text:
\section{Introduction}

Topological insulator (TI) materials are characterized by a bulk gap with band inversions and metallic states on the borders.
These edge (surface) states are topologically protected by symmetry.
A class of TIs protected by time-reversal symmetry has been predicted and realized experimentally
\cite{Kane2005,Bernevig2006,Konig_Science2007,HsiehNat2008,RevMPhys82-3045-2010},
where a $Z_2$ topological invariant has been used to characterize them.
The crystal lattice symmetry can also lead to topological protection on the topological crystalline insulators (TCIs)
\cite{Fu2011,HsiehNC-2012,Tanaka2012,Dziawa2012,Okada2013,ReviewAndo-Fu-2015,Xu2012,ozawa2014topological}, where the topological nontrivial states are characterized by a crystal symmetry Chern number.
Recently, it has been shown that yet a new class of topological nonsymmorphic crystalline insulators \cite{parameswaran2013topological,liu2014topological,shiozaki2015z,fang2015new,Varjas2015NonSym,Kane2015Nonsymm,chen2015topological} presenting unique properties with respect to the topological order exists.
The overall classification of topological insulators has been discussed based on space group symmetry of the bulk systems
\cite{Kane2015Nonsymm,Slager-NatPhys,fang2012bulk,jadaun2013topological}.
However, by reducing the symmetry, forming surfaces or edges, a question arises -- are the topological protected edge states completely described only by the parent bulk symmetry?

\begin{figure}[ht!]
  \centering
  \includegraphics[width=\columnwidth,keepaspectratio=true]{StripeLattices3}
  \caption{(a) Unit cell of the PbSe monolayer. (b) The first Brillouin zone (BZ) with the $\Gamma$, X, Y, and M TRIMs. Confinement (in red) along $y$ ($y'$) projects the TRIMs onto $k_x$ ($k_x'$) to form the one-dimensional BZ given by $\bar{X}$ and $\bar{\Gamma}$ ($\bar{X}'$ and $\bar{\Gamma}'$).
  (A-E) Illustration of the five possible crystallographic terminations of PbSe ribbons.
  The unit cell of each ribbon is highlighted in gray. The point group symmetries are indicated with usual notation, except for panel E, where ``NS'' stands for nonsymmorphic.
  The ribbons considered here have about 45 atoms ($\sim 10$~nm) along $y$ ($y'$).
  }
  \label{fig:StripeLattices}
\end{figure}

In this paper we build effective Hamiltonians using group theory \cite{voon2009kp, dresselhaus2007group, car1976optimal, koster2012space, FazzioTeoGrupos} for a TCI monolayer and ribbons to investigate the effects of the edge terminations on its topological properties. A PbSe monolayer is chosen as a representative two-dimensional (2D) TCI for our discussion \cite{Wrasse2014PbSeTCI,Fu-NL-2015,PRB91-201401-15,kobayashi2015electronic}. The band structures from the effective Hamiltonians are compared with {\it ab initio} results obtained from density functional theory (DFT) calculations using the {\sc VASP} code \cite{kresse1996efficient}. We consider five possible crystallographic ribbon cuts, starting from the simpler case A (Fig.~\ref{fig:StripeLattices}) building up in complexity towards our main result in ribbon E. We find that the energy dispersion of the topological edge states is strongly dependent on both the reduced symmetry and boundary conditions, resembling graphene's zigzag and armchair edges \cite{divincenzo1984graphene,BreyFertig2006Ribbons}. Interestingly, we show that while our bulk monolayer is a symmorphic lattice, one particular cut leads the nonsymmorphic ribbon E, whose symmetry group is not a subgroup of its bulk counterpart. It is known that nonsymmorphism yields extra degenerescences with respect to its underlying point group \cite{voon2009kp, dresselhaus2007group, car1976optimal, koster2012space, FazzioTeoGrupos}, which in our case results in an extra protection that preserves the Dirac cone for ribbons of arbitrary width. In addition to the fundamental physics presented here, the nonsymmorphic systems could be potential materials for nanoscale 2D devices, preserving the topological state properties even for nanosized ribbons.

Experimentally, atomic layer growth control of IV-VI materials has been achieved via electrochemical atomic layer epitaxy/deposition \cite{vaidyanathan2004quantum, vaidyanathan2006preliminary}, and PbSe nanorods and nanotubes were recently grown \cite{li2012facile}. However, a refined edge control remains as challenging as for any other 2D material. Recently developed chemical bottom-up approaches were successful in graphene \cite{narita2015bottom,jacobberger2015direct}.
Effects of edge saturation and substrates are yet to be experimentally explored.
Recently, first-principles calculations showed that the topological properties and the energetic stability of IV-VI monolayers can be manipulated using appropriate substrate \cite{kobayashi2015electronic}.

\section{Model for the infinite monolayer}

The PbSe monolayer has a square Bravais lattice [Fig.~\ref{fig:StripeLattices}(a)] with a space group symmetry $D_{4h}$. The time-reversal invariant momenta (TRIMs) are $\Gamma$, X, Y, and M, as shown in Fig.~\ref{fig:StripeLattices}(b). From first principles \cite{Wrasse2014PbSeTCI} it is known that the band inversions occur at $X$ and $Y$, where the symmetry is reduced to the $D_{2h}$ space group. At X, without spin-orbit (SO) couplings the top of the valence band is composed mostly by $p_x$ orbitals of Se, while the bottom of the conduction band is dominated by $p_z$ orbitals of Pb. At Y, all properties are given by a $C_4$ rotation of X, which allow us to focus our discussion on the X point. To satisfy the Bloch theorem at X the orbitals must be arranged periodically along $y$ and anti-periodically along the $x$ direction, as shown in Fig.~\ref{fig:Lattice-BZ}. To emphasize the Cartesian symmetry of these basis states, we label the kets referring to the axes through which the state is odd. Hence, the states in Figs.~\ref{fig:Lattice-BZ}(a) and \ref{fig:Lattice-BZ}(b) become $\ket{xz;s}$ and $\ket{x;s}$, respectively. Here $s = \{\uparrow, \downarrow\}$ denotes the spin.

\begin{figure}[ht!]
  \centering
  \includegraphics[width=\columnwidth,keepaspectratio=true]{Lattice-BZ3}
  \caption{Representation on the unit cell of the spinless eigenstates of (a) conduction and (b) valence bands at $X$. The orientation of the $p_z$ orbitals of Pb in (a) are chosen to satisfy the Bloch periodicity at $X$, and the resulting state $\ket{xz;s}$ is odd along both $x$ and $z$ directions. The state $\ket{x;s}$ in (b) is composed by a single $p_x$ orbital of Se on the unit cell.}
  \label{fig:Lattice-BZ}
\end{figure}

From this set of orbitals, $\{ \ket{xz;\uparrow}, \ket{xz;\downarrow}, \ket{x;\uparrow}, \ket{x;\downarrow} \}$, we construct the effective Hamiltonian for the monolayer considering a $k$-space expansion \cite{divincenzo1984graphene}. Following this ordering, one obtains a matrix representation for the symmetry elements of the $D_{2h}$ group, plus the time-reversal operator $\mathcal{T}$ \footnote{See Appendix for the matrix representation of the symmetry elements, and character tables of space groups.}. Requiring that the Hamiltonian $H_{X}$, for $\bm{k}$ around X, commutes with these symmetry elements and $\mathcal{T}$ up to second order in $\bm{k}$, we obtain

\begin{multline}
 H_{X} = \Delta\tau_z + (\alpha_y k_y \sigma_x  - \alpha_x k_x \sigma_y)\tau_x \\
  + (m_{x}\tau_z + \delta m_x)k_x^2 +(m_{y}\tau_z + \delta m_y)k_y^2,
 \label{eq:Hmonolayer}
\end{multline}
where the Pauli matrices $\sigma_i$ ($\tau_i$) act on the spin (orbital) degrees of freedom.
From the $k\cdot p$ theory one can associate the $\alpha_x$ and $\alpha_y$ with the $k$-dependent SO contribution, while the gap $\Delta$ has contributions both from the bare lattice potential $V(r)$ and from the $k$-independent SO term via remote bands. Here $\Delta$ plays the role of the Dirac mass and changes sign as a function of the SO intensity. The mass (parabolic) terms $m_{(x,y)}$ are anisotropic, and $\delta m_{(x,y)}$ could break the particle-hole symmetry. This Hamiltonian describes the bulk PbSe monolayer, as we can see in Fig.~\ref{fig:bsX}, where the band structure around $k=X$ without ($\Delta = 1$) and with SO couplings ($\Delta = -1$) are in qualitative agreement with {\it ab initio} data \cite{Wrasse2014PbSeTCI}.

From the effective bulk Hamiltonian, we can calculate the topological invariants of the system, i.e., the Chern numbers. The bulk monolayer and all possible ribbons share only the identity and mirror $\mathcal{M}$ ($z\rightarrow -z$) symmetry elements. Therefore, all eigenstates belong to one of two classes \cite{ReviewAndo-Fu-2015} defined by the eigenvalues $\eta = \pm i$ of the mirror operator, i.e., $\mathcal{M} \ket{\psi_\eta} = \eta \ket{\psi_\eta}$. For each class one defines a Chern number $N_\eta$, which allows us to calculate the total Chern number $N_T = N_{+i} + N_{-i}$, and the mirror Chern number $N_\mathcal{M} = (N_{+i}-N_{-i})/2$. For $\Delta > 0$ we find all $N_\eta = 0$ and the system is on the trivial regime as expected. For $\Delta < 0$ the states from the occupied bands give $N_{\pm i} = \mp 2$, which yields $N_T = 0$ and $N_\mathcal{M} = -2$, thus characterizing the TCI phase \cite{ReviewAndo-Fu-2015}.

\section{TCI Ribbons}

By cutting the monolayer into ribbons, the introduced lateral confinement may break some symmetries of the system, allowing new terms into the effective Hamiltonian. There are two main crystallographic orientations for the ribbons: $x \parallel [1\bar{1}0]$ and $x' \parallel [100]$ directions. The first has three possible edge terminations, illustrated in Fig.~\ref{fig:StripeLattices}, panels A, B, and C, while the latter has two more possibilities, shown in Fig.~\ref{fig:StripeLattices}, panels D and E. Hereafter we refer to each termination by these capital letters. Next to each panel in Fig.~\ref{fig:StripeLattices} we label the corresponding space group symmetry.

\begin{figure}[ht!]
  \centering
  \includegraphics[width=0.95\columnwidth,keepaspectratio=true]{BulkBS}
  \caption{Band structure of the PbSe monolayer from the effective model for $k_y = 0$ and as a function of $k_x$. (a) Without SO we consider $\Delta = m_{x} = 1$, and $\delta m_x = \alpha_x = 0$. (b) With SO the gap changes sign $\Delta = -1$, the masses remain the same, and $\alpha_x = 2$. The colors represent the contributions from the $\ket{x;s}$ (red) and $\ket{xz;s}$ (blue) orbitals in accordance with the \textit{ab initio} data \cite{Wrasse2014PbSeTCI}. The arrows represent the spin projection along $z$.
  }
  \label{fig:bsX}
\end{figure}

\subsection{Ribbons A, B, and C}

Let us first consider ribbons A, B, and C, which constitute our simplest cases and provide the context to advance to more complex scenarios. First, since ribbons A and B belong to the same $D_{2h}$ space group, they must have the same Hamiltonian $H_A = H_B$.
The confinement along $y$ projects Y and $\Gamma$ into $\bar{\Gamma}$, and M and X into $\bar{\rm X}$ (see Fig.~\ref{fig:StripeLattices}). As the bulk gaps at $\Gamma$ and M are much larger than the gap at X and Y, we can neglect the extra bands coming from these projections. The resulting Brillouin zone of the ribbon is given by the $\bar{\rm X}$ and $\bar{\Gamma}$ TRIMs, whose effective Hamiltonians are obtained replacing $k_y \rightarrow -i \partial/\partial y$ in $H_X$ and $H_Y = C_4 H_X C_4^{-1}$, respectively. Both are in the TCI regime and one can expect topologically protected states at both $\bar{\Gamma}$ and $\bar{\rm X}$.
Second, ribbon C belongs to the $C_{2v}$ space group, which is a subgroup of $D_{2h}$.
However, we find that the extra terms \cite{Note1} in the Hamiltonian for ribbon C play no significant role in the qualitative analysis of the topological properties discussed here. Hence, its effective Hamiltonian $H_C\approx H_A=H_B$. Ultimately, the distinction between ribbons A, B, and C arises from their different terminations, which enter our effective model via boundary conditions.

