figure}

\section{model \label{sec:model}}
Here, we introduce the twisted Bernevig-Hughes-Zhang (BHZ) model, which is proposed in Ref. \cite{tateishi2022quantum}. The twisted BHZ model is used in this paper to discuss the relation between domain structure in the moiré unit cell and a topological invariant at the Fermi level. We first define the original (untwisted) BHZ model, and then we introduce a twist effect in it.

The untwisted BHZ model \cite{bernevig2006quantum} is a half-filled four-by-four (two orbitals and spin $1/2$ on each orbital) model in a two-dimensional (2D) space that describes the $\mathbb{Z}_2$ time-reversal protected topological insulator (quantum spin Hall insulator) in the class AII. We consider the $\bm{k} \cdot \bm{p}$ perturbation around the $\Gamma$ point, and the model is given as
\footnotesize
\begin{equation}
    \begin{split}
        & H_{\mathrm{BHZ}}(M,\bm{k}) \\
        &= \left( M - A k^2 \right) \tau_z \sigma_y + v k_x \tau_x \sigma_0 + v k_y \tau_y \sigma_0 \\
        &= \left(
        \begin{array}{cccc}
             & v k_- & -i(M-Ak^2) & \\
            v k_+ & & & i(M-Ak^2) \\
            i(M-Ak^2) & & & v k_- \\
             & -i(M-Ak^2) & v k_+ & \\
        \end{array}
        \right) ,
    \end{split}
    \label{eq:untwisted_BHZ}
\end{equation}
\normalsize
where $k_\pm = k_x \pm i k_y$, $k^2 = k_x^2 + k_y^2$, $A$ and $v$ are positive constant parameters. The $\sigma_{x,y,z}$, $\sigma_0$, $\tau_{x,y,z}$, $\tau_0$ are Pauli matrices and the identity matrix for the orbital and spin degree of freedom, respectively. Note that the basis is set to match the twist introduced later. This model describes a topological insulator when the mass term $M>0$ and a normal insulator when $M<0$.

Next, we define the twisted BHZ model. Generally in a moiré material with a small twist angle or small lattice constant mismatch, an atomic scale local lattice structure is approximated well with an untwisted lattice with a particular interlayer displacement \cite{bistritzer2011moire,jung2014ab}. Due to the difference in the local lattice structure, the interlayer terms have position dependence that is periodic in the moiré scale.
To introduce the twisted BHZ model, we assume that a Hamiltonian of the local structure is described by Eq.(\ref{eq:untwisted_BHZ}). The upper (lower) two rows are the spin degree of freedom on an orbital in the upper (lower) layer. It is also assumed that the mass term has a Moiré scale modulation as $M(\bm{r})$, and all the other parameters are constant. Depending on the sign of the local mass term $M(\bm{r})$, a TI (NI) domain in the moiré unit cell is defined as where $M(\bm{r})>0$ ($M(\bm{r})<0$) (Figs. \ref{fig:sche_tBHZ}(a)(b)). Because $M(\bm{r})$ is moiré-scale periodic, $H_{\mathrm{BHZ}}(M(\bm{r}),\bm{k})$ can be decomposed into components of moiré reciprocal lattice vectors $\bm{G}_l$ by Fourier transform,
\begin{equation}
    \begin{split}
        H_{\mathrm{BHZ}}(M(\bm{r}),\bm{k}) = \sum_{\bm{G}_l} e^{i \bm{G}_l \cdot \bm{r}} t_{\bm{k},\bm{k}-\bm{G}_l} .
    \end{split}
    \label{eq:BHZ_FT}
\end{equation}
By using the Fourier components $t_{\bm{k},\bm{k}-\bm{G}_l}$, the Hamiltonian of the twisted BHZ model is given as
\begin{equation}
    \begin{split}
        H = \int d \bm{k} \sum_{\alpha,\beta} \sum_{\bm{G}_l} t_{\bm{k},\bm{k}-\bm{G}_l}^{\alpha,\beta} c_{\alpha,\bm{k}}^\dagger c_{\beta,\bm{k}-\bm{G}}^{\phantom{\dagger}} ,
    \end{split}
    \label{eq:H_twistedBHZ}
\end{equation}
where $\alpha$ and $\beta$ are orbital-spin index ($\alpha, \beta = 1 \sim 4 $), $c^\dagger$ ($c$) is a creation (annihilation) operator, and $t_{\bm{k},\bm{k}-\bm{G}_l}^{\alpha,\beta}$ is a matrix element of $t_{\bm{k},\bm{k}-\bm{G}_l}$.

The untwisted BHZ model Eq.(\ref{eq:untwisted_BHZ}) has the continuous rotation symmetry but the twisted BHZ model has a lower symmetry determined by the distribution of $M(\bm{r})$. In the following, we consider two cases with different symmetries because symmetry restricts an allowed domain structure. The first one is the case where $M(\bm{r})$ has $C_{3z}$ rotation symmetry and the other is where $M(\bm{r})$ has $C_{2z}$ rotation symmetry. To discuss both in the same lattice, we assume a hexagonal unit cell for the untwisted model. Basic lattice vectors of the untwisted model are set to $\bm{a}_1 = (1,0)$ and $\bm{a}_2 = (-1/2, \sqrt{3}/2)$ although they do not explicitly appear in $\bm{k} \cdot \bm{p}$ model Eq.(\ref{eq:untwisted_BHZ}). Moiré lattice vectors are then $\bm{L}_1 = L(\frac{\sqrt{3}}{2},\frac{1}{2})$ and $\bm{L}_2 = L(0,1)$, where $L=1/ \left( 2 \sin \frac{\theta}{2} \right) $ is a moiré lattice constant for a twist angle $\theta$. In the $M(\bm{r})$ setting, a finite number of sampling points are taken and the intermediate region is interpolated by a discrete Fourier transform. Because finite sampling points are taken, finite $\bm{G}_l$ are taken into account in Eqs.(\ref{eq:BHZ_FT})(\ref{eq:H_twistedBHZ}) and higher oscillating terms are neglected. In both cases of $C_3$ symmetric $M(\bm{r})$ and $C_2$ symmetric $M(\bm{r})$, seven moiré reciprocal lattice vectors $\bm{G}_l$ ($l= 0 \sim 6$) are taken (Fig. \ref{fig:sche_tBHZ}(c)). The seven $\bm{G}_l$ are defined as $\bm{G}_0=(0,0)$ and $\bm{G}_l = \frac{4 \pi}{\sqrt{3} L} \left( \cos \frac{(l-1)\pi}{3},\sin \frac{(l-1)\pi}{3} \right)$ ($l =1 \sim 6$). The moiré Brillouin Zone (BZ) is shown in Fig. \ref{fig:sche_tBHZ}(c).

\section{calculation method and parameter space \label{sec:method_para}}

We calculate topological phase diagrams of the twisted BHZ model by tuning the position-dependent mass term $M(\bm{r})$. As described above, $M(\bm{r})$ is determined from finite sampling points, a phase diagram is given in a parameter space made by sampled mass values $\{ M_n \}$. Because the interpolation method for the intermediate area has been determined, the setting of $\{ M_n \}$ is equivalent to the setting of the domain structure. Therefore, in the parameter space $\{ M_n \}$, we can discuss the relation between the topological phases and the domain structure.

Although it is not feasible to evaluate a topological invariant for all occupied bands in a moiré system, it is possible to find points where gap closing occurs at the Fermi level even with an approximated model. In other words, a topological phase boundary can be determined. Then we determine the topological invariant for each phase. To determine the topological invariants of each phase, it is sufficient to calculate them at one point in each phase. In the parameter space, there are some points where the topological invariant is determined without numerical evaluations. For example, when $M(\bm{r})$ is constant, the topological invariant of the twisted BHZ model is the same as that of the untwisted BHZ model with the same mass value. Referring to those points, the topological invariants of each phase are explicitly determined. Note that although a gap-closing is not necessarily accompanied by a topological phase transition, in the following cases we have only one candidate of the phase boundary (gapless line) and thus there is no ambiguity.