To establish the appropriate boundary conditions for the envelope functions for each termination, we extend Brey and Fertig's approach \cite{BreyFertig2006Ribbons} from graphene to our PbSe monolayer ribbon of width $2W$. In ribbon A the edges are composed by Pb atoms, say at $y = \pm W$. If the ribbon was uncut, the next line of atoms on top would be of Se at $y = W + a/2$, where $a$ is the lattice parameter (Fig.~\ref{fig:StripeLattices}). Following those, there would be yet a line of Pb atoms at $y = W + a$. However, since those atom lines were cut off to form the ribbon, we set the envelope function of each sublattice to zero at these positions. A similar definition follows for the bottom edge of ribbon A, and a generalization to ribbons B and C is immediate. Note that the boundary condition for the top edge of ribbon C is equivalent to those of ribbon B, while the bottom of C is equivalent to the boundaries of A.

The resulting band structures of ribbons A, B, and C are shown in the bottom panels of Fig.~\ref{fig:BSABCDE} to be compared with the {\it ab initio} data on top. We can see some differences between the effective model and the {\it ab initio} results. First, we observe a band gap at top panels A and B, which is absent from our model (bottom panels). The band gap opening occurs because the ribbon in the DFT calculation is narrow, $2W \approx 10$~nm, and quantum tunnel coupling between topological states from opposite edges takes place. This hybridization gap vanishes asymptotically with the ribbon width. We also observe additional states crossing the Fermi level in the \textit{ab initio} results (upper panels of Fig.~\ref{fig:BSABCDE}, panels A-C), due to dangling bonds at the edges.

\begin{figure*}[ht!]
  \centering
  \includegraphics[width=\textwidth,keepaspectratio=true]{bs-abcde5}
  \caption{Comparison of the \textit{ab initio} (top) and effective model (bottom) band structures of PbSe topological insulator ribbons A, B, C, D and E. The colors represent the spinfull mirror parity $+i$ (red) and $-i$ (blue). The thickness of the lines for the effective model represents the localization of the state into an edge. In A, D, and E we show the states and mirror parities projected on the top edge of the ribbons. In B these projections are taken for the bottom edge. In C the upper (lower) Dirac crossing belongs to the top (bottom) edge states. In A, B, D, and E the states shown here are degenerate with ones from the opposite edge, with opposite mirror parity. The {\it ab initio} data are colored by hand as a guide to the eyes.}
  \label{fig:BSABCDE}
\end{figure*}

\subsection{Ribbons D and E}

The other possible terminations occur in ribbons aligned along the $(x', y')$ coordinates, illustrated in Fig.~\ref{fig:StripeLattices}, panels D and E, having both Pb and Se atoms at the edges.
In these cases we set the envelope functions to zero on the next (absent) line of atoms of both lattices, i.e., at $|y'|=W+a'$, with $a' = a/\sqrt{2}$. Since the boundary conditions for ribbons D and E are the same, their distinction occurs only via the different space groups. Next we show that this translates into distinct XY valley couplings. Interestingly, for ribbon E, the nonsymmorphism of the crystal lattice introduces extra topological protections.

Ribbon D belongs to the $D_{2h}$ space group, the same of ribbons A and B.
The confinement along $y'$ projects M and $\Gamma$ into $\bar{\Gamma}$ and both X and Y into $\bar{\rm X'}$ [see Fig.~\ref{fig:StripeLattices}(a)]. Therefore one can expect topological states only at $\bar{\rm X'}$. Since the monolayer bands around Y are simply the ones at X rotated by $C_4$, to obtain the effective Hamiltonian around $\bar{\rm X'}$ we have to expand our basis to incorporate the bands coming from Y. Therefore we establish a new matrix representation for the symmetry elements of $D_{2h}$ with a basis set as $\{ \ket{xz;\uparrow}, \ket{xz;\downarrow}, \ket{x;\uparrow}, \ket{x;\downarrow}, \ket{yz;\uparrow}, \ket{yz;\downarrow}, \ket{y;\uparrow}, \ket{y;\downarrow} \}$. Following the same procedure discussed previously for $H_X$, we obtain

\begin{equation}
H_{X'} =
\begin{pmatrix}
  \tilde{H}_X & V_{XY}\\
  V_{XY}^\dagger & \tilde{H}_Y
\end{pmatrix},
\label{eq:HDE}
\end{equation}
where $\tilde{H}_X$ and $\tilde{H}_Y$ are equivalent to $H_X$ and $H_Y$ rotated towards the $\bm{r}'$ coordinates, i.e., $\hat{x} \rightarrow (\hat{x}'-\hat{y}')/\sqrt{2}$, $\hat{y} \rightarrow (\hat{x}'+\hat{y}')/\sqrt{2}$, and equivalent rotations for $k_x$, $k_y$, $\sigma_x$ and $\sigma_y$. The relevant term in the XY valley hybridization $V_{XY}$ for ribbon D is

\begin{equation}
V_{XY} \approx i v_D k_y^2\tau_z\sigma_z.
\label{eq:vxyD}
\end{equation}

If $V_{XY}$ were zero, the boundary conditions of ribbon D would give us four degenerate Dirac cones at $E=0$, leading to eight-fold degeneracy (labeled by $\mathcal{M} = \pm i$, X/Y valleys, and top/bottom edges). However, the main contribution to $V_{XY}$ shown in Eq.~\eqref{eq:vxyD}, which is proportional to the mirror symmetry operator $\mathcal{M} = i\tau_z\sigma_z$, couples states from opposite valleys with the same mirror eigenvalue ($\pm i$). This splits the Dirac points into the top and bottom (gapped) cones of Fig.~\ref{fig:BSABCDE}, panel D. The hybridization gap opens due to the coupling between top and bottom edge states, which is allowed by Eq.~\eqref{eq:vxyD}, and consistent with the group character tables shown in the Appendices, which guarantees only two-fold degeneracy for ribbon D. Other terms of $V_{XY}$ are shown in the Appendices. Their contribution is only quantitative to the fine tuning of the band structure.

Our main result is the unexpected nonsymmorphic space group $D_{2h}^{NS}$ of ribbon E, which yields extra topological protections \cite{dresselhaus2007group,Kane2015Nonsymm}.
Here the point group symmetry elements are the same as in $D_{2h}$, however, some of them must be complemented by a nonprimitive translation $\bm{\chi} = a'\hat{x}'$ of half a unit cell along $x'$, i.e., glide planes and screw axis elements \cite{voon2009kp, dresselhaus2007group, car1976optimal, koster2012space, FazzioTeoGrupos}. To obtain the matrix representation for these symmetry elements we use the same basis set from ribbon D above, but with the coordinates shifted (see Fig.~\ref{fig:StripeLattices}).
Requiring that the Hamiltonian commutes with these elements and $\mathcal{T}$, we obtain again $H_{X'}$, but with different XY valley couplings $V_{XY}$, whose relevant terms for ribbon E are

\begin{equation}
V_{XY} \approx v_E k_y^2(i\tau_x \sigma_y - \tau_y \sigma_x).
\end{equation}

Similarly to ribbon D, this XY valley coupling splits the otherwise eight-fold degeneracy into the top and bottom Dirac cones of Fig.~\ref{fig:BSABCDE}, panel E. Here they remain gapless. Other terms of $V_{XY}$ compatible with the symmetries of ribbon E contribute only with the fine tuning of the band structure. These are shown in the Appendices.

We emphasize that the edge state dispersions for ribbons D and E, shown in Fig.~\ref{fig:BSABCDE}, panels D-E, differ only by the hybridization gaps at X, which is the main consequence of the nonsymmorphic lattice of ribbon E.
Here, all edge state branches are doubly degenerate with states located at opposite edges having opposite mirror parities. The color code in the figure refers to the states located on the top edge. Therefore, at each crossing around X$'$ there are four states. The agreement between the effective Hamiltonian and the {\it ab initio} results is patent.
In ribbon D the gap between edge branches is a consequence of top/bottom edge hybridization for narrow ribbons. The gap is closed in the nonsymmorphic ribbon E, which is consistent with its double group character table\cite{Note1}. We have calculated this character table using standard group theory method \cite{dresselhaus2007group} to find that the double group is composed by two-dimensional irreducible representations (IRREPs), which yields two-fold degeneracies. However, while for ribbons A, B, C, and D the time-reversal symmetry does not lead to extra degeneracies, for ribbon E the pair of 2D IRREPs form Kramers partners. This leads to the four-fold degeneracy of the edge states of ribbon E at X$'$, which \textit{must survive even for narrow ribbons or arbitrary width, despite the overlap between top and bottom edge states}. Usual edge state branches, as in ribbon D, can only close the gap asymptotically for wide ribbons, constituting an accidental degeneracy, which is not protected by symmetry.

\section{Final remarks and conclusions}

The double crossing band structure of ribbon C resembles those of D and E, with closed gaps. However, here edge state branches are nondegenerate. The bottom crossing at X corresponds to a pair of opposite mirror parity states coming from the top edge, which are equivalent to half of the edge states of ribbon B. Similarly the top crossing at X involves states from the bottom edge of ribbon C, which are equivalent to half of the states of ribbon A.
Consequently, the crossings of pairs of edge states from opposite sides are already split in energy, thus avoiding a direct hybridization, which keeps the gap closed, in contrast to its counterparts in ribbons A and B.

Interestingly, the gap oscillation with even/odd number of layers recently reported in Ref.~\onlinecite{ozawa2014topological} originates in the alternation between symmorphic and nonsymmorphic lattices in three dimensions, which can be understood as a 3D counterpart of our results.

In conclusion, we showed that, although the Chern number and topological classification of insulators remain a bulk property, the reduced symmetry of the ribbons and the characteristics of its edge terminations play a fundamental role in the topological state properties. Particularly, we focused on the TCIs given by IV-VI monolayers, whose pair of distinct atoms lead to distinct sublattices, similarly to graphene. While different cuts of the bulk in graphene give us the armchair and zigzag ribbons, here we identify five main types of ribbons due to the more complex structure of the lattice. Interestingly, we find that the extra topological protection introduced by nonsymmorphic symmetry yields protected crossings for ribbons of arbitrary width. This is in contrast with the usual topological protections, where the gaps are only asymptotically closed for large enough samples. The extra nonsymmorphic protection of the ribbon could not be predicted by the bulk topological classification, since the bulk is symmorphic. This feature may allow topological properties to be explored in nanoscale nonsymmorphic TIs.

\begin{acknowledgments}
The authors acknowledge the financial support from the Brazilian Agencies CNPq, CAPES, and FAPEMIG, and the computational facilities from CENAPAD.
\end{acknowledgments}

\section{Matrix Representations and Effective Hamiltonians}

In order to obtain the effective Hamiltonian for each PbSe ribbon via the method of invariants\cite{voon2009kp,dresselhaus2007group}, we define a matrix representation for each symmetry element of the space group of the ribbon. Then, imposing that the effective Hamiltonian must commute with these symmetry elements and the time-reversal operator, we find the allowed finite elements of the effective Hamiltonian. Below we present these matrix representations for each ribbon. Except for ribbon E, in all other ribbons the space group matches the point group of the unit cell plus primitive translations. Therefore we label the space groups with usual Schönflies notation of its corresponding point group. Ribbon E is a particularly interesting case, as it belongs to a nonsymmorphic space group\cite{car1976optimal, koster2012space, dresselhaus2007group}, and its symmetry operations are a combination of point group symmetries and translations by half a unit cell, i.e. glide planes and screw axes.

\subsection{Monolayer Sheet and Ribbons A and B}
\label{app:monolayer}

The full PbSe monolayer belongs to the $D_{4h}$ space group. However, the space group for $\bm{k} = X$ point is $D_{2h}$. For ribbons A and B, both the lattice and the $\bm{k} = X$ point belong to the $D_{2h}$ as well. Therefore, the effective Hamiltonians around $\bm{k}=X$ for the full monolayer ($H_X$) and for ribbons A ($H_A$) and B ($H_B$) are essentially the same, i.e. $H_A = H_B = H_X$. The distinction between these cases arises only via the boundary conditions. For the full monolayer sheet there is no boundaries and both $k_x$ and $k_y$ remain good quantum numbers. For ribbons A and B, the confinement along $y$ requires $k_y \rightarrow -i \partial/\partial y$, and the different boundary conditions for A and B are discussed in the main text of this paper.

Let us consider only the effective Hamiltonian around $\bm{k} = X$, which must commute with the symmetry operations of $D_{2h}$: identity $E$; two-fold rotations around the $x$, $y$ and $z$ axes, $C_2(x)$, $C_2(y)$, and $C_2(z)$; inversion $I$, and mirror planes $M(xy)$, $M(xz)$, $M(yz)$. From the \textit{ab-initio} data, we know that the relevant orbitals around the Fermi level are $\{ \ket{xz;\uparrow}, \ket{xz;\downarrow}, \ket{x;\uparrow}, \ket{x;\downarrow} \}$. These orbitals are shown in Fig.~\ref{fig:Lattice-BZ}, from which we obtain by inspection the matrix representation of the symmetry operations as

\begin{align}
 \nonumber
 E =& \tau_0 \otimes \sigma_0,\\
 \nonumber
 C_2(z) =& -\tau_0 \otimes (-i \sigma_z),\\
 \nonumber
 C_2(x) =& -\tau_z \otimes (-i \sigma_x),\\
 \nonumber
 C_2(y) =& \tau_z \otimes (-i \sigma_y),\\
 I =& \tau_z \otimes \sigma_0,\\
 \nonumber \label{eq:mirrorAB}
 M(xy) =& -\tau_z \otimes (-i \sigma_z),\\
 \nonumber
 M(xz) =& \tau_0 \otimes (i \sigma_y),\\
 \nonumber
 M(yz) =& -\tau_0 \otimes (-i \sigma_x),
\end{align}
where $\sigma_0$ and $\tau_0$ are $2\times2$ identity matrices, $\sigma_{x,y,z}$ are the Pauli matrices acting on spin space, $\tau_{x,y,z}$ are the Pauli matrices acting on the orbitals, and $\otimes$ is the Kronecker product. Additionally, the time-reversal operator is $\mathcal{T} = \tau_0\otimes(i\sigma_y)\mathcal{K}$, where $\mathcal{K}$ is the complex conjugation.

To find the effective Hamiltonian, we start with the most general expression up to second order in $k_x$ and $k_y$,

\begin{equation}
 H_{X} = \sum_{i=0}^2 \sum_{j=0}^2 Q_{i,j} k_x^i k_y^j,
 \label{eq:HQ}
\end{equation}
where each $Q_{i,j}$ is a general Hermitian $4\times 4$ matrix, and $\bm{k}$ is deviation from the $X$ point of the BZ. Requiring that $H_{X}$ commutes with all the symmetry elements of $D_{2h}$ and $\mathcal{T}$, we obtain the effective Hamiltonian for the full monolayer and ribbons A and B, Eq.~\eqref{eq:Hmonolayer}.

Note that in order to evaluate the commutation of $H_X$ with the symmetry elements, one must consider also the action of the symmetry operation in $k_x$ and $k_y$. For instance, taking the term $i=0$, $j=1$ of the sum above, and the symmetry operation $M(xz)$, we have

\begin{align}
\nonumber
 [Q_{0,1}k_y, M(xz)] =& Q_{0,1}k_y M(xz)- M(xz)Q_{0,1}k_y\\
 \nonumber
 =& -Q_{0,1}M(xz)k_y - M(xz)Q_{0,1}k_y \\
 =& -\{Q_{0,1}, M(xz)\}k_y,
\end{align}
where $[p,q]$ and $\{p,q\}$ are the commutator and anti-commutator of $p$ and $q$. On the second line above we have used $\{k_y, M(xz)\} = 0$, since $M(xz)$ makes $y \rightarrow -y$. Similar considerations must be taken carefully for all other terms of the sum and symmetry operations.

\subsection{Ribbon C}
\label{app:ribbonC}

To obtain the effective Hamiltonian for ribbon C we follow the same procedure presented above for ribbons A and B. However, both the lattice and the $\bm{k} = X$ point of ribbon C belong to the $C_{2v}$ space group, which is composed the by the symmetry elements $E$, $C_2(y)$, $M(xy)$, and $M(yz)$, \textit{i.e.}, a subgroup of $D_{2h}$. Consequently, we can use the same matrix representations as above. Due to the reduced symmetry of $C_{2v}$, the effective Hamiltonian for C is given by $H_X$ above, plus extra allowed terms,

\begin{equation}
\begin{split}
 H_C =& H_X + (\gamma_0 + \gamma_1 \tau_z) k_x \sigma_z + \Delta_1 \tau_y \sigma_x\\
      &+ m_{1x} k_x^2 \tau_y\sigma_x + m_{1y} k_y^2 \tau_y\sigma_x\\
      &+ \beta k_x k_y \tau_y\sigma_y.
\end{split}
\end{equation}

These extra terms contribute to the fine tunning of band structure. However, they are not relevant for the qualitatively analysis of the topological edge states presented in the main text, therefore we choose to set $H_C \approx H_X = H_A = H_B$. In Fig.~\ref{fig:BSABCDE}(A-C) we show the band structure of ribbons A, B and C, all taken from the same $H_X$. The results differ only by the boundary conditions applied in each case, showing already a good qualitatively agreement with the \textit{ab-initio} data.

\subsection{Ribbon D}

In Fig.~\ref{fig:StripeLattices}(D) we have again the point group $D_{2h}$. However, here the lattice is aligned along the $\bm{r}' = (x',y')$ coordinates. In this case, the confinement along $y'$ projects both $X$ and $Y$ TRIMs into $X'$, doubling the number of relevant bands near the Fermi level. Since $Y$ is equivalent to $X$ rotated by $C_4(z)$, the new set of relevant states are $\{ \ket{xz;\uparrow}, \ket{xz;\downarrow}, \ket{x;\uparrow}, \ket{x;\downarrow}, \ket{yz;\uparrow}, \ket{yz;\downarrow}, \ket{y;\uparrow}, \ket{y;\downarrow} \}$. The last four states there are simply those of Fig.~\ref{fig:Lattice-BZ} rotated by $C_4(z)$. From these states, the symmetry operations take the form of  $8\times 8$ matrices,

\begin{align}
 \nonumber
 E &= \Lambda_{00} \otimes \sigma_0,\\
 \nonumber
 C_2(z') &= -\Lambda_{00} \otimes (-i \sigma_z),\\
 \nonumber
 C_2(x') &= \Lambda_{zx} \otimes (-i \sigma_x),\\
 \nonumber
 C_2(y') &= -\Lambda_{zx} \otimes (-i \sigma_y),\\
 I &= \Lambda_{z0} \otimes \sigma_0,\\
 \nonumber
 M(x'y') &= -\Lambda_{z0} \otimes (-i \sigma_z),\\
 \nonumber
 M(x'z') &= -\Lambda_{0x} \otimes (i \sigma_y),\\
 \nonumber
 M(y'z') &= \Lambda_{0x} \otimes (-i \sigma_x).
\end{align}
The $4\times 4$  $\Lambda$-matrices act on the orbitals from both $X$ and $Y$ valleys, while the \mbox{$\sigma$-matrices} act on spin. The $\Lambda$-matrices are

\begin{align}
\nonumber
 \Lambda_{00} =&
 \begin{pmatrix}
   \tau_0 & 0\\
   0 & \tau_0
 \end{pmatrix},
&
 \Lambda_{zx} =&
 \begin{pmatrix}
   0 & \tau_z\\
   \tau_z & 0
 \end{pmatrix},
\\
 \Lambda_{0x} =&
 \begin{pmatrix}
   0 & \tau_0\\
   \tau_0 & 0
 \end{pmatrix},
&
 \Lambda_{z0} =&
 \begin{pmatrix}
   \tau_z & 0\\
   0 & \tau_z
 \end{pmatrix},
\end{align}
More generally, $\Lambda_{\mu\nu} = \lambda_\nu \otimes \tau_\mu$,
where $\lambda_0$ is the $2\times 2$ identity matrix, and $\lambda_{(x,y,z)}$ are Pauli matrices acting on the $\{X, Y\}$ valley subspace.
Now the time-reversal operator is \mbox{$\mathcal{T} = \Lambda_{00} \otimes (i\sigma_y)\mathcal{K}$}.

To find the effective Hamiltonian $H_{D}$ we consider again an expansion of the form of Eq.~\eqref{eq:HQ}, but now the $Q_{i,j}$ are general Hermitian $8\times 8$ matrices. Requiring that $H_{D}$ commutes with the symmetry elements above, we obtain the $H_{D}$ shown in Eq.~\eqref{eq:HDE}, with

\begin{equation}
\label{eq:fullVXYD}
\begin{split}
 V_{XY} =& (V_{r}+\delta V_{r}\tau_z) + i(V_{i}+\delta V_{i}\tau_z)\sigma_z\\
         +& (w_{rx}+\delta w_{rx}\tau_z)k_{x'}^2 + i(w_{ix}+\delta w_{ix}\tau_z)k_{x'}^2\sigma_z\\
         +& (w_{ry}+\delta w_{ry}\tau_z)k_{y'}^2 + i(w_{iy}+\delta w_{iy}\tau_z)k_{y'}^2\sigma_z\\
         +& (i \beta_{ix} \tau_y \sigma_x - \beta_{rx} \tau_x\sigma_y)k_{x'}\\
         +& (-i \beta_{iy} \tau_y \sigma_y - \beta_{ry} \tau_x\sigma_x)k_{y'}.
\end{split}
\end{equation}
Most of these terms of the $XY$ intervalley coupling contribute only to the fine tuning of the band structure. In the main text we show only the term that is relevant for the qualitatively analysis of the topological edge states.