\section{Topological phase diagram in $C_3$ symmetric case \label{sec:topo_phase_C3}}

\subsection{Bulk topological invariant}

\begin{figure}
    \centering
    \includegraphics[width=0.45\textwidth]{fig3.pdf}
    \caption{Sampling points to determine $M(\bm{r})$. (a) Case for a $C_3$ symmetric $M(\bm{r})$. A marker with an integer $n$ indicates a point where $M_n$ is sampled. (b) Case for a $C_2$ symmetric $M(\bm{r})$. A marker with an integer $mn$ indicates a point where $M_{mn}$ is sampled.}
    \label{fig:sampling}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=0.45\textwidth]{fig4.pdf}
    \caption{Parameter space ${M_0,M_1,M_2}$ for the $C_3$ symmetric case. (a) Parameter space drawn in the 3D space. Two figures are the same one viewed from (111) direction and another viewpoint. The gray sphere is where $\bar{M}=0.5$ and the blue sector is where a phase diagram is calculated. The blue, green, and red lines are $M_0=0$, $M_1=0$, and $M_2=0$, respectively. (b) Projection of the blue sector in (a) by the Lambert azimuthal equal-area projection.}
    \label{fig:C3paraspace}
\end{figure}

To set a $C_3$ symmetric $M(\bm{r})$, we take three sampling points $\bm{r}_n = \frac{n}{3} (\bm{L}_1 + \bm{L}_2)$ ($n=0,1,2$) in the moiré unit cell (Fig. \ref{fig:sampling}(a)) \footnote{We can take more sampling points to set a more detailed distribution of $M(\bm{r})$. When more sampling points are taken, we need to take in more $\bm{G}_l$ in the calculation. Here, we assume the most simplest case with three sampling points.}. In this case, the obtained moiré lattice belongs to the layer group No. 67 ($p312$). The mass values at the sampling points are defined as $M_n$. To obtain a $C_3$ symmetric twisted BHZ model, we assume equivalences between the seven Fourier components $t_{\bm{k},\bm{k}-\bm{G}_l}$ ($l=0 \sim 6$) as
\begin{equation}
    \begin{split}
        t_{\bm{k},\bm{k}-\bm{G}_1} &= t_{\bm{k},\bm{k}-\bm{G}_3} = t_{\bm{k},\bm{k}-\bm{G}_5}, \\
        t_{\bm{k},\bm{k}-\bm{G}_2} &= t_{\bm{k},\bm{k}-\bm{G}_4} = t_{\bm{k},\bm{k}-\bm{G}_6}. \\
    \end{split}
\end{equation}
With these relations, the seven $t_{\bm{k},\bm{k}-\bm{G}_l}$ are uniquely determined from the three sampling points. $t_{\bm{k},\bm{k}-\bm{G}_l}$ are written as
\begin{equation}
    \begin{split}
        t_{\bm{k},\bm{k}-\bm{G}_0} &= \frac{1}{3} \sum_{n=0}^2 H_{\mathrm{BHZ}}(M_n,\bm{k}), \\
        t_{\bm{k},\bm{k}-\bm{G}_l} &= \frac{1}{9} \sum_{n=0}^2 H_{\mathrm{BHZ}}(M_n,\bm{k}-\frac{\bm{G}_l}{2}) ~ e^{-i \frac{2\pi}{3} n} ~~~ (l=1,3,5), \\
        t_{\bm{k},\bm{k}-\bm{G}_l} &= \frac{1}{9} \sum_{n=0}^2 H_{\mathrm{BHZ}}(M_n,\bm{k}-\frac{\bm{G}_l}{2}) ~ e^{i \frac{2\pi}{3} n} ~~~ (l=2,4,6). \\
    \end{split}
    \label{eq:C3_t_def}
\end{equation}
Note that a correction $-\frac{\bm{G}_l}{2}$ is added in the second and third equations to recover an exact $C_3$ symmetry in the twisted model \cite{tateishi2022quantum}, although it is negligible in a small angle limit.

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{fig5.pdf}
    \caption{Calculated band gap and details in some representative points for the $C_3$ symmetric twisted BHZ model. (a) Calculated band gap for $\theta=0.10^\circ$ shown as a contour plot (gap map). The parameter space is defined in Fig. \ref{fig:C3paraspace}. The darker colored represents the smaller band gap at the Fermi level. The magenta dashed line is where the domain reconnection occurs. (b)-(g) Domain structure and band dispersion of six representative points (magenta dots in (a)). Integers in band dispersion plots indicate the degeneracy of the bands. In the counting of the degeneracy in (e) and (g), a small gap given by the interaction between domain boundaries is neglected.}
    \label{fig:C3phased1}
\end{figure*}

In a parameter space of the three sampled mass values $(M_0,M_1,M_2)$, we calculate a topological phase diagram. Before the calculation, we reduce the parameter space that we need to see by considering a symmetry between $M_n$. A cyclic exchange of the mass values $(M_0,M_1,M_2)$ $\to$ $(M_2,M_0,M_1)$ is a translation $(\bm{L}_1 + \bm{L}_2)/3$ of the moiré lattice. The time reversal protected $\mathbb{Z}_2$ invariant is independent of this translation and thus they give the same invariant. Further, exchanging two of them, for example $(M_0,M_1,M_2)$ $\to$ $(M_0,M_2,M_1)$, works as the inversion operation. Although the moiré lattice does not have the inversion symmetry, the inversion image has the same topological invariant as the original one. From the above two symmetries in $(M_0,M_1,M_2)$, the parameter space is reduced to 1/6. The origin $(0,0,0)$ gives a constant mass $M(\bm{r})=0$ that is not of our interest, so we restrict the parameters on a sphere in the parameter space to avoid the origin as
\begin{equation}
    M_{0}^2 + M_{1}^2 + M_{2}^2 =  \bar{M}^2~ =\mathrm{constant}.
    \label{eq:C3mass_sphere}
\end{equation}
Setting a north pole at where $M_0=M_1=M_2>0$ and a south pole at $M_0=M_1=M_2<0$, we calculate a phase diagram on a 1/6 sector in the longitude direction (Fig. \ref{fig:C3paraspace}). In the region above the red $M_2=0$ line (below the blue $M_0=0$ line), all $M_n$ are positive (negative) and thus the whole moiré unit cell belongs to the TI (NI) domain, while TI and NI domains coexist in the moiré unit cell in the middle region between the two lines $M_2=0$ and $M_0=0$.

As described at the beginning of section \ref{sec:method_para}, we calculate a band gap at the Fermi level and find a gap closing point in the parameter space to determine a topological phase boundary. Generally in a noncentrosymmetric 2D system, the gap closing occurs in a generic momentum in BZ \cite{murakami2007phase,murakami2007tuning}. However, when additional crystalline symmetry is present, it can be restricted to high symmetry lines \cite{yu2020piezoelectricity,tateishi2022quantum}. In the case of $C_3$ symmetric twisted BHZ model (layer group No.67), there are in-plane $C'_2$ rotation axes and the gap closing always occurs on $C'_2 {\cal T}$ invariant lines, which is $\Gamma_M$-K$_M$-M$_M$ lines. Therefore, to find a phase transition point we calculate the minimum direct gap on the $C'_2 {\cal T}$ invariant line
\begin{equation}
    \Delta E = \mathrm{min} \left\{ E_{\mathrm{LCB}}(\bm{k}) - E_{\mathrm{HVB}}(\bm{k}) \left| \bm{k} \in (\Gamma_M-\mathrm{K}_M-\mathrm{M}_M) \right. \right\}
\end{equation}
in the parameter space, where LCB stands for the lowest conduction band and HVB stands for the highest valence band.

Setting the parameters in Eqs.(\ref{eq:untwisted_BHZ}) and (\ref{eq:C3mass_sphere}) as $v=1$, $A=1$, and $\bar{M}=0.5$, we calculated $\Delta E$ in the parameter space defined in Fig. \ref{fig:C3paraspace}. In Fig. \ref{fig:C3phased1}, an obtained gap map for twist angle $\theta=0.10^\circ$ (Fig.\ref{fig:C3phased1}(a)) and domain structures of some representative points (Figs. \ref{fig:C3phased1}(b)-(g)) are shown. Fig. \ref{fig:C3phased1}(a) is a contour plot of $\Delta E$. Note that the gap is normalized with a twist angle-dependent factor
\begin{equation}
   \Delta E_0 (\theta) = \frac{v \left| \bm{G}_1 \right|}{2} = v \frac{4 \pi}{\sqrt{3}} \sin \frac{\theta}{2},
   \label{eq:gap_normal}
\end{equation}
which is a typical gap value for a case where TI (or NI) domains are isolated in the moiré unit cell (see Appendix \ref{sec:App_gap_normal} for its derivation) \cite{tateishi2022quantum}. The darker color represents where the gap is smaller. It can be seen that a gapless line goes from the lower right to the upper left. The upper (bottom) end of the parameter space is a point with $M_0=M_1=M_2>0$ ($<0$), and at that point, the moiré modulation terms vanish and thus the moiré bands are given by just folding a band of the untwisted system. Because the band folding does not change the $\mathbb{Z}_2$ topological invariant, the upper (bottom) end belongs to a TI (NI) domain. Because there is only one gapless line in the gap map, we can determine that it is the phase boundary and the upper (lower) phase is a TI (NI) phase. Next, we discuss what determines the shape of the domain boundary by reference to the domain structure in the moiré unit cell. For six representative points (magenta dots in Fig. \ref{fig:C3phased1}(a)), the domain structure in the moiré unit cell and the band dispersion are shown in Figs. \ref{fig:C3phased1}(b)-(g). The numbers in the band dispersion figures are numbers of degenerate bands including the spin degree of freedom. First, we focus on (e), (f), and (g). In (e), the TI domain is connected over the moiré lattice but the NI domains are disconnected from each other. This case belongs to the TI phase as a moiré system. Conversely, in (g), the TI domains are disconnected but the NI domains are connected. This case belongs to the NI phase as a moiré system. In the case of (f), where $M_1=0$, both domains are triangles and are touching at where $M_1$ is sampled, and the moiré system becomes gapless as shown in the right of (f). Because the inversion symmetry is broken in these cases, Rashba splitting appears clearly in the band dispersion in (f). However, in (e) and (g), the splitting is unnoticeable due to a negligible interaction between helical edge states on the domain boundary of isolated domains. Next, we focus on (b), (c), and (d), which are calculated on the left edge of the parameter space. The left edge is a line where $M_1=M_2$ is satisfied, and thus the moiré system has the $C_6$ symmetry and the (approximate) inversion symmetry as the domain structure indicates (detailed discussion about the symmetry is given in Appendix \ref{sec:App_sym_of_moire}). Due to the inversion symmetry, there is no Rashba splitting in the band dispersion in (b), (c), and (d). Also in these cases, when the TI (NI) domain is connected as (b) (as (d)), the moiré system is TI (NI). The calculated domain structures suggest a correspondence between the domain connectivity and the topological invariant of the moiré system. In Fig. \ref{fig:C3phased1}(a), a line where domain reconnection occurs (magenta dashed line in Fig. \ref{fig:C3phased1}) is given and it is qualitatively coincident with the gapless line (the dark colored region in (a)). It is noteworthy that the connectivity of the domains determines the topological phase of the system, not the size of the area of each domain. The case of (d) is a good example, where the system is NI although roughly 62\% of the moiré unit cell is the TI domain.

As shown in Fig. \ref{fig:C3phased1}, the shape of the phase boundary is understood mainly by the domain connectivity. However, on the side edge, the gapless point is slightly shifted from the point where domain reconnection occurs. On the left edge, domain reconnection occurs at a point of Fig. \ref{fig:C3phased1}(c), where $M_0 = -8 M_1$, $M_1=M_2$ is satisfied (intersection of the edge and the dashed magenta line) and Kagomé domain structure is realized (the middle left case). However, the band dispersion of Fig. \ref{fig:C3phased1}(c) is gapped and the system is TI as a moiré system. This difference is explained by an effect of the interaction between the helical edge states on the domain boundary. Fig. \ref{fig:C3angle_depend} shows a twist angle dependence of the gap map. As the twist angle increases from Fig. \ref{fig:C3angle_depend}(a) to Fig. \ref{fig:C3angle_depend}(c), the difference between the gapless line and the domain reconnection line becomes more significant. Because the moiré unit cell becomes smaller for a larger twist angle case, the width of the helical edge state on the domain boundary becomes wider compared to the moiré lattice scale, as reported in Ref. \cite{tateishi2022quantum}. As a result, interactions are no longer negligible in cases where domain boundaries get close to each other. This interaction shifts the parameter at which the reconnection of the helical edge states occurs from that at which the domain reconnection occurs. This is a source of the shift of the gapless line from the domain reconnection line. This effect is not found in the case of Fig. \ref{fig:C3phased1}(f) because the TI and NI domains are symmetric and the edge states cannot choose which domain to go through.

\begin{figure}
    \centering
    \includegraphics[width=0.45\textwidth]{fig6.pdf}
    \caption{Twist angle dependence of the gap map for the $C_3$ symmetric twisted BHZ model. (a) $\theta=0.10^\circ$ (b) $\theta=0.50^\circ$, and (c) $\theta=1.00^\circ$, respectively.}
    \label{fig:C3angle_depend}
\end{figure}

\subsection{Edge state}
The obtained correspondence between the topological invariant and domain connectivity is consistent with the existence of edge states. In Fig. \ref{fig:C3edge}, examples of some domain structures and truncation conditions are shown. When an edge cuts a TI domain, the edge is locally considered a boundary between a TI and the vacuum and thus there must be an edge state (Fig. \ref{fig:C3edge}(a)). Combined with edge states on the TI and NI domain boundary, we can see there always is a connected edge state along the edge when the system has a TI-connected domain structure (Figs. \ref{fig:C3edge}(a)-(c)). Although NI domains can be cut in some parts of the edge, a connected edge state exists through the TI-NI domain boundary (Figs. \ref{fig:C3edge}(b)-(c)). In contrast, there cannot be a connected edge state along the edge when the system has a NI-connected domain structure, i. e., a TI-disconnected domain structure (Figs. \ref{fig:C3edge}(d)-(f)). Even if most parts of the edge cut TI domains, the edge state is disconnected by the connected NI domain (Fig. \ref{fig:C3edge}(f)). These results show a clear correspondence between the bulk topological invariant and the edge state, and the connected edge state is a corresponding edge state of the moiré topological insulator. It is noteworthy that the existence of the connected edge state is independent of a truncation condition. This is consistent with the fact that the $\mathbb{Z}_2$ bulk invariant in the class AII generally guarantees the existence of helical edge states regardless of the truncation condition. In a normal (non-moiré) crystal, only discretized truncation conditions are allowed because one cannot divide an atom, while in a moiré system, effectively continuous truncation conditions are allowed especially in the small twist angle limit. The obtained bulk-edge correspondence is consistent with this moiré-specific continuous truncation conditions.

\begin{figure}
    \centering
    \includegraphics[width=0.45\textwidth]{fig7.pdf}
    \caption{Domain connectivity and edge states. (a)(b)(c) When the TI domain is connected, there is a connected edge state along the edge from one end to the other end. Even if some parts of the edge are in the NI domains, the edge state is connected though the domain boundary as shown in (b) and (c). (d)(e)(f) When the NI domain is connected, there cannot be a connected edge state along the edge.}
    \label{fig:C3edge}
\end{figure}

\section{Topological phase diagram in $C_2$ symmetric case \label{sec:topo_phase_C2}}
In Sec.\ref{sec:topo_phase_C3}, we found a correspondence between the topological invariant and the domain structure. In the $C_3$ symmetric case, one of the TI and NI domains is connected and the other is disconnected. This setup suits the $\mathbb{Z}_2$ nature of the topological phase of the class AII. However, in a general case, the domain structure is not necessarily classified into two classes. For example, a stripe pattern of TI and NI domains is allowed, in which both domains are connected in one direction but disconnected to the other perpendicular direction. However, we do not know any anisotropic topological phase in 2D like the weak TI in three-dimensional (3D) space. In the following, we discuss what topological phase a system with such stripe domain structures belongs to. To reduce the number of sampling points while allowing a stripe pattern, we assume $C_2$ symmetry.

\subsection{Bulk topological invariant}

\begin{figure*}
    \centering
    \includegraphics[width=\textwidth]{fig8.pdf}
    \caption{Calculated band gap and details in some representative points for the $C_2$ symmetric twisted BHZ model. (a) Calculated band gap for $\theta=0.10^\circ$ shown as a contour plot. The parameter space is ${M_{10},M_{11}}$ and the other two are fixed as $M_{00}=0.5$ and $M_{01}=-0.5$. The dark-colored region is where the band gap at the Fermi level closes. (b)-(i) Domain structure and band dispersion of eight representative points (magenta dots in (a)). Integers in band dispersion plots indicate the degeneracy of the bands. (j) Path of momentum space used to plot the band dispersions in (b)-(i).}
    \label{fig:C2phase}
\end{figure*}