\subsection{Ribbon E}

Ribbon E in Fig.~\ref{fig:StripeLattices}(E) belongs to a nonsymmorphic symmetry group, which we label as $D_{2h}^{NS}$. Some of the symmetry elements require a translation $\chi$ by half a unit cell along $x'$, i.e. glide planes and screw axes. Using the standard notation\cite{car1976optimal,dresselhaus2007group}, the symmetry elements are $\{E,0\}$, $\{C_2(z'),0\}$, $\{C_2(x'),\chi\}$, $\{C_2(y'),\chi\}$, $\{I,0\}$, $\{M(x'y'),0\}$, $\{M(x'z'),\chi\}$, $\{M(y'z'),\chi\}$. Using the same set of states as for Ribbon D, by inspection we find the matrix representation for these operations as

\begin{align}
 \nonumber
 \{E,0\} =& \Lambda_{0,0}\otimes \sigma_0,\\
 \nonumber
 \{C_2(z'),0\} =& \Lambda_{0,z}\otimes (-i \sigma_z),\\
 \nonumber
 \{C_2(x'),\chi\} =& -i\Lambda_{z,y}\otimes (-i \sigma_x),\\
 \nonumber
 \{C_2(y'),\chi\} =& \Lambda_{z,x}\otimes (-i \sigma_y),\\
 \label{eq:NSelements}
 \{I,0\} =& -\Lambda_{z,z}\otimes \sigma_0,\\
 \nonumber
 \{M(x'y'),0\} =& -\Lambda_{z,0}\otimes (-i \sigma_z),\\
 \nonumber
 \{M(x'z'),\chi\} =& i\Lambda_{0,y}\otimes (i \sigma_y),\\
 \nonumber
 \{M(y'z'),\chi\} =& -\Lambda_{0,x}\otimes (-i \sigma_x),
\end{align}

Once again, to find $H_E$ we require it to commute with all symmetry elements above and the time-reversal operator $\mathcal{T} = \Lambda_{00} \otimes (i\sigma_y)\mathcal{K}$. The resulting effective Hamiltonian is written again as in Eq.~\eqref{eq:HDE}, but with a different $XY$ inter-valley coupling

\begin{equation}
\label{eq:fullVXYE}
\begin{split}
  V_{XY} =& -d_0 \tau_y \sigma_x + i d_1 \tau_x\sigma_y\\
         +& (a_1 + \delta a_1\tau_z \sigma_z)k_{x'} + i(a_2 + \delta a_2 \tau_z)k_{x'}\\
         +& (-w_{0x}\tau_y\sigma_x + i w_{1x} \tau_x\sigma_y)k_{x'}^2\\
         +& (-w_{0y}\tau_y\sigma_x + i w_{1y} \tau_x\sigma_y)k_{y'}^2\\
         +& (-w_{xy0}\tau_y\sigma_y + i w_{xy1}\tau_x\sigma_x)k_{x'}k_{y'}
\end{split}
\end{equation}
Once again, in the main text we show only the term relevant for the qualitatively analysis of the topological edge states.

\section{Character Tables, Irreducible Representations, and Degeneracies}
\label{app:tables}

\subsection{Ribbons A, B, C, and D}

The character tables of the space groups of ribbons A, B, C, and D are simply those of their equivalent point groups. Those can be found in Koster's book\cite{koster2012space}, and we reproduce them here for convenience. The $D_{2h}$ group of the monolayer sheet and ribbons A, B, and D is shown in Table \ref{tab:D2h}, and the $C_{2v}$ group of ribbon C is shown in Table \ref{tab:C2v}.

\begin{table}
 \caption{Character Table for the $D_{2h}$ double group. The first line labels the symmetry operations in short notation. For the full monolayer and ribbons A and B we have
 $C_2 = C_2(z)$, $C'_2 = C_2(x)$, $C''_2 = C_2(y)$, $M = M(xy)$, $M' = M(xz)$, and $M''=M(yz)$. For ribbon D simply replace the coordinates $(x,y,z)$ by $(x', y', z')$. Barred and unbarred operations refer to $4\pi$ and $2\pi$ rotations on spin space. The first set, from $\Gamma_0$ to $\Gamma_7$, are single group irreducible representations, and $\Gamma_8$ and $\Gamma_9$ are the double group irreducible representations.}
 \label{tab:D2h}
\begin{center}
\begin{tabular}{l | c c c c c c c c c c}
\hline\hline
 & $E$ & $\bar{E}$ & $\begin{array}{c}C_2 \\ \bar{C}_2\end{array}$ & $\begin{array}{c}C'_2 \\ \bar{C}'_2\end{array}$ & $\begin{array}{c}C''_2 \\ \bar{C}''_2\end{array}$ & $I$ & $\bar{I}$ & $\begin{array}{c}M \\ \bar{M}\end{array}$ & $\begin{array}{c}M' \\ \bar{M}'\end{array}$ & $\begin{array}{c}M'' \\ \bar{M}''\end{array}$\\
\hline
$\Gamma_0$ & 1 & 1 &  1 &  1 &  1 &  1 &  1 &  1 &  1 &  1 \\
$\Gamma_1$ & 1 & 1 & -1 &  1 & -1 &  1 &  1 & -1 &  1 & -1 \\
$\Gamma_2$ & 1 & 1 &  1 & -1 & -1 &  1 &  1 &  1 & -1 & -1 \\
$\Gamma_3$ & 1 & 1 & -1 & -1 &  1 &  1 &  1 & -1 & -1 &  1 \\
$\Gamma_4$ & 1 & 1 &  1 &  1 &  1 & -1 & -1 & -1 & -1 & -1 \\
$\Gamma_5$ & 1 & 1 & -1 &  1 & -1 & -1 & -1 &  1 & -1 &  1 \\
$\Gamma_6$ & 1 & 1 &  1 & -1 & -1 & -1 & -1 & -1 &  1 &  1 \\
$\Gamma_7$ & 1 & 1 & -1 & -1 &  1 & -1 & -1 &  1 &  1 & -1 \\
\hline
$\Gamma_8$ & 2 & -2 &  0 & 0 &  0 &  2 & -2 &  0 &  0 &  0 \\
$\Gamma_9$ & 2 & -2 &  0 & 0 &  0 & -2 &  2 &  0 &  0 &  0 \\
\hline\hline
 \end{tabular}
\end{center}
\end{table}

\begin{table}
 \caption{Character Table for the $C_{2v}$ double group. The first line labels the symmetry operations in short notation. For ribbon C we have
 $C_2 = C_2(y)$, $M = M(xy)$, and $M'=M(yz)$. Barred and unbarred operations refer to $4\pi$ and $2\pi$ rotations on spin space. The first set, from $\Gamma'_0$ to $\Gamma'_3$, are single group irreducible representations, and $\Gamma'_4$ is the double group irreducible representation.}
 \label{tab:C2v}
\begin{center}
\begin{tabular}{l | c c c c c}
\hline\hline
 & $E$ & $\bar{E}$ & $\begin{array}{c}C_2 \\ \bar{C}_2\end{array}$ & $\begin{array}{c}M \\ \bar{M}\end{array}$ & $\begin{array}{c}M' \\ \bar{M}'\end{array}$\\
\hline
$\Gamma'_0$ & 1 & 1 &  1 &  1 &  1 \\
$\Gamma'_1$ & 1 & 1 & -1 &  1 & -1 \\
$\Gamma'_2$ & 1 & 1 &  1 & -1 & -1 \\
$\Gamma'_3$ & 1 & 1 & -1 & -1 &  1 \\
\hline
$\Gamma'_4$ & 2 & -2 &  0 & 0 &  0 \\
\hline\hline
 \end{tabular}
\end{center}
\end{table}

\begin{table*}
 \caption{Character Table for the $D_{2h}^{NS}$ nonsymmorphic double group. The first line labels the symmetry operations in short notation, where $\mathcal{O}_0 = \{\mathcal{O},0\}$ and $\mathcal{O}_\chi = \{\mathcal{O},\chi\}$ in the nonsymmorphic element representation, $\chi$ is the translation by half a unit cell, and the point group operations follow the ones of Ribbon D in Table \ref{tab:D2h}. The first set, from $\Gamma''_0$ to $\Gamma''_9$, are single group irreducible representations (IRREPs), and from $\Gamma''_{10}$ to $\Gamma''_{12}$ are the double group IRREPs. The highlighted IRREPs are the ones allowed for the $\bm{k} = X$ TRIM due to Bloch periodicity, i.e. $E_\chi = -E_0$.}
 \label{tab:D2hNS}
\begin{center}
\begin{tabular}{l !{\vrule width -4pt} | !{\vrule width -4pt} c !{\vrule width -4pt} c !{\vrule width -4pt} c!{\vrule width -4pt} c!{\vrule width -4pt} c!{\vrule width -4pt} c !{\vrule width -4pt} c !{\vrule width -4pt} c !{\vrule width -4pt} c !{\vrule width -4pt} c !{\vrule width -4pt} c !{\vrule width -4pt} c !{\vrule width -4pt} c !{\vrule width -4pt} c}
\hline\hline
 & $E_0$ & $\bar{E}_0$ & $\begin{array}{c}M''_\chi\\\bar{M}''_\chi\\M''_{3\chi}\\\bar{M}''_{3\chi}\end{array}$ & $E_{2\chi}$ & $\bar{E}_{2\chi}$ & $\begin{array}{c}M'\chi\\\bar{M}'_\chi\\M'_{3\chi}\\\bar{M}'_{3\chi}\end{array}$ & $\begin{array}{c}C_{2,0}\\C_{2,2\chi}\end{array}$ & $\begin{array}{c}\bar{C}_{2,0}\\\bar{C}_{2,2\chi}\end{array}$ & $\begin{array}{c}M_0\\\bar{M}_0\end{array}$ & $\begin{array}{c}C''_\chi\\\bar{C}''_\chi\\C''_{3\chi}\\\bar{C}''_{3\chi}\end{array}$ & $\begin{array}{c}M_{2\chi}\\\bar{M}_{2\chi}\end{array}$ & $\begin{array}{c}C'_\chi\\\bar{C}'_\chi\\C'_{3\chi}\\\bar{C}'_{3\chi}\end{array}$ & $\begin{array}{c}I_0\\I_{2\chi}\end{array}$ & $\begin{array}{c}\bar{I}_0\\\bar{I}_{2\chi}\end{array}$\\
\hline
$\Gamma''_0$ & 1 & 1 &  1 &  1 &  1 &  1 &  1 &  1 &  1 &  1 & 1 &  1 &  1 &  1\\
$\Gamma''_1$ & 1 & 1 &  1 &  1 &  1 & -1 & -1 & -1 &  1 &  1 & 1 & -1 & -1 & -1\\
$\Gamma''_2$ & 1 & 1 & -1 &  1 &  1 &  1 & -1 & -1 &  1 & -1 & 1 &  1 & -1 & -1\\
$\Gamma''_3$ & 1 & 1 & -1 &  1 &  1 & -1 &  1 &  1 &  1 & -1 & 1 & -1 &  1 &  1\\
\rowcolor{gray!25}
$\Gamma''_4$ & 2 & 2 & 0 & -2 & -2 & 0 & 0 & 0 & 2 & 0 & -2 & 0 & 0 & 0\\
$\Gamma''_5$ & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1\\
$\Gamma''_6$ & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1\\
$\Gamma''_7$ & 1 & 1 & -1 & 1 & 1 & 1 & -1 & -1 & -1 & 1 & -1 & -1 & 1 & 1\\
$\Gamma''_8$ & 1 & 1 & -1 & 1 & 1 & -1 & 1 & 1 & -1 & 1 & -1 & 1 & -1 & -1\\
\rowcolor{gray!25}
$\Gamma''_9$ & 2 & 2 & 0 & -2 & -2 & 0 & 0 & 0 & -2 & 0 & 2 & 0 & 0 & 0\\
\hline\hline
$\Gamma''_{10}$ & 2 & -2 & 0 & 2 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & -2\\
$\Gamma''_{11}$ & 2 & -2 & 0 & 2 & -2 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -2 & 2\\
\rowcolor{gray!25}
              & 2 & -2 & 0 & -2 & 2 & 0 & -2 & 2 & 0 & 0 & 0 & 0 & 0 & 0\\
\rowcolor{gray!25}
\multirow{-2}{*}{$\Gamma''_{12}\Big\{$}
              & 2 & -2 & 0 & -2 & 2 & 0 & 2 & -2 & 0 & 0 & 0 & 0 & 0 & 0\\
\hline\hline
\end{tabular}
\end{center}
\end{table*}

Since we are dealing with a spinfull system, the eigenstates must belong to the double group irreducible representations (IRREPs). For the monolayer sheet, and ribbons A and B the relevant IRREPs are $\Gamma_8$ + $\Gamma_9$ in Table \ref{tab:D2h}, both two-dimensional. Consequently, the band structure of ribbons A and B can only have twofold degeneracies at $\bm{k}=X$. This is clearly seen in Fig.~\ref{fig:BSABCDE}(A-B) on the minigap between edge states. Each line is doubly degenerate, and the minigap can only close asymptotically for wide ribbons to form fourfold degeneracies. In other words, the gapless crossing point of the edge states is not protected for narrow ribbons.