To set a $C_2$ symmetric $M(\bm{r})$, we take four sampling points $\bm{r}_{mn} = \frac{1}{2} \left( m \bm{L}_1 + n \bm{L}_2 \right)$ ($m,n=0,1$) in the moiré unit cell (Fig. \ref{fig:sampling}(b)). In this case, the obtained moiré lattice belongs to the layer group No. 3 ($p112$). However, in our model, the inversion symmetry is approximately recovered due to the small angle approximation and too simple untwisted models in the sampling points (see Appendix \ref{sec:App_sym_of_moire} for details). The mass values at the sampling points are defined as $M_{mn}$. To obtain a $C_2$ symmetric twisted BHZ model, we assume equivalence between the seven Fourier components $t_{\bm{k},\bm{k}-\bm{G}_l}$ as
\begin{equation}
    \begin{split}
        t_{\bm{k},\bm{k}-\bm{G}_1} &= t_{\bm{k},\bm{k}-\bm{G}_4}, \\
        t_{\bm{k},\bm{k}-\bm{G}_2} &= t_{\bm{k},\bm{k}-\bm{G}_5}, \\
        t_{\bm{k},\bm{k}-\bm{G}_3} &= t_{\bm{k},\bm{k}-\bm{G}_6}. \\
    \end{split}
\end{equation}
With these relations, the seven $t_{\bm{k},\bm{k}-\bm{G}_l}$ are uniquely determined from the four sampling points. $t_{\bm{k},\bm{k}-\bm{G}_l}$ are written as
\begin{equation}
    \begin{split}
        t_{\bm{k},\bm{k}-\bm{G}_0} &= \frac{1}{4} \sum_{\substack{m=0,1\\n=0,1}} H_{\mathrm{BHZ}}(M_{mn},\bm{k}), \\
        t_{\bm{k},\bm{k}-\bm{G}_l} &= \frac{1}{8} \sum_{\substack{m=0,1\\n=0,1}} H_{\mathrm{BHZ}}(M_{mn},\bm{k}-\frac{\bm{G}_l}{2}) ~e^{i \pi n} ~~(l=1,4), \\
        t_{\bm{k},\bm{k}-\bm{G}_l} &= \frac{1}{8} \sum_{\substack{m=0,1\\n=0,1}} H_{\mathrm{BHZ}}(M_{mn},\bm{k}-\frac{\bm{G}_l}{2}) ~e^{i \pi (m+n)} ~~(l=2,5), \\
        t_{\bm{k},\bm{k}-\bm{G}_l} &= \frac{1}{8} \sum_{\substack{m=0,1\\n=0,1}} H_{\mathrm{BHZ}}(M_{mn},\bm{k}-\frac{\bm{G}_l}{2}) ~e^{i \pi m} ~~(l=3,6). \\
    \end{split}
    \label{eq:C2_t_def}
\end{equation}
A correction $-\frac{\bm{G}_l}{2}$ is added as explained in Sec.\ref{sec:topo_phase_C3}.

Next, we determine a parameter space in which to calculate a topological phase diagram. The parameter space is in principle four-dimensional space of $M_{mn}$. However, now we are interested in the topological invariant of stripe cases. Therefore, we fix two of them as $M_{00}=0.5$ and $M_{01}=-0.5$ and use the other two as axes of a phase diagram. In this parameter setting, we can see TI-connected, NI-connected, and stripe domain structures in the parameter space.

In the parameter space $(M_{10},M_{11})$, we calculate a band gap and find a gap closing point to determine a topological phase boundary. In this case, approximate inversion symmetry is recovered
as described above. Therefore, a gap closing of a topological phase transition occurs on a time-reversal invariant momentum (TRIM). Then, a band gap $\Delta E$ is defined as
\begin{equation}
    \Delta E = \min \left\{ E_{\mathrm{LCB}}(\bm{k}) - E_{\mathrm{HVB}}(\bm{k}) \left| \bm{k} \in \mathrm{TRIM} \right. \right\} .
\end{equation}

Setting the parameters in Eq.(\ref{eq:untwisted_BHZ}) as $v=1$ and $A=1$, we calculate $\Delta E$ in the parameter space $(M_{10},M_{11}) \in [-0.5,0.5] \times [-0.5,0.5] $. An obtained gap map for twist angle $\theta = 0.10 ^\circ$ is shown in Fig. \ref{fig:C2phase}(a) as a contour plot. Note that the gap is normalized with $\Delta_0(\theta)$. In Figs. \ref{fig:C2phase}(b)-(i), domain structures and band dispersions are also shown for some representative points in the parameter space. The band dispersion figures are plotted along a path shown in (j). In the cases of (d) and (g), the domain structures are NI- and TI-connected, respectively. In the cases of (b) and (i), the domain structures are stripe structures. As shown in the gap map (a), parameter regions of stripe domain structure, \{$M_{10}>0$ and $M_{11}<0$\} or \{$M_{10}<0$ and $M_{11}>0$\}, are gapless as a moiré system (dark color). This is a reasonable result because there should be helical edge states on the parallel domain boundaries. When the twist angle is small enough and the helical edge states are ideally isolated, the helical edge states give gapless linear dispersion. In the band dispersion of (b), we can see a clear linear dispersion. The double degeneracy is due to the presence of two domain boundaries in the moiré unit cell . In the other stripe case of (i), we can see flat zero-energy bands in the $\Gamma_M$-Y$_M$ line. This is because the direction of the $k$ path of that part is perpendicular to the direction of the stripe and thus the helical edge states cannot run in that direction. On the two axes, (c), (e), (f), and (h) that are on $M_{10}=0$ or $M_{11}=0$, a domain reconnection occurs from a TI-connected (or NI-connected) to a stripe domain structure. On the domain reconnection points, the domain boundaries singularly touch each other and thus the system is gapped due to the interaction between helical edge states. From these results, we have obtained a qualitative picture of the topological phase diagram in a small twist-angle case. We know the case of (g) (the case of (d)) with a TI-connected (NI-connected) domain structure is a TI (NI) as a moiré system as shown in Sec. \ref{sec:topo_phase_C3}. The cases with stripe domain structures are gapless and thus the topological invariant is not well-defined.

However, in the general theory of the topological phase transition in the 2D class AII, a phase transition occurs at a point in a single parameter tuning, i. e., the gapless points should be a line with no width in a 2D parameter space \cite{murakami2007phase,murakami2007tuning}. Next, we explain why gapless regions can be obtained contrary to the general theory. The gapless region is a result of an additional condition that interactions between neighboring helical edge states can be neglected in the small angle limit. It is confirmed by examining the twist angle dependence of the gap map (Fig. \ref{fig:C2angle_depend}). In the bottom of Fig. \ref{fig:C2angle_depend}, The band gap on the $M_{11}=-0.2$ line is also shown. While the stripe region is (almost) gapless when $\theta=0.10^\circ$ (Fig. \ref{fig:C2angle_depend}(a)), there is a small but non-negligible gap when $\theta=1.00^\circ$ (Fig. \ref{fig:C2angle_depend}(c)). The exact gapless points in the case of $\theta=1.00^\circ$ exist on a line $M_{10}=-M_{11}$, which is a phase boundary. The small gap in the stripe region is given by an interaction between neighboring helical edge states. The location of the gapless line is determined by whether interactions across the TI or NI domain are dominant, like the Su–Schrieffer–Heeger model \cite{su1979solitons}. The interaction is always non-zero in a strict sense but, when the twist angle is small enough, each domain boundaries are distant enough in the real space and thus the interaction is negligible. In that case, the stripe region becomes a gapless region approximately even in the normalized scale by $\Delta_0(\theta)$, as shown in Fig. \ref{fig:C2angle_depend}(a). On the other hand, the gap in TI-connected (NI-connected) region is given by a finite size effect along the closed loop of the domain boundary. Therefore, the band gap in those regions is roughly 1 and independent of the twist angle in the normalized scale. The general theory of the topological phase transition assumes all perturbations allowed in the symmetry. Therefore, when we consider the correspondence to the general theory in present cases, the interactions between neighboring domain boundaries, which are allowed to exist by the symmetry of the system, must be included. When the interaction is negligible as in a small angle case, neglecting the interaction works as an additional condition and a gapless region with finite width can appear.

To summarize the result above, the property of the moiré system is still mainly determined by the domain structure in the $C_2$ symmetric case, and the case with a stripe domain structure is a gapless system. The effect of the interaction between helical edge states on the domain boundaries comes out differently, and it reduces the dimension of the gapless area to a line, as expected in the general theory of the topological phase transition. Here, whether the interaction between neighboring domain boundaries is negligible or not is judged by comparison with the typical gap value $\Delta E_0(\theta)$, which comes from the finite size effect along the closed loop of the domain boundary.

\begin{figure}
    \centering
    \includegraphics[width=0.45\textwidth]{fig9.pdf}
    \caption{Twist angle dependence of the gap map for the $C_2$ symmetric twisted BHZ model. From left to right: one for $\theta=0.10^\circ$, $\theta=0.50^\circ$, and $\theta=1.00^\circ$, respectively. In the bottom of each one, the normalized gap on the $M_{11}=-0.2$ (green line) is shown. For $\theta=1.00^\circ$, a line (point) where the band gap exactly closes is shown as a megenta dashed line (magenta arrow).}
    \label{fig:C2angle_depend}
\end{figure}

\subsection{Edge state}
In the case of a stripe domain structure, the system is gapless and the edge transport is indistinguishable from the bulk transport. Figs. \ref{fig:C2edge}(a) and (b) show the cases when the edge is truncated parallel to the stripe pattern. If the edge is in the TI domain, there are helical edge states on the edge (Fig. \ref{fig:C2edge}(a)). However, there also are helical edge states on the domain boundaries in the bulk region that contribute to the gapless bulk transport. When the twist angle is small enough and the helical edge states are not interacting with each other, the helical edge states in the bulk region and edge are equivalent and no edge-specific transport is obtained. When the edge is not parallel to the stripe pattern (Fig. \ref{fig:C2edge}(c)), there is no connected edge state on the edge. In this case, the bulk region is not conducting in the direction parallel to the edge either. If the interaction between helical edge states on the domain boundary is not negligible and that across NI domains is dominant, the helical edge states get gapped by making pairs across NI domains. In this process, if the edge is in a TI domain (Fig. \ref{fig:C2edge}(b)), the helical edge states on the edge are left, and thus only the edge remains gapless. If the edge is not parallel to the stripe pattern, the disconnected parts are effectively connected by the interaction and gapless edge states are obtained.

\begin{figure}
    \centering
    \includegraphics[width=0.45\textwidth]{fig10.pdf}
    \caption{Stripe domain structure and edge states. (a) When the edge is parallel to the stripe and in a NI domain. (b) When the edge is parallel to the stripe and in a TI domain. In this case, there is an edge state but it is indistinguishable from the bulk transport. (c) When the edge is not parallel to the stripe.}
    \label{fig:C2edge}
\end{figure}

\section{Discussion and conclusion \label{sec:conclusion}}
In this paper, we discussed the topological invariant of the twisted BHZ model at the Fermi level, in particular for the cases when TI and NI domains coexist in the moiré unit cell. As a result, we found the topological invariant of the moiré system is determined by the topology of the domain connectivity in the real space when the twist angle is small enough to neglect interactions between neighboring domain boundaries. We also found a bulk-edge correspondence that is described by the presence or absence of a connected line of edge states along the truncated edge. The obtained bulk-edge correspondence is compatible with the continuous change of the edge truncation condition that is specific to moiré materials. The effect of the interaction between neighboring domain boundaries is also discussed, and it is shown to work as a correction of the location or width of the phase boundary. Although we discussed the topological properties of the twisted BHZ model in this paper, the obtained results suggest that they can be applied to other topological phases, at least $\mathbb{Z}_2$ topological phases. These results give a method to calculate a topological invariant for cases where several topological domains coexist in the moiré unit cell due to the moiré modulation terms. The significance of the method is that it does not require a high-cost calculation such as the all-band calculation. The system we consider in this study, which has a superlattice structure of different topological domains, can be a platform for realizing novel topological systems such as a Weyl semimetal in a multilayer heterostructure proposed by Burkov and Balents \cite{burkov2011weyl}. This understanding of the topological properties of moiré materials is expected to allow us to design novel topological moiré materials with unique properties, in a way like a ``puzzle" with pieces of topological phases.

\section*{Acknowledgements}
We thank Aaron Merlin M\"uller for discussions.
This work was supported by JST CREST (Grants No. JPMJCR19T2).
M.H. was supported by PRESTO, JST (JPMJPR21Q6) and JSPS KAKENHI Grants No. 20K14390.

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Q: Multiple sorting conditions of a WPF combobox/listbox or CollectionView I haven't been able to find this as a previous request by searching, which is strange. I am simply trying to apply multiple sort conditions to a collection view that is bound to a comboBox.
I have tried this:
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Syllabuses of disciplines
Executors of Projects
Technical Base
Studying Laboratories
Interdepartmental laboratories
The Department of Biomedical Engineering (BME) was established in accordance with the order of NTUU «KPI» №1-61 of May 13, 2004.
In its activities the Department of Biomedical Engineering is guided by the Constitution of Ukraine, laws and other regulations of Ukraine, the Charter of Igor Sikorsky Kyiv Polytechnic Institute, Rules internal regulations of Igor Sikorsky Kyiv Polytechnic Institute and the Regulations on the Department Biomedical Engineering.
The training bases of the department are the National Institute of Cardiovascular Surgery M. Amosov of National Academy of Medical Sciences of Ukraine, Institute of Electric Welding E. Paton of NAS Ukraine, Institute of Molecular Biology and Genetics of NAS Ukraine, Institute of Problems of Materials Science. І.Frantsevych of NAS Ukraine, Research and Training center of cardiovascular engineering Igor Sikorsky Kyiv Polytechnic Institute, modern laboratories and production facilities.
The Graduates of the Department of Biomedical Engineering can work as engineers, heads of engineering services, researchers and consultants in the Commercial Medical and Pharmaceutical Organizations, participate in scientific and technical programs for the introduction of new engineering technologies in health care.
News of Department
Theme: HB Education by Hummingbird Themes.


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The large historical docks are a short distance from the centre of London, located at a prime location near London City Airport and the Olympic stadium.
Yachtsmen will be able to enjoy concierge services, 24 hour security, a VIP lounge, VIP parking and crew facilities.
More information is available on their website www.royaldocks2012.com.