For ribbon C, all spinfull states belong to the $\Gamma'_4$ IRREP of Table \ref{tab:C2v}, which is again two-dimensional, and ribbon C can only have doubly degenerate states at $\bm{k}=X$. However, here the edge states from opposite sites see different atomic terminations, and their linear dispersions occur at different energies, see Fig.~\ref{fig:BSABCDE}(C). Consequently, the states from opposite edges that would hybridize for narrow ribbons are already energy splitted due to the boundary conditions. This implies that the gapless edge state dispersions seen in Fig.~\ref{fig:BSABCDE}(C) are robust even for narrow ribbons, as long as they remain energy splitted.

Ribbon D also has two-dimensional IRREPs only, $\Gamma_8$ and $\Gamma_9$ of Table \ref{tab:D2h}, and once again, it can only have twofold degeneracies at $\bm{k}=X$. In Fig.~\ref{fig:BSABCDE}(D) each edge state is doubly degenerate, therefore, at the crossing at $\bm{k}=X$ a hybridization gap opens to maintain a two-fold degeneracy. This gap closes asymptotically with the ribbon width to form four-fold degeneracies.

\subsection{Nonsymmorphic Ribbon E}

The nonsymmorphic $D_{2h}^{NS}$ group of ribbon E is shown in Table \ref{tab:D2hNS}. To obtain this character table we have to deal with the nonsymmorphic multiplications defined as \cite{car1976optimal,koster2012space,dresselhaus2007group}

\begin{align}
 \{\alpha | \bm{\chi}_1 \}\{\beta | \bm{\chi}_2 \} =& \{\alpha\beta | \alpha\bm{\chi}_2+\bm{\chi}_1 \},\\
 \{\alpha | \bm{\chi}_1 \}^{-1} =& \{\alpha^{-1} | - \alpha^{-1}\bm{\chi}_1 \},
\end{align}
where $\alpha$ and $\beta$ are regular point group symmetry operations (e.g., inversion, mirrors, rotations), and $\bm{\chi}$ are lattice translations. A crystal is said nonsymmorphic if it is not possible to find an origin for the coordinates such that all symmetry operations can be written using only the regular point group operations and primitive translations. Instead, nonsymmorphic crystals require symmetry operations that contain translations $\bm{\chi}$ by less than a unit cell. This is the case of ribbon E, see Eqs.~\eqref{eq:NSelements}.

Reference \cite{car1976optimal,dresselhaus2007group} shows that for a nonsymmorphic crystal, one typically needs a factor group that is usually twice the size of the wave-vector group in order to close the multiplication table (not shown here). Indeed in our case we find that one needs the symmetry elements of Eqs.~\eqref{eq:NSelements}, plus equivalent ones with an extra translation by $\{0, 2\chi\}$, where $2\chi$ is one unit cell along $\hat{x}$. With the multiplication table at hand, we identify the symmetry classes and construct the Character Table \ref{tab:D2hNS} following the usual procedure\cite{voon2009kp, dresselhaus2007group, car1976optimal, koster2012space, FazzioTeoGrupos}. However, not all IRREPs are compatible with the eigenstates of a given point $\bm{k}$. The matrix representation of a nonsymmorphic symmetry element $\{\alpha | \bm{\chi} \}$ is $D(\{\alpha | \bm{\chi} \}) = e^{i\bm{k}\cdot\bm{\chi}}D(\alpha)$, where $D(\alpha)$ is the matrix representation of the point group element $\alpha$. Take now the elements $\{E | 0\}$ and $\{E | 2\chi\}$,

\begin{align}
 D(\{E|0\}) &= D(E),\\
 D(\{E|2\chi\}) &= e^{i k_x 2\chi} D(E) = -D(E),
\end{align}
where $e^{i k_x 2\chi} = -1$ for $\bm{k} = X$ refers to the Bloch periodicity at the X TRIM. Consequently, only the IRREPs that satisfy this condition are compatible with the eigenstates at X. These IRREPs are highlighted in grey in Table \ref{tab:D2hNS}.

For the spinful system, only the $\Gamma''_{12}$ double group IRREPs are compatible with the Bloch periodicity. From the Frobenius-Schur test, the Herring rules \cite{dresselhaus2007group} state that this pair of IRREPs stick together to form a four-dimensional IRREP $\Gamma''_{12}$ (given by the sum of both lines) in order to satisfy time-reversal symmetry. Therefore the states of ribbon E are expected to show four-fold degeneracy at $\bm{k} = X$, as seen in Fig.~\ref{fig:BSABCDE}(E). This degeneracy requirement determinies that the Dirac cone in ribbon E must remain gapless even for narrow ribbons.

redpajama_set_name: RedPajamaArXiv


text:
Toma del interior de la Abadía de San José, Güigüe, edo. Carabobo, cropped | By María Auxiliadora Ramírez Prato - Own work, CC BY-SA 3.0 |link|
Brother Oscar Echeverría Criollo OSB
Sant'Anselmo2020-12-23T18:09:19+01:0023 Dicembre 2020|
Brother Oscar Echeverría Criollo, OSB
30-VI-1930 17-XII-2020
A few minutes before two o'clock in the afternoon on Thursday, 17 December 2020, Bro. Oscar Echeverría Criollo died suddenly and unexpectedly at the age of 90. Very early that morning, accompanied by two of our brothers, he went to the Senamet Clinic in the city of Valencia to have a cystoscopy recommended by his doctors. On his way back to the monastery, he began to feel a little ill, so when he arrived, just before noon, he was immediately taken to his room in a wheelchair. He seemed to recover a little and even, lucid as he was at that moment, he made the beautiful gesture of congratulating Fr. Prior Marco Antonio on the anniversary of his priestly ordination. But soon after he lost consciousness and seemed to faint, so we transferred him to the Santa Paula Clinic in Güigüe around 1:30 p.m. Although he apparently arrived with some faint signs of life, the doctors who attended to him shortly afterwards could do nothing but confirm and certify his death due to respiratory failure. May rest in peace!
Brother Oscar was born in Maracaibo, Zulia State, Venezuela on 30 June 1930 into a large family of ten brothers and sisters with deep Christian roots. His parents were Jesús Echeverría and María Luisa Criollo. Oscar was baptized on 30August 1930. He attended primary and secondary school and then went on to study accounting, working with his father for a time in the field of commerce, as well as in sales and administration. When he was in his thirties, he entered the seminary of Caracas and studied philosophy and theology. He was ordained a priest on 29 June 1966 in the cathedral of Caracas by the then archbishop of Caracas, Cardinal Quintero. He exercised his priestly ministry in the seminary and in the Caracas parishes assigned to him. Many years later, after a process of clarification and discernment, he decided to ask the Holy See to reduce him to the lay state and to dispense him from the obligations and duties inherent in the priesthood. This was granted by Pope Paul VI on the 26 April 1974. Having left the priestly ministry, Brother Oscar continued to lead a life in accordance with his Christian principles and convictions. He studied at the Universidad Metropolitana de Caracas, graduating with a degree in modern languages, specifically English. From then on he served as an English language teacher at the American-Venezuelan Institute in Caracas.
Brother Oscar's first contacts with our Benedictine community date back to 1990. For some time he had given thought to monastic life and wondered if God was not calling him to become a monk. Previously he had an initial experience with the Trappist monks in Chile. In July and August 1990 he repeated this experience, this time with us here in our monastery in Güigüe. A few years passed and finally, on 22 May 1993, Brother Oscar joined our community. On 27 November of that same year he began his canonical novitiate, at the end of which, on 3 June 1995, he himself chose to make his oblation as a regular oblate of our monastery. From that date until his death, Brother Oscar was part of our Benedictine community in Güigüe, always giving a beautiful testimony of fidelity, joy and availability. His service within the monastery was mainly in the area of hospitality and the reception area, caring for and attending to guests and visitors, answering the telephone, etc. He always had a smile on his face, radiating kindness and closeness, but also discretion and respect. Many people who dealt with him commented that Brother Oscar transmitted peace, serenity and joy to them. A man of innate goodness and a great heart, he was one of those people who seemed to have no malice and who was always animated by noble and clear feelings. "I shared the closeness of a kind and good man," said someone who knew him when he received the news of his death. To this kindness and affability of Brother Oscar, we should add his availability: he was very helpful and always ready to do a favor to anyone who asked him. And to do so willingly. He integrated very well into his Benedictine family and participated with joy and fidelity in the regular life, in the liturgy and the daily celebration of the Eucharist, in community meetings, in recreation and leisure activities, etc. Yes, besides being a wonderful person, Brother Oscar was a good monk.
The funeral Mass for Br. Oscar was celebrated at 10 a.m. on Saturday, 19 December 2020 in the abbey church of San José Abbey and was presided over by Fr. Prior Marco Antonio. Afterwards, the mortal remains of Br. Oscar were buried in the monastery cemetery.
Güigüe, 19 December 2020
P. Prior Marco Antonio González and the community of San José Abbey
Obituary pdf |ES|
San José Abbey Wikipedia page |EN|

redpajama_set_name: RedPajamaCommonCrawl


text:
The group stage of the 2022 World Cup is coming to an end, and viewers from around the world are eagerly anticipating the start of the knockout rounds. The group stage has been an exciting one, with some surprising results along the way and plenty of goals scored. As teams battle for a chance to make it through to the next round, all eyes will be on these final matches as they decide who progresses and who is eliminated.
Ecuador vs Senegal
The stage is set for a high stakes match between Ecuador and Senegal in their last Group match of the FIFA World Cup. With both sides needing a result to advance to the next stage, every play of this game could make or break each team's dreams of progressing further.
Ecuador need only to draw this match in order to qualify for the next round, while Senegal must win in order to guarantee their place in the top 16 teams in the tournament. This situation has created an intriguing setup, with both teams likely pushing hard for a result – but Ecuador will have one eye on holding onto their point and securing passage through while Senegal must attack with all effort if they want to progress.
The pressure is sure to be high as both nations look to secure what would be a major achievement at this year's FIFA World Cup.
Prediction: Senegal Win
Netherlands vs Qatar
The Netherlands will face Qatar in their final match of Group A at the FIFA World Cup 2022 on Monday. With the Dutch yet to secure their place in the round of 16, this match is a chance for the them to scrore goals, secure top spot and remain unbeaten in the group stage.
For Qatar, they would want to give their fans something to cheer about so they would be hoping for a good performance. This game also serves as an opportunity for players who haven't featured in the tournament to showcase their talent.
Prediction: Netherlands Win
Iran vs USA
Both teams go into this match with impressive performances so far, and there's anticipation amongst fans and experts alike that we are going to witness something special from both sides. Iran have proven themselves to be resilient, and showing no signs of weakening.
Similarly, USA boast some big stars who have brought invaluable experience to their side throughout these tournament.The stakes have never been higher for either country, with the winner of this match ensuring their place in the round of 16.
Prediction: USA Win
Wales vs England
Wales and England will battle it out in what is sure to be a thrilling match that could decide the fate of both teams. With England needing a victory or draw to secure qualification for the next round, all eyes will be on them as they try to seal their place in the competition. However, Wales are determined to spoil their hopes and put an end to England's dreams of glory with a big upset.
On paper, England have greater quality throughout their team and should have no trouble coming away with three points but don't write off Wales just yet as they look set to make things difficult for Gareth Southgate's side. Known for their passionate attacking play, Wales can certainly cause problems if given too much room by the English defence.
Prediction: Wales Win


text:
layout: post
title:  "ELAP - User Testing"
duration: 0
start: 2014-01-01
end: 2014-04-25
hours: 15h/week
client: Human-centered Computing Lab, FU Berlin
workplace: office

imgstart: img/portfolio/elap-usertest/elap-usertest-start.png
imgs:
- url: img/portfolio/elap-usertest/elap-usertest-landing.png
  alt: Mockup
  caption: Mockup for new ELAP landing page.
- url: img/portfolio/elap-usertest/elap-usertest-filter.png
  alt: User Testing
  caption: User testing with paper prototypes, testing the search and filter interface.