text:
Top 10 Trends Lead To Gold
The year 2018 was a memorable year of great transitions. They involved changes in the political arena. They saw enormous changes in the debt picture, for both the USGovt and the major Western corporations. They saw a struggle to terminate the QE bond monetization, laced with hype-inflation. They offered staggering damage to California, whose effects are easily 100 times greater than the World Trade Center fallout. They offered resistance to the US-led bully tactics, in slapping sanctions even on the US allies, a forecast by the Jackass two years ago. The globalist cabal agenda has been dealt a powerful damaging blow, perhaps lethal, during a year of great exposure for their criminality. The transitions offered a complete shift away from the perception of USMilitary full spectrum dominance. But the most important changes have come in the finance & economic sectors. The Gold Standard has seen a paved road for its implementation, arrival, and acceptance. The road can be identified for its several major constructed arteries. The pathways are built by the Eastern nations, which will continue to champion the financial reform, and thus wrest global control from New York and London. History is being made. It will still take time, but the momentum is gathering in a notable and convincing manner. The common theme of all the leading factors is the movement away from the USDollar, a theme so popular and widespread that it has been given a name, de-Dollarization. In the next year, even the compromised corrupted Wall Street bank community will openly discuss that Gold must be the solution to the unresolved crisis.
TOP 10 FACTORS & EVENTS OF 2018, EACH WITH IMPORTANT IMPACT ON THE NEW YEAR TOWARD THE GOLDEN DIRECTION:
USGovt debt volume over $22 trillion, which grows well over $1 trillion annually, with no prospect of repayment except from criminal elite asset seizures, amidst high volume dumping of USTreasury Bonds. The future Gold price estimates are flowing in, with Jim Sinclair posting a $20,000/oz estimate based solely upon foreign holdings of USGovt debt. The USDollar money supply has tripled since 2008, with no gain yet in the Gold price. It is a coiled spring, ready to respond to the current crisis.
Gold as the best performing asset in 2018, but with almost zero gain in value, which will next become a major beneficiary of the nascent Global Financial Crisis, part 2. The crisis is unfolding in full glory after six years of QE monetary excess, which has transformed the USTreasury Bond into the new global subprime bond. Its failed structure and horrible integrity demand the new Gold Standard in full spectrum.
USMilitary in retreat on a global basis, after full displays of no superiority on the battlefields, thus removing the ultimate support pylon for the USDollar. The USNavy is in port for the first time in a century. The United States is departing from its absurd role of global police and international bully. Without such violent USDollar support, the Gold Standard has much less resistance for its broad implementation, even if in numerous pockets.
Saudi Arabia breaks ranks from official US support, their $3 trillion in USTBonds confiscated at the ESFund within the USGovt, their gold pilfered in Swiss bullion banks. Even their dirty Yemen War is no longer supported. The recent Saudi budget is a laughable absurdity, which depends upon an $80 crude oil price. With the US having lost its Petro-Dollar ally, the Gold Standard lies directly ahead, aided by gravity, pushed forward by the Russians and Chinese.
Potential failure of large Western banks and financial firms, led by Deutsche Bank, General Electric, and possibly a couple Wall Street banks. Do not ever overlook the contagion impact to the French banks, which will fall quickly upon any Italian banking system collapse. Expect around $1 trillion in Western corporate bond downgrades this year. The events will let loose a panic, which will call for the Gold Standard as remedy.
The Belt & Road Initiative blossom, as the biggest development effort since the Marshall Plan, many times larger. It continues to be led by China, joined by dozens of nations with perhaps $6 trillion in slated projects to come. The grand feature of the BRI cornucopia of large-scale projects is that all are to be non-USD in trade and payment systems. They will form a massive cascade of industry and commerce, outside the USD realm. Worse, many BRI projects will be funded by the Chinese, who dump USTBonds en masse. With commerce comes banking procedural changes, leading to the Gold Standard.
Rosneft Oil Cartel emergence to fill the OPEC void, as the Russians develop their oil consortium for mixture and purity standards. The Russian Rosneft is joined by Saudis, Iran, Venezuela, and soon Mexico, all to be non-USD in trade and payment systems. The Russian initiatives also enable greater liquidity for nations set in opposition to the United States. Couple the Russian initiatives with the Chinese recent practice to grant national loans based in USTBonds ,like to Angola. The result is grand momentum in the direction toward the Gold Standard eventually.
Rising price inflation, with major factors being monetary expansion, trade war, supply decrease, and ineffective asset allocation are added strain to the global financial system. The response will be a call to Gold as a safe haven, while the USTBond loses the status as a haven of security since its debt load is too great and its prestige is long gone. Besides, the hidden derivatives to produce its fake demand are being exposed.
Rise of global trade outside the USDollar, often called de-Dollarization, in avoidance of pressured rules, in workarounds of US-led sanctions. The result of seeking a fair trade payment system will be the pursuit of the Gold Standard. The USTBill payment structure will yield to the Gold Trade Note even in the energy sector. This revolutionary vehicle will usher in the Gold Standard, first in trade, next in banking, and finally in currencies. Note that the third and final step in sequence is not required.
Exposure of global banker cabal, complete with their fascist corporate network of high level criminality in child murder, trafficking, racketeering, genocide, and counterfeit will remove the crucial upper layer in the many hidden control rooms. They thrive on USD self-dealing and gifts to themselves, as well as major monopolies. Their control room has long been the central bank franchise system. With both King Rothschild and King Rockefeller gone to dwell with Lucifer, the roadway for the Gold Standard is visible, potential, within reach, and currently being implemented. It stands as the final remedy.
FORECAST DIRECTIONS FOR 2019
The USTreasury Bond will seek continued status as safe haven asset, but the struggle will be on full tilt. The USGovt debt continues to grow without control. The global reputation of the USTBond as safe haven is being dismissed, primarily in the East. The global dumping of USTBonds is magnificent, whether in normal sales or from Indirect Exchange. The image and role of the USDollar as global reserve currency has been irreparably damaged. The main demand for USTBonds is from Wall Street, the USFed, and misled investors exiting the stock market. Without derivatives forcing the way with fabricated demand into the false safe haven, the USTBond would skyrocket in yield, as in, it would rival what Greece and Italy showed in 2010 bond yields.
Big Western banks are extremely vulnerable to failures. Their insolvency renders them weak and unprepared for further portfolio losses. Their easy game of bond carry trade has ended with a full year of interest rate hikes. The have little or no bond issuance business segments. Their exposure to the energy sector is astounding and enormous. A bond convexity problem might arise from the carry trade reversal, which could push bond yields much higher. However, it would be managed by the JPMorgan derivative control room. The contagion factor is very real, ready to catch fire when any big bank or national banking system undergoes failure. As Bill Holter states, if any one big Western bank goes under, they all go under. True indeed!
The Western globalist banker cabal has lost its former formidable power, still with residual power. Their kings of Rockefeller and Rothschild have departed this world. Their middle level captains have been depleted in ranks, whether by conversion (flipped) to join the reform, or by lost wealth (stripped) in majority of assets, or by elimination (killed) by the White Dragon enforcers known as the TRIAD. Their inadequate ranks make their agenda impossible to carry out, and their vengeance impossible to occur.
USMilitary retreat has been global after full scale ignominy, following displays of inferior weapon systems. Refer to jet fighter aircraft, to missile systems, to anti-missile defense systems, to targeting systems, to jamming methods. The Pentagon weapons system funding and appropriation methods are a massive fraud center and gigantic crime scene, resulting in over $6 trillion in missing funds. The result has been both retreat from the global police sentry role by the United States, and possibly an accord toward a termination to the endless Western war agenda which serves the military industrial complex. The USGovt might actually seek a better more productive usage of $billions in annual budgets, after having squandered $25 trillion in the last 40 years. The tragic result of four decades of wasteful military spending has been a crumbling US infra-structure and numerous alienated allies.
Advent of the Gold Standard adoption on a global basis. It begins with the gold basis for trade payments, soon to be seen in the Gold Trade Note. Expect the GTNote to be launched by China, for purchase of Gulf Region oil, from both Arab monarchies and Iran. The emerging standard continues with gold bullion playing a primary role in bank reserves management, which requires the sale of USTBonds and the purchase of Gold bullion. The final step will be the launch of gold-backed currencies, which carries with it many complications.
The last forecast is the most important, since all the above forecasts merge into the Global Financial Crisis that has begun to unfold. It will be at least three to five times more powerful and widespread than the Lehman crisis in 2008. It will feature numerous crisis fronts simultaneously, and all these fronts will present intractable problems. No solution will be seen, and none offered will be viable. Nothing was fixed. The solution of monetizing every dead decrepit financial entity will be proposed, which will ignite the Gold price. The entire King Dollar Realm stands atop the USTreasury Bond, which is a haggard relic of its past.
In fact, all the horrendous policies toward mortgage bonds have been directed to the USTreasury Bond. It is the new global subprime bond, but the globalist's problem bond child. As time passes, the obvious answer to the global crisis which will fester, grow, and intensify, will be the implementation of the Gold Standard. The major challenge with the true viable solution is that the Eastern nations are far ahead in the process. They will continue to take charge of implementing the Gold Standard with numerous non-USD platforms. Meanwhile the Western nations fester and face tremendous pressures to keep the system in place. In other words, the West will strive to keep the political and financial oligarchies and elite castles in power. They will fail. The East will face a clear pathway in putting the Gold platforms in place. They are the natural remedy, the veritable magic elixir, the remedy for debt suffocation and the toxic debt-based monetary system. It is not only upside down, but also rotten to the core.
BANK STOCK INDEX UPDATE
Sometimes a single graph can tell a very big and important story, even as a preview of what lies directly ahead. Sometimes a picture can tell a thousand words. In this case, a single stock index chart screams a major financial crisis. It is the US big bank stock index BKX, which is in deep trouble. The Jackass featured the BKX two months ago, after a mere 15% decline. Since then the three consecutive weekly powerful declines have heralded the Global Financial Crisis, part 2. The entire gap from 70 to 90 must be filled, with deep groaning and gnashing of teeth amidst cries of pain in the pits. The BKX had fallen by 30% since its January and March highs, now to have rebounded only slightly. My name for the current unfolding crisis has been steadily the Systemic Lehman Event, since nothing was fixed, all the errors repeated on the monetary side, with exclamation point the fall in the BKX index itself. In fact, the USTreasury Bond has become the new global subprime bond. The banker stock index has recovered only to the previous critical support level, which will next serve as critical resistance. Expect the BKX to fall to the 2016 summer level with a 70 handle, another 20% below the current price posted. The next decline will shake the global financial offices in a big way, and herald the full bloom of financial crisis. Recall that nothing was fixed in the last ten years. Thus one can expect a bigger fallout from the broad nasty powerful diverse damage. It will loosen the elite power structure.
THE GLOBAL SUBPRIME BOND
QE was a grand failure. The bond support helped avert big bank failures. The bond purchases averted Treasury auction failures. The end result of the insanity of QE is a repeat global financial crisis, marking the end of the multi-year hyper monetary inflation chapter. The USTBond has all the characteristics of not just a subprime bond, but a Third World nation foundation bond to underpin its currency. Here ten years later, nothing has been fixed. In fact, all the abuses heaped upon the mortgage finance sector have been repeated in sovereign bonds. The USTreasury Bond has become a subprime bond, financed by pure monetization, almost no actual bonds buyers, $trillion annual deficits, auctions rigged, with hidden demand from the derivative machinery. It qualifies as a Third World debt security. The major US corporate bonds are moving quickly to junk status, soon to be shed by the tens of $billions by pension and mutual funds in an endless parade. Expect some loud shrill sounds from afar very soon, as the $10 trillion in Emerging Market loan defaults begin. The figure is in doubt only from the definition of Emerging Market, since all their debts are ready to default from deadly currency declines. They were lured by low interest rates, but fell into the currency decline trap with spiked bamboo shoots barely covered below. In the next few months, expect that QE will be resumed, in order to monetize the SIFI important big Western banks, the elite control rooms and power centers. They are almost all vulnerable to failure. The official return to QE will light a bonfire under the Gold price, and invite debate toward the Gold Standard. It comes after the damage is more visible, and the problems are concluded as intractable (not solvable).
SYSTEMIC LEHMAN EVENT
Regardless of the name, a major crisis has begun. Some call it the Everything Bond Bubble, since the QE monetary policy has funded sovereign and corporate bonds. The major central banks have truly wrecked the entire global bond market. The debt downgrade process by debt rating agencies has only begun. It will become an absolute firestorm. Some call it the Global Financial Crisis, part 2. The Jackass prefers the name of Systemic Lehman Event, since it is part 2 with the exact same monetary abuse, bond fraud in underwriting, with a longstanding QE chaser downed each year for seven full years. The Quantitative Easing is old fashioned hyper monetary inflation of the worst kind, unsterilized, meaning huge volume of funds added to the financial system with no extractions. The global financial crisis is upon us, having entered an intermediate level of debt saturation, of bond issuance deep abuse, of market rigging corruption, of banking system insolvency at acute levels, and of economic rot setting in. The outcome of the unfolding crisis will be three to five times more magnificent that what was witnessed in 2008 and 2009, since ten more years of the same recklessness has endured, but on a grander scale.
Expect the current crisis to wreck a few big Western SIFI banks, collapse at least one national banking system, destroy at least five major Western corporations, and result in open discussion of the USGovt debt restructure, technically a default. The systemically important financial institutions (SIFI) cannot not be saved, since too many are insolvent, gigantic hollow reeds. The dirty secret is that the big Western banks are dependent upon bond carry trade easy profits and narco money laundering fees. They rely upon hidden central bank welfare, to cover their $trillion exposure to derivatives. As the Petro-Dollar dissolves, these derivatives become unmanageable. The derivatives focal point, ground zero, is Deutsche Bank. Nothing can save once mighty DBank. As a confirmation, they announce on a quarterly basis that they cannot any longer manage the mountain of nearly $50 trillion in derivatives. As additional evidence, notice the multi-$billion bonuses handed out to their executives last week. No way would that happen if the big bank were to be brought back to a healthy remedial structure. Well then again, maybe they have inside word of a major new QE initiative to monetize the big SIFI Western insolvent banks, best described as corrupted empty silos filled with Western elite excrement and stained confetti as garnish.
Jim Willie CB, also known as the "Golden Jackass", is an insightful and forward-thinking writer and analyst of today's events, the economy and markets. In 2004 he launched the popular website http://www.goldenjackass.com that offers his articles of original "out of the box" thinking as well as content from top analysts and authors. He also has a popular and affordable subscription-based newsletter service, The Hat Trick Letter, which you can learn more about here.
Jim Willie Background
Jim Willie has experience in three fields of statistical practice during 23 industry years after earning a Statistics PhD at Carnegie Mellon University. The career began at Digital Equipment Corp in Metro Boston, where two positions involved quality control procedures used worldwide and marketing research for the computer industry. An engineering spec was authored, and my group worked through a transition with UNIX. The next post was at Staples HQ in Metro Boston, where work focused on forecasting and sales analysis for their retail business amidst tremendous growth.
Jim's career continues to make waves in the financial editorial world, free from the limitations of economic credentials.
Jim is gifted with an extremely oversized brain as is evidenced by his bio picture. The output of that brain can be found in his articles below, and on the Silver-Phoenix500 website, on his own website, and other well-known financial websites worldwide.
For personal questions about subscriptions, contact Jim Willie at JimWillieCB@aol.com


This voucher is valid against any snare drum building course that has availability on it. The voucher is valid for one year from the date of purchase. When you are ready to redeem your voucher, please email us with your date preference and we will book you on the course, as long as there are spaces on the course desired. If there are no spaces then alternative course dates will be available.


text:
About CMAY
Kathleen Cranfield
Kathleen is the founding member of CMAY and the current president. She has been a registered midwife in Canada since 2007 after graduating from Ryerson University's International Midwifery Pre-Registration Program and is currently registered with the College of Midwives of British Columbia and is licensed in the NWT. Kathleen has sat on the board of directors of the Canadian Association of Midwives as Yukon's representative since 2011. Kathleen first moved to Yukon in 1998 and in 2002 left to pursue her calling to be a midwife with every intention of returning. Kathleen has worked as a registered midwife in NWT, British Columbia, Ontario and Northern Quebec. Kathleen believes wholeheartedly in informed choice as one of the main tenets of midwifery care. She believes that education de-mystifies and helps integrate all the unique aspects of childbearing and in turn empowers people in their individual experiences. Kathleen is determined to see midwifery become a regulated and funded profession in Yukon so that all birthing people, and their families may have the same birthing options as are enjoyed in the rest of Canada. Kathleen and her husband have two beautiful, young children and a wonderful dog, Gertie.
Patricia Kulachkosky
Patricia retired to the Yukon in 2013 after 35 years of being a Registered Nurse in B.C. Part of my nursing career included 15 years as a Maternity, Labour Delivery Nurse, those years were in Dawson Creek and well before Midwives were part of any hospital birth. My grandsons were born with the assistance of a midwife, not all women can afford to have this as an option. I believe that Legislated, Registered and funded Midwives will give all Yukon women a choice in how and where they deliver their babies. Birth is a natural process and medical intervention is not always needed or necessary.
Kristin Kulachkosky
Kristin is originally from northern BC. She has lived in the Yukon for since 2003. After working for the Department of Justice for 13 years, she has now refocused her life around staying at home with her kids, running her ``micro-farm`` and managing her business. She co-owns and operates The Gravy Train, a food truck specializing in poutine, with her partner Ron. Kristin was under a midwife's care for both of her pregnancies, planning for a homebirth each time. In the Spring of 2013 she had her first baby in the hospital, with her midwife and family present. In the summer of 2015 she had a water birth in her home at Marsh Lake. Kristin's has been the secretary for CMAY since its conception and strongly believes every family should have the option to choose their place of birth and have access to Midwifery care.
Christina Kaiser
Christina is a Certified Midwife (German Diploma), mother of wonderful children who were born at home, here in the Yukon. She immigrated to Canada from Germany in 2000 and has lived, loved and worked here as a mother, wife and midwife ever since, providing home births and care for women and families throughout the childbearing year in the absence of regulations. It has always been Christina's goal that all families have access to midwifery care while keeping choices open. This is Christina's fourth term with CMAY.
Elizabeth Morrison is a Registered Midwife at Matraea Midwives in Duncan, BC on Cowichan Territories. She completed her midwifery training at the University of British Columbia and has an undergraduate in history/environmental studies from the University of Victoria. She also works regularly at the Rankin Inlet Birth Center in Rankin Inlet, Nunavut.
Elizabeth is passionate about increasing access to midwifery care in rural, underserved, and First Nations communities, as well as inter-professional collaboration and practice. In her free time she can usually be found in the mountains exploring the beautiful outdoors, loves gardening, and is mama to new baby Théo.
Bonnee Bingham
A mother of two daughters, Brianna and Esther; a born and raised Yukoner and member of the Vuntut Gwitchin First Nation, moved to Alberta to attend College and work. She returned home to have her first daughter in 2006. It was then that she started attending the Canadian Prenatal Nutrition Program (CPNP) at Skookum Jim Friendship Centre. After graduating from the program, she spent a short time volunteering and as the program assistant before taking over the program in 2008.
Bonnee took a year secondment to go work in her home community of Old Crow, which led to a three year political term as Deputy Chief. Upon the completion of the term, Bonnee returned to Whitehorse and when Skookum Jim Friendship Centre posted the position of CPNP Coordinator, she knew that was where she wanted to be.
Bonnee is passionate about traditional indigenous practices in medicine, birthing and parenting. She is also passionate about pre and postnatal care and support. Along with helping families with new babies get the best start possible. So much so that over the past year she has become a Birth and Postpartum Doula and is working on her Dona Certification.
Catherine Lalonde
Originally from the East Kootenays in British Columbia, Catherine has lived in Dawson City since 2010. She has been trained and attended births as a doula and dreams of one day becoming a midwife. In 2016 she was accepted into the UBC Midwifery Program but postponed her education when she found out she was pregnant with her first baby. Being unable to find somewhere in Whitehorse to have a home birth she traveled to her sister's in the Kispiox Valley in northern BC to have a home birth with a registered midwife. Catherine joined the board in 2015 but took a hiatus when her son was born. Her amazing experience with a midwife strengthened her desire to see families of the Yukon have the same choices as other jurisdictions across Canada. She re-joined the board to continue to advocate for the funding and regulation of midwifery in the Yukon and hopes to one day see birth brought back to the communities.
Jocelyn Land Murphy
Dr Jocelyn Land-Murphy is a BC-licensed Naturopathic Doctor who relocated to Whitehorse with her young family in 2017. Dr Land-Murphy is the President of the Yukon Association of Naturopathic Doctors, and has an exclusive focus on women and children's health - including fertility, pregnancy/birth and ongoing post-partum and family health. Jocelyn is also the creator of My Healthy Pregnancy Plan, an evidence-based, online integrative pregnancy program in use by women and their care providers around the world.
Jocelyn delivered both of her children with midwifery care in Ontario, and is passionate about providing women in the Yukon with the same birthing and pre-natal options available to women across Canada. She is honoured to be a part of the CMAY and to help bring midwifery to the Yukon.
Erika Oppen Smith
Like many Yukoners Erika wears several hats. She is a Licensed Practical Nurse at Whitehorse General Hospital and small business owner and sessional Instructor for the Health Care Assistant program at Yukon College. She was born and raised in the Yukon. In 2014 Erika welcomed her first daughter, Ivy. It was the expert care she received from her midwife that prompted Erika and her husband Jonas to become advocates for regulating and funding midwifery in the Yukon. On May 5th 2017 in celebration of International Day of the Midwife Erika told her daughter's birth story, she went into labour that evening with her second baby and welcomed Liv the very next day (on her due date).
Rebecca Shrubb
Rebecca is from a small town in Ontario but lived and worked in Old Crow from 2016-2018. She was pregnant in Old Crow and decided to have a home birth with a midwife in Ontario after learning that midwifery was not covered/regulated in the Yukon. Being pregnant and delivering her baby under the care of a midwife was a life changing experience for Rebecca, which impassioned her to join CMAY to work towards all Yukon women having access to regulated midwifery services – including women in the smaller, remote communities. Rebecca now lives in Whitehorse with her husband and baby girl, Flora. Rebecca has an MA in Sociology from the University of Victoria and currently works for Vuntut Gwitchin Government from Whitehorse.
Paige Galette
Haitian, activist and feminist, Paige Galette is passionately involved in political movements fighting for social justice; the labour movement, women's movement, Queer movement and the Black liberation. Strong advocate of reproductive justice, Paige hopes to see the implementation of regulated midwifery throughout the Territory, providing access for all Yukoners, including but not limited to; Yukon First Nations, Inuit and Métis people, racialized people, francophones, LGBQ2S and Trans and non-binary people. Paige is excited to be joining the CMAY board. With a Bachelor's Degree in Social Sciences and Political Sciences, Paige is currently training to become a Full-Spectrum Doula, with the hopes of integrating an intersectionality lens to her practice.
Leanne Watson
Leann is a certified, Whitehorse Doula, Childbirth Education Instructor, Lactation Educator, Infant Massage instructor and parenting support coach with over 15 years of experience. Leanne moved to the Yukon in 2000, as has been part of the birth community and passionate about birth choices and access ever since.
Rosemary Oslund
Rosemary is a homeschooling mother of three, gender equality advocate and lifelong student. Through Rosemary's own experience of midwifery supported births across three provinces as well as barriers to access she became an active advocate for access to midwifery care for all birthing folks! With a background in public policy and administration and passion for women's rights Rosemary aims to advocate for effective and responsive change through public policy.
We are always looking to connect with people to help us on our mission of bettering midwifery for Yukon women.
Fireworks Design - Whitehorse / Victoria Web Design