modalID: modalElapUsertest
category: heuristic evaluation and user testing

tags:
- heuristics
- usability inspection
- low fidelity prototyping
- Balsamic Mockups

orga:
- confluence
- jira
- slack

links:
- text: Website
  link: http://elap.imp.fu-berlin.de/

---
With the help of the Entrepreneurship Learning and Exchange Platform (ELAP) teachers can design courses, manage teaching materials from the field of entrepreneurship and exchange them with colleagues.

We conducted a heuristic evaluation, using the results of that I prepared low fidelity prototype for the ELAP landing page and for the search and filter interface. Both paper prototypes were evaluated in a user study with four participants.

redpajama_set_name: RedPajamaGithub


text:
[ARCHIVED] DUI Traffic Collision
On September 8, 2019, at 5:12 p.m., Deputies from the Riverside County Sheriff's Department, Palm Desert Station,
Press Release: DUI Traffic Collision
Agency: Riverside County Sheriff's Department
Station Area: Palm Desert
Written Date: 09/09/19
Incident Date: 09/08/19
Incident Location: 45900 block of Highway 74, Palm Desert
Reporting Officer: Sergeant Marcus Abbe
File Number(s): T192510074
On September 8, 2019, at 5:12 p.m., Deputies from the Riverside County Sheriff's Department, Palm Desert Station, investigated a single vehicle traffic collision within the 45900 block of Highway 74, Palm Desert. The investigation determined a white Ford sedan, driven by a Collen Cosner, age 48 of Palm Desert, veered off the roadway and struck a parked vehicle at the location. Collen Cosner was found to have been operating a motor vehicle under the influence alcohol. After being medically cleared at a local hospital, Collen Cosner was booked into the Riverside County Jail in Indio for driving under the influence.
The investigation is still ongoing and anyone with information about this incident is urged to contact, Deputy Christopher Williams from the Riverside County Sheriff's Department, Palm Desert Station at 760-836-1600, or Crime Stoppers at 760-341-STOP (7867). The Riverside County Sheriff's Department urges all drivers not to drink and drive.
The Riverside County Sheriff's Department is seeking applicants for Deputy Sheriff, Deputy Sheriff Trainee, Correctional Deputy, Sheriff's 911 Communications Officer, and other employment opportunities such as clerical and support positions. If you are interested in a career with us, please apply at www.joinrsd.org or call 1-888-Join-RSD
Other News in Palm Desert Station
Driving Under the Influence (DUI) Checkpoint
Assault on a peace Officer with a Firearm, Vehicle Pursuit, Domestic Violence, False Imprisonment
Driving Under the Influence Fatal Traffic Collision
Attempted Murder Suspect Apprehended
Driving Under the Influence Checkpoint
Armed Robbery Suspects Apprehended
Armed Robbery Suspect Apprehended
Know Your Limit Campaign
Fatal Traffic Collision
Winter Enforcement Mobilization


text:
CBS Looking to Reinvent 'Sherlock Holmes' and Other Mysteries
CBS is tapping into the world of literature for two new mystery projects, including a reinvention of the classic "Sherlock Holmes" mysteries, Deadline.com reports.
The network also has a project in the works based on the "Mommy-Track Mysteries" by Ayelet Waldman, the story reports.
The "Sherlock Holmes" project is described as a modern version of Arthur Conan Doyle's detective, with Rob Doherty writing and executive producing with Sarah Timberman and Carl Beverly.
Waldman is adapting her comedic book series about Juliet Applebaum, a public defender who becomes a stay-at-home-mom and private investigator, the story notes. The series includes six novels, including "The Big Nap" and "A Playdate With Death," the piece adds.
John Lee Hancock, the Talented Director and Screenwriter of the Huge Hit 'The Blind Side' (The No. 1-Grossing Sports Drama of All Time) Is Developing a Crime Drama With ABC. 'Transformers' Producer Also on the Project
Showtime Drama Pilot to Debut Online
rhianjane
BBC/PBS already HAS done an updated version of Sherlock Holmes–set in modern-day England. It's been very successful and well-received. Three eps have aired in America with at least three more to come.
The Applebaum books are great for a TV series. Holmes is miniseries material. BBC/PBS have done it right. That is a great series. Doing a credible Holmes on a weekly basis will not work. For him to be credible it can't be neatly wrapped up in a weekly episode. The cases have to have a certain of complexity that episodic television has rarely been able to handle.
TheWarden
and by "reinvention" we mean stealing an already existing and successful concept and totally ruining it. This is already being done to perfection by Steven Moffat and Mark Gatiss on the BBC with "Sherlock". Back off, CBS! We don't need "Sherlock: CSI" !


After almost 10 years since the idea of creating a magazine on emerging socio-legal studies began, and despite the difficulties that an altruistic and voluntary but rigorous project could face, Sortuz is a ongoing project! 10 numbers published, with several of them in guest editing system, numerous authors, with their anonymous reviewers, 10 artistic and photographic covers in every issue, an excellent web-site (thanks Antonio Ariza), and permanently adapting to authors and readers needs. In few works: a hard but good work!
And this good work will continue thanks to the very new general editors Lucero Ibarra and Alexander Kondakov! To them we hand tem over the baton, being fully confident that they will not only keep the machinery of the magazine ready, but provide innovative apps. The challenge is to find a space in the difficult world of scientific journals with impacts, indexes and major publishers. The new social networking and open-access can be great allies in this new journey. Sortuz has its own potential and an invaluable human capital: students and young researchers participating in the International Institute of Sociology of Law of Oñati. They are those who, from a constant and necessary critical perspective, open the magazine to new socio-legal horizons.
Good luck and full steam ahead!


Here's my first set of value studies. I'm trying to keep to the 1 hour max time frame, but a few went over (with some revisited a few days later). Thanks for looking!
#1 Edwin study: I like how Edwin keeps the bottom of the frame darker and moves up to a lighter value at top. Seems to give the rock formation weight and solidarity.
#2 Lamplough study: The dark values are mostly on the screen right and are balanced by subtle detail on the left. Lamplough's play of silhouettes and lines are really cool.
#3 Mullins study: I'm a big fan of Craig Mullins and enjoy his almost controlled chaotic strokes and simple indications that seem to be just enough to read exactly what's going on in the scene. In this one, I like how he connects the fg, mid, and bg masses with the legs of the robot.
#4 Beirstadt study: He seems to get a sense of scale and weight by using the light snow to push the rock formation upward while using darker values to push it back down. I like the contrast between the small trees and large massive rock.
#5 Bouguereau study: I like the gesture of the pose with the lines of the heels driving up through the hips and spine toward the face. Bouguereau also creates focus by playing the dark values of the face against a light sky, while the body tends to be a closer value to the ground and environment.
#6 Lamplough: Like the mid key and use of dark silhouettes against a darker background. I think my version turned out a bit soft, and I'd probably sharpen the edges and shapes some more given more time.
#7 Jones: I like how he draws focus to the areas of most contrast. I also like his use of various textures. It's a neat look, very similar to Mullins.
you're getting to a good place with these. I felt on the first ones you were missing a little bit of the right tones, but the later ones got that fixed quite nicely. I like the way you work with your mark making. Maybe you could try to vary the brushes to see if you can improve the differences between soft and sharp edges. The overall shapes are nice, but it could be interesting to try and be as careful on the inner smaller shapes. But I really really dig your work.
Yo Andre', thanks! It's great to get a second set of eyes on these. Will experiment a bit more with some brush varieties on the next set.
#11 Mateu: Like the clarity in his compositions. Big shapes are clear, and he overlaps mids and darks to give depth and to make things read.
#14 Levitan: I like his use of dark to lighter values to get a sense of depth.
#15 Surikov: Neat how he gave the impression of night time, with the ground snow being a higher value then the overall sky.
#16 N. Baker: Her poses are really clear and appealing, and I like how she varies her edge work to draw focus.
#17 Sargent: He has a nice economy of stroke and gets really subtle values in the face. Found this one quite difficult.
#18 Jones: He gets really clear shapes to read by layering high value over dark and over medium.
#19 Jones: I like the economy of stroke and how the detail is put more in the areas of focus. It was interesting to try and mimic how he addresses the edges in armor.
#20 Sargent: I like the rough strokes in the painting, and how he sneaks in a sharper edge near the eye.
My only comment at this point, other than more more more...is to really keep focused on pushing accuracy as far as you can with shapes, values and edges while at the same time it would be great to see just a bit more analysis of the composition. You are doing great. I am looking forward to getting through these studies with you and into the more advanced assignments. You are very talented.


text:
Exxon Mobil, Chevron join climate initiative
By Timothy Cama - 09/20/18 12:02 PM EDT
Three of the United States' largest oil and natural gas companies are joining a major fossil fuel–backed international coalition to battle climate change.
Exxon Mobil Corp., Chevron Corp. and Occidental Petroleum Corp. all announced that they're joining the Oil and Gas Climate Initiative (OGCI) Thursday, in the lead-up to the major Climate Week event in New York City next week, where the group will have a meeting.
The group was launched in 2014. Initially, United States–based companies avoided the initiative, and it was dominated by foreign companies like BP, Total and Royal Dutch Shell.
"It will take the collective efforts of many in the energy industry and society to develop scalable, affordable solutions that will be needed to address the risks of climate change," Darren Woods, CEO of Exxon Mobil, said in a statement.
"Our mission is to supply energy for modern life and improve living standards around the world while minimizing impacts on the environment. This dual challenge is one of the most important issues facing society and our company."
Chevron CEO Michael Wirth said the company wants "to work constructively on addressing the risks of climate change."
The OGCI said its membership of 13 companies now accounts for about 30 percent of global oil and gas production.
The group works toward reducing greenhouse gas emissions in oil and gas industry operations and pushing for investments in new technologies that could reduce emissions.
Tags Exxon Mobil Chevron oil Natural gas Climate change


WATER SAFETY AND SUVIVAL is a unique program designed to give students working or traveling on, over, or near water with the knowledge and skills necessary to react appropriately. This course provides information about water safety, drowning prevention, emergency response, hydrodynamic principles, aquatic skills, and stroke mechanics. These are the key principles needed to survive and which can be the difference between life and death.
AUDIENCE: This course is for anyone who works on, over, or near water who want to enhance their situational awareness and response to water related incidents while working.
COURSE FORMAT: This course is classroom-based which includes instructor, video, and/or PowerPoint throughout the course. This course is approximately 6 hours in length.
CERTIFICATION: Upon completion of this course, students receives a Water Safety and Survival completion certification valid for two years.