text:
// Copyright (c) 2017 James Skimming. All rights reserved.
// Licensed under the Apache License, Version 2.0. See LICENSE in the project root for license information.

namespace Abioc.Registration
{
    using System;
    using System.Collections.Generic;
    using System.Diagnostics;
    using System.Linq;

    /// <summary>
    /// A <see cref="IRegistration"/> entry that produces the code to provided services of type
    /// <see cref="IRegistration.ImplementationType"/> through a factory function.
    /// </summary>
    [DebuggerDisplay("{DebuggerDisplay,nq}")]
    internal class SingletonRegistration : RegistrationBase
    {
        /// <summary>
        /// Initializes a new instance of the <see cref="SingletonRegistration"/> class.
        /// </summary>
        /// <param name="inner">The <see cref="Inner"/> <see cref="IRegistration"/>.</param>
        public SingletonRegistration(IRegistration inner)
        {
            if (inner == null)
                throw new ArgumentNullException(nameof(inner));

            Inner = inner;
        }

        /// <summary>
        /// Gets the <see cref="IRegistration.ImplementationType"/> of the <see cref="IRegistration"/>.
        /// </summary>
        public override Type ImplementationType => Inner.ImplementationType;

        /// <summary>
        /// Gets the <see cref="Inner"/> <see cref="IRegistration"/>.
        /// </summary>
        public IRegistration Inner { get; }

        private string DebuggerDisplay => $"{GetType().Name}: Type={ImplementationType.Name}";
    }
}

redpajama_set_name: RedPajamaGithub


text:
A Guide To A Grey Day In Geneva's Old Town
by Nick Nomi | Destinations, Switzerland
Geneva's dirty, busy, tram ridden high-street reminds me of Manchester in a strange kind of way. But the old town is beautiful and charming, and the red light district dizzying and gritty, and a neon soaked reminder of Switzerland's open sex laws, but also a great place for Thai food.
Our my last visit to Geneva I found a grey mono sky covering most of the mountains and descending at a rapid rate towards the cobbled paths of the old town. While walking, it became apparent that this kind of weather does absolutely nothing for the city – not like places such as York and Venice, whose streets find a new lease of life during darker times. No, the streets of Geneva lacked a certain vigour. The life seemed drained from them and the lake? A large pool of lifeless grey waters mimicking the sky above (though shades of its usual blue were there … hidden). Tired from a late night and an early morning I headed to the old town to grab a coffee in one of the prettiest cafes by the old carousel.
Once in the Vieille Ville I found dank stoney streets and a pleasant, and almost empty old town, complete with beautiful old squares, antique bookstores and a lovely cathedral whose façades show a history that spans some 850 years.
The cathedral sits at the highest point of the Old Town, it was built in the 12th century, and had various bits and pieces added later beginning in the 16th century. On a bluer day I would suggest climbing the 157 steps up the north tower to take in the incredible views of the city and the lake.
The Maison Tavel or Tavel House is the oldest house in the city and dates back to the 12th century. In the 14th century, some of the walls were destroyed and led to the delightful castle-like restoration of high grey walls and a large round tower that can still be seen today. And though it was built and maintained by the Tavel family the house now belongs to the city of Geneva and currently houses a museum that explores the history of Geneva through a series of exhibits and installations.
The Old Arsenal with its original 17th century canons and three frescoes by Alexandre Cingria, depicting different periods in Geneva's history is well worth a strooll, especially if the rain hits. The arsenal was originally a granary built in the 17th century and later used as a military storehouse up until 1877. There are five cannons exhibited under the archways – each of which were still in use well into the 19th century. The building now houses the Geneva State Archives.
The 15th century Geneva Town Hall, built between 1555 and 1578 by Peter Desfosses is in a quiet and beautiful little square. Wrapped around the exterior is a unique access ramp, which is said to have been built in such a way as to allow access to the building on both foot and horseback. This building also houses the Alabama Room, the very room where the first Geneva Convention was signed in 1864.
The streets of Geneva's old town are laced with beautiful minor sights. The Librairie Ancienne Antiquités for example is a stunning antique bookshop with bookshelves built into its exterior façade, while plaques commemorating the likes of of Jean-Jacques Rousseau and Jean Calvin are dotted throughout the city's walls.
There's a large collection of old antique stores, libraries and galleries dotted around Geneva's old town – many of them with signage as old as the shops themselves, some grand and others minimalistic to the point of obscurity but none the less beautiful.
If you look carefully as you make your way around Geneva's old town you'll note lots of beautiful, ornate and intricate embellishments on the city's architecture – the doors are mostly grand and wooden, many have beautiful keyholes in extinct shapes and door knockers scultped to perfection.
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Chiesa dei Santi Apostoli | Florence
The Glass In The Oculus
Autumn In Strasbourg
The Poet In The Jardin du Luxembourg