text:
Michelle Grimes
Meet Michelle, founder of Maven Hair. In 2014, after almost 20 years in the business, Michelle opened the doors to her own studio. Feeling a change rising through Ireland's hairdressing industry, she sought a new and fresh approach to hairdressing; sensing many people were now jaded with the generic big salon experience. She wanted to provide a more personal approach to hair and was acutely aware many stylists around the country wanted to be a part of this shift in attitude.
Michelle wanted to create a "relaxed, creative and inspiring environment" for stylists where their individualism was nurtured; a space where they were encouraged to spend time with their clients, rather than viewing them as an entry in the business timetable. And so, Maven was born…
You've got to give it to her, the lady is a dab hand in every aspect of her field – cutting, colouring and dressing hair. Whether it's hair up, loose and down, short and blunt or choppy, she's a doer of all types of hair and works great with them all. With a Master Colour Award, not to mention the highest level of exams in Ireland under her belt, Michelle sees education as a key element in raising standards into the future.
All this has allowed her to teach advanced cutting and upstyling prior to the opening of Maven. You may also have seen her mixing-it-up on Xspose and Off the Rails or viewed her work in magazines such as U, VIP, Confetti and Image Brides. Michelle also contributes hair tips and forecasts on Xspose.ie.
Likes: Her two gorgeous and crazy kids, music, interiors, fashion, food and travelling. She's loving a bit of Dingle gin at the moment…
Dislikes: Ignorance and being hungry!
Claim(s) to Fame: Oh, she has a few…. She's shot some hoops with Kings of Leon, had food fights with The Strokes, hung out in a van for the night with The Beta Band and has had the chats with Gaz Coombes and Paul Weller. Watching a gig beside Roisin Murphy has been her highlight so far.
Bookings appointments@hairmaven.ie
Instagram: @hairmaven.ie
Aoife Callaghan


Opportunity Zone property listed at below appraised value!
Bathrooms 4 - 2 full bathrooms on the first floor and one full bathroom on the 2nd and 3rd floors.
Located in historic downtown Fayetteville, NC with hotel next door and across the street from City Hall. Adjacent to the future site of Houston Astros downtown Minor League Baseball Stadium to open April 2019. Newly developed mixed use property adjacent to lot that includes condominiums and town homes by the same entity that developed the Durham Bulls project. There are also many restaurants and shops within walking distance. Airport is 10 minutes driving distance. Train station is within walking distance. City Festival Park and Plaza also adjoins the property. This location is at the epicenter of city events and festivals. It is also located in a HUB zone, Opportunity zone and a downtown historical district with associate tax credits available for redevelopment. **Update on the Baseball Stadium Construction(Located Adjacent to the Property): http://www.fayobserver.com/opinion/20180816/our-view-it-really-is-start-of-something-big http://www.fayobserver.com/photogallery/NC/20180727/NEWS/718009979/PH/1 - **The property is the blue/grey building adjacent to the construction site. http://www.fayobserver.com/news/20180718/fayetteville-ballpark-lands-big-south-tournament Property: 421 Maiden Lane, Fayetteville NC 28301. Cumberland County Tax Records PIN 0437-54-1813. Description: Three story 93,000 SF concrete building primarily flex space. Currently configured as multi-purpose datacenter, rental auditorium, office and retail space. Owner is currently and deliberately the only tenant to lend maximum flexibility to the new owner. Parking: Large Property size allows for a portion of the property to be converted into a parking deck. Multi-level parking deck could be constructed on existing ground level parking lot and connected to the main building. Could accommodate new baseball stadium and surrounding development. Separate Third party financing may be available for parking deck construction. Seller: Ace Capital LLC / Advanced Internet Technologies, Inc. Property is owned outright by Seller Sales Price: $4.8 Million due at Closing, less the earnest deposit (See Lease Back/ Owner Financing Below). Two previous existing appraisals $6.5 million and $7.5 million prior to the recent $100 (+) million downtown investment in adjacent construction for new minor league baseball stadium (Houston Astros), hotel, retail and condominiums. Previous asset based financing for a $4 million loan executed and paid off. Lease Back/ Owner Financing: At closing Seller will execute at ten year lease with two five year options for an estimated $13,000 SF at $6 per SF. Property has been leased in the past using full leases at $16 per SF using full leases. However, with new surrounding construction, this price is subject to a likely increase. Current surrounding retail and office renovated construction is leasing between $25 and $35 a SF. CAP Rate: 24% Fully Leased. Estimated net rental income $85,00 to 95,000 per month at $16 per square foot not including parking if deck if constructed on existing ground level parking lot and land. Earnest Money: $100,000 to be applied toward Closing. Inspection Period: Ninety (90) days from later to occur (1) the date a purchase contract is signed, (2) the date requested due diligence materials been delivered to Purchaser. Due diligence items include all physical aspects of the property, regulatory requirements and environmental studies. There are two existing previous bank appraisals on hand and Environmental Study Phases 1 and 2. Closing: Closing shall take place within 60 days after the end of the inspection period Closing Costs: TBD Zoning: Zoning is a Downtown Historic District located in a HUB Zone and Opportunity Zone. Contract: Purchase Agreement to be drafted.


text:
Modern, Green Playhouse Designed To Inspire Imagination
September 20, 2011 Blueplate PRLeave a comment
Frank Harmon Architect PA participates in Playhouse Parade fundraiser, auction.
Color scheme, elevations
September 20, 2011 (Raleigh, NC) — Award-winning architect Frank Harmon, FAIA, believes "the best toy is one that allows the greatest freedom. Lego is a good example, a child under a table with a tablecloth surrounding her is another, and nothing is better than a muddy stream." That's why the custom-built playhouse his firm has designed for the upcoming Playhouse Parade in Raleigh is about creating spaces that will inspire a child's imagination.
The Playhouse Parade is a collaboration among the City of Raleigh Parks & Recreation Department, Cameron Village Shopping Center, the Triangle Builders Guild, and a variety of designers, architects, businesses, and individuals to raise funds for the Sassafras All Children's Playground, a new playground in Laurel Hills that will be accessible for children with special needs.
Frank Harmon's design team is well-known for modern, sustainable and regionally appropriate
Exterior under construction
architecture, and this playhouse – like the Dog House the firm designed in 2005 to raise funds for Triangle Beagle Rescue of North Carolina — is no exception.
In modern architecture, form follows function. But in the playhouse, form follows play — to allow children's imagination the greatest freedom.
Rather than designing a themed playhouse — a pirate ship or a firehouse, for example — Harmon's playhouse "lets a child use his or her imagination," he says, "from tea parties to puppet shows and even making mud-pies."
The tall, narrow structure features a covered porch/stage, a lower-level playroom with two windows, and a loft level with a balcony or "Juliet" window. On the first level, behind the ladder that rises to the loft, is the "kitchen," where a shelf with buckets sits ready for mud-pie making. Sliding shutters at both lower windows open for puppet shows but close to keep out rain — and imaginary forces attacking a fort. The
Interior showing upper level loft.
large main door at the front of the playhouse can be thrown open for stage productions. In its closed position, a smaller door-within-a door allows children to enter and exit, and a "peep hole" window above the small door allows sun light in and serves as a "spy portal." A planter in front of the porch/stage invites children to grow flowers and vegetables.
"How important is it," Harmon asks, "for children to learn where a tomato comes from?"
In keeping with the principals of green, or sustainable, design, the structure is composed of locally available materials: painted wood (plywood and 2x4s and 2x2s), metal (galvanized pipe), and translucent corrugated polycarbonate for the roof. The windows provide natural ventilation and lighting, and the deep roof overhang protects the interior from the hot summer sun.
Harmon and his design team consulted with a child psychologist and several children during the design process, and built the playhouse to the scale of a three- to seven-year-old child.
"It's real, but small," says Courtney Evans, Harmon's architectural intern, who spearheaded the project.
Twelve design teams are designing, building, and donating playhouses that will be displayed in Cameron Village on two Saturdays, October 8 and 15, then auctioned off on October 22 during the "Night Under
Window with sliding shutter.
The Stars Playhouse Parade Gala." Proceeds from the auction will be used to restore the city's one-of-a-kind playground that gives kids, no matter what their abilities, the chance to play. For more information: http://sassafrasplay.org/playhouse.
For more information on Frank Harmon Architect PA, visit www.frankharmon.com.
About Frank Harmon Architect PA
Frank Harmon Architect PA is an award-winning architectural firm that is recognized nationally as a leader in modern, innovative, sustainable and regionally appropriate design. Its competition-winning design for the AIA NC Center for Architecture & Design is currently under construction in downtown Raleigh. The firm's work has been featured in numerous books, magazines, journals and online magazines on architecture, including ArchDaily.com, Dwell, Architectural Record, Architect and Residential Architect. The firm ranked 21st in Architecture magazine's Top 50 firms in the nation this year and Frank Harmon, FAIA, founder and principal, was included in Residential Architect magazine's first "RA 50: The short list of architects we love." For more information, go to www.frankharmon.com.
architecture, construction, green architecture, modern architectureFrank Harmon Architect, green playhouse, modern playhouse, playhouse, playhouse design, Playhouse Parade, Raleigh NC


text:
Il meglio è un album di Gian Pieretti del 2005. È stato prodotto da Dino Angelini.

Tracce

redpajama_set_name: RedPajamaWikipedia


AP's Red Safelight offers table-top or wall mounting, is manufactured in compliance with current EU safety standards and makes a great inexpensive option for every enlarger workstation.
You can use it for high sensitivity, desensitised, orthochromatic emulsions and both Ilford and Kentmere multigrade papers. Minimum recommended working distance is 1 metre.


Learn how to utilize Social Trading and become a successful Forex Broker.
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What are some of the most important things to consider when joining a Scotland chat room? If you said the ability to search the profiles of the people you're chatting with, then we have the site for you. Our online chatting site for Scotland is the key to helping you find the best relationships online and that involves doing a bit of research. After all, everyone wants to get involved with someone that is similar and attractive to them. Using this site's personals profiles, you'll be able to find a Scottish man or woman that is hot and has the right dating qualifications. You can search for people by age, looks, location, and even deeper things like religion or political affiliation. No matter what you want out of your potential friends or dates this site is the best way to find it. You just have to sign up and start looking for matches on our website today. Since this is the largest site with the most Scots looking for some fun chat, it's also your best chance to find them online or in person. By coming to this site to start your relationship, you are taking the best step towards finding the right people for you. Take some time to check out the site and see what we can offer you, and then sign up if you have a few minutes. We promise you'll never find another experience like this one!
Come to our online dating website ad chat with people in Scotland tonight. Nothing is more exciting than being able to get access to talk with people from such a unique and amazing culture. That's why we are providing you with free access to a site that is going to change the way that you meet Scottish people. Aside from the large number of people on the website and the site's low costs, you get other benefits to joining this site as well. Most notably, you'll have the chance to be picky with the dates that you attract on the site. Some places just stick you with people and hope that you form a relationship. Our site lets you have more control so you can search for people with certain characteristics or traits that will make them the perfect partner for you. This ability to be picky allows you to select the best of the best so that you never have to settle for less in friendship or love. You can be a member of this website in less than half an hour. Just bring a picture, sign up, and tell the site about you and what you want in a partner and you'll be chatting before you know it. Fast and simple chatting experiences are just a few clicks away right now!


text:
Q: redux-thunk dispatch method fires undefined action Here is the code I'm playing with
import { createStore, applyMiddleware } from 'redux'
import thunk from 'redux-thunk'
import axios from 'axios'

const initialState = {
    user: {},
    requesting: false,
    err: null
}

const reducer = (state = initialState, action) => {
    switch (action.type) {
        case 'REQ_USER_INIT': return { ...state, requesting: true }
        case 'REQ_USER_DATA': return { ...state, requesting: false, user: action.user }
        case 'REQ_USER_ERR': return { ...state, requesting: false, err: action.err }
    }
    return state;
}

const logger = (store) => (next) => (action) => {
    let previous = JSON.stringify(store.getState())
    next(action)
    console.log(
        'action: ' + JSON.stringify(action) +
        '\n\tprevious: ' + previous +
        '\n\tcurrent: ' + JSON.stringify(store.getState())
    )
}

const store = createStore(reducer, applyMiddleware(logger, thunk))

store.dispatch((dispatch) => {
    dispatch({ type: 'REQ_USER_INIT' })

    // Fake Online REST API for Testing and Prototyping
    // break url to get an error response
    let usersEndpoint = 'https://jsonplaceholder.typicode.com/users/1'

    axios.get(usersEndpoint)
        .then((response) => {
            dispatch({
                type: 'REQ_USER_DATA',
                user:  {
                    id: response.data.id,
                    username: response.data.username,
                    email: response.data.email,
                }
            })
        })
        .catch((error) => {
            dispatch({
                type: 'REQ_USER_ERR',
                err: error.message
            })
    })
})

I believe it is pretty straightforward, right? I dispatch REQ_USER_INIT and then REQ_USER_DATA once the response is received. I should log two actions, however I get 3. Second action is undefined and I am strugling to figure out what causes it. Is it a bug with redux-thunk or am I doing something wrong?
Here is the output from my console:
action: {"type":"REQ_USER_INIT"}
·previous: {"user":{},"requesting":false,"err":null}
·current: {"user":{},"requesting":true,"err":null}
action: undefined
·previous: {"user":{},"requesting":false,"err":null}
·current: {"user":{},"requesting":true,"err":null}
action: {"type":"REQ_USER_DATA","user":{"id":1,"username":"Bret","email":"Sincere@april.biz"}}
·previous: {"user":{},"requesting":true,"err":null}
·current: {"user":{"id":1,"username":"Bret","email":"Sincere@april.biz"},"requesting":false,"err":null}

A: The order of middlewares matters. Try making logger last
const store = createStore(reducer, applyMiddleware(thunk, logger))

redpajama_set_name: RedPajamaStackExchange


text:
India All India 25 Jun 2020 T-series pulls down Pakistan singer's song from YouTube after MNS issues warning
T-series pulls down Pakistan singer's song from YouTube after MNS issues warning
AGE CORRESPONDENT
Published : Jun 25, 2020, 9:59 am IST
Updated : Jun 25, 2020, 9:59 am IST
The T-Series has stated in its apology letter that the song was uploaded on the YouTube 'by mistake' and it will be removed.
Mumbai: Following the warning from the Raj Thackeray-led Maharashtra Navnirman Sena, the T-Series, a music record label, removed a video and has tendered a public apology for uploading a song of Pakistani singer Atif Aslam on its social media channel. The label has also promised not to assist Pakistani artists in any manner.
The T-Series, also known as Super Cassettes Industries Private Limited, has stated in its apology letter that the song was uploaded on the YouTube channel by an employee of the promotions team 'by mistake' and it will be removed from the channel. The song will no longer be released or promoted on the channel of T-series.
Ameya Khopkar, the president of MNS Chitrapat Sena, had warned Bhushan Kumar, the owner of T-series after the label uploaded the song 'Kinna Sona' sung by Atif Aslam. The song is from the film Marjaavaan, which stars Siddharth Malhotra and Tara Sutaria in lead roles. Khopkar asked the owner of T-series to immediately delete the song from its social media channel and also threatened of dire consequences if the song was not removed.
Khopkar, in his warning, had also mentioned popular singer Sonu Nigam, who had blamed T-Series for several reasons. In a video released by Nigam, he had said that mafias in the music industry are trying to malign his name after he said that music companies don't welcome newcomers.
"If the accusations of Sonu Nigam are true, we will not hesitate to take action. We will not tolerate mafiagiri," he had said. However, the apology letter issued by the T-series does not mention Nigam's name.
Tags: maharashtra navnirman sena (mns), t-series, music video, pakistani artists
Location: India, Maharashtra, Mumbai (Bombay)
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text:
Focus on Clinical Health Justice
Columbia clinicians seek to create new pathways to mental health for patients and communities they serve
In December, Adrian Jacques H Ambrose, MD, MPH, the senior medical director of the Columbia Psychiatry Faculty Practice, brought together a cross-section of the clinical community—medical students, residents, fellows, early career faculty, senior faculty, and staff—to discuss and collaborate on a sensitive and critical topic: how clinicians can better address health equity on behalf of patients and communities.
The intergenerational Clinical Health Justice Forum, made possible by a grant from Johnson & Johnson focused on medical education and health equity, took place at the Red Rooster, an iconic Harlem restaurant, drawing more than 60 people from the Columbia medical community.
The forum was an opportunity for open conversations about racism and discrimination, poverty and income inequality, and cultural barriers that impede the delivery of effective behavioral health care to marginalized groups, including residents in neighborhoods surrounding the medical center.
New pathways to mental health
"It is incumbent on us to create new pathways to mental health and make a concerted effort to remain rooted in this community that we serve," Dr. Ambrose said. "As mental health champions, we are uniquely positioned to leverage our expertise, not just as clinical providers but also as health advocates who recognize and respond to the various social determinants that impact our patients' health and lives."
With the help of many clinical leaders and the Columbia Women's Program, this year's theme focused on women in minoritized spaces—the structural and environmental factors that create and perpetuate inequity for women, especially women and pregnant people of color.
Attendees tackled a wide range of topics, from reproductive justice and abortion rights, maternal mortality, to inequities around parental leave in the United States versus the rest of the world, and the imperative for a more inclusive clinical framework for women's mental health that spans the gender spectrum, such as, gender nonbinary people and transgender men.
The attendees agreed that Columbia Psychiatry must expand its efforts into the community and not preach from the "ivory tower."
Dr. Ambrose hopes to offer a similar platform to the Columbia community next year, focusing on children, adolescents, and young adults and ways in which practitioners can meet the deepening youth mental health crisis and fill gaps in access to quality behavioral health treatment and care.


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Left Coast Voices
"I would hurl words into the darkness and wait for an echo. If an echo sounded, no matter how faintly, I would send other words to tell, to march, to fight." Richard Wright, American Hunger
Archive for the tag "Stephen Boyd"
Writing About Justice
The following article was taken with permission from Bookmarks, the blog of Southern Celebrations.
Dr. Steve Boyd, a Religion professor at Wake Forest University, fights for justice in his writing as well as inside his classroom. Dr. Boyd's book Making Justice Our Business: The Wrongful Conviction of Darryl Hunt and the Work of Faith has just been released. His first talk about his book and book signing will be held on Monday, November 28th at Emmanuel Baptist Church. Below is a description (from Wake Forest University's website) about Dr. Boyd's course "Religion and Public Life." A course that has taught him just as much as it has the students who have taken it.
(from WFU website)
…For nearly twenty years, Winston-Salem resident Darryl Hunt spent every day in a dreary prison cell serving a life sentence for a crime he did not commit. In spite of a trial that was devoid of physical evidence tying Hunt to the scene of the crime, he was convicted of first-degree murder in 1984. Hunt was just nineteen years old at the time.
Facing perhaps the cruelest fate a human being can endure, Hunt maintained his own innocence, and his spirit remained unfettered as he called on God to give him strength and to comfort him. As his days behind bars grew in number from the hundreds to the thousands, Hunt's faith in God only intensified and served as much more than a means of preserving a glimmer of hope for life outside of prison.
Nine years after being convicted, DNA evidence surfaced indicating that Hunt, an African American, could not have committed the crime, yet the appeal of his conviction was denied. In 2003, his attorney, who served him for eighteen years pro bono, threw one last "hail Mary" pass in the form of a motion to compare the DNA in the 1984 rape kit to a state database of DNA profiles. Miraculously, he got a "hit." Finally, the real murderer was found and Hunt was freed. Hunt's remarkable story gained national recognition and became emblematic of Winston-Salem's historically tense race relations.
Building upon his experience, Hunt founded the Darryl Hunt Project with community leaders to help prevent the criminal justice system from convicting innocent parties, educating the public about faults in the system, and helping ex-offenders re-enter society and become productive, contributing citizens.
Just one year after Hunt's exoneration, Wake Forest student Rashad Daker had the opportunity to transcribe Hunt's daily journal entries that he wrote during his imprisonment, an assignment that Daker chose as part of Professor Stephen Boyd's "Religion and Public Life" course. Daker and Hunt are both practicing Muslims, and according to Boyd, both individuals found the experience cathartic and spiritually engaging.
In addition to Daker's work with the Darryl Hunt Project, each student in Boyd's class worked with a local nonprofit organization that is addressing a significant need in the community. For instance, one student worked with Advocacy for the Poor, researching issues related to poverty, affordable housing, homelessness, and hunger. The in-class portion of the course focuses on issues of religious leadership, social entrepreneurship, the separation of church and state, and the differences among service, advocacy, and community organizing, as well as their roots in three dominant theological paradigms in Christian history.
Boyd also sees great value in simply getting students involved in projects off campus – outside the "Wake Forest bubble."
"As a student, it is easy to get consumed with life on campus," said Boyd. "Students sometimes forget there is an exciting world outside the 'Wake Forest bubble', one that is full of challenging issues that can be gratifying to work on."
The students and the organizations were not the only ones touched by the course, however. Boyd described the experience as "the most rewarding course I ever taught" and is offering it for the second time in 2011.
Alon Shalev is the author of The Accidental Activist and A Gardener's Tale. He is the Executive Director of the San Francisco Hillel Foundation, a non-profit that provides spiritual and social justice opportunities to Jewish students in the Bay Area. More on Alon Shalev at http://www.alonshalev.com/ and on Twitter (#alonshalevsf).
Posted in Books that Make a Difference and tagged African-American, author, BOOKMARKS, Bookmarks Festival of Books, books, Darryl Hunt, Darryl Hunt Project, Local Authors, non-fiction, North Carolina, North Carolina Authors, social justice, Southern Celebrations, Stephen Boyd, Wake Forest University, Winston-Salem | Leave a comment
The Accidental Activist
Alon Shalev is an author of novels that highlight social injustice. His latest novel is The Accidental Activist. Click on the icon above for more about the author and his books.
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Cate McGuire is a visual artist who uses various media to build spaces that mimic both the natural and the built world we live in. Her goal is to provoke reflection and to spark cultural memory by re-animating existing images. She has a varied and extensive background in art and design, including a bachelor of fine arts degree from Concordia and a post-graduate degree of architecture from UBC.
McGuire has shown her work at various venues including two recent solo shows at the Red Head Gallery in addition to the Artist Project, Toronto Outdoor Art Exhibition, Elora Centre for the Arts, and the Gladstone Hotel. She was recently awarded best of Mixed Media at the Riverdale Art Walk and Best of Paper at the Toronto Outdoor Art Exhibition.


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FANS QUEUE FOR HOURS TO RIDE HONG KONG'S FIRST COMMERCIAL ELECTRIC DOUBLE-DECKER
By James Ockenden on June 19, 2022 • ( Leave a comment )
Around 250 people, mainly youngsters, had joined the queue to ride the first electric 5B today. With a bus capacity of just 125, some would be disappointed.
Hundreds of eager bus fans queued for hours to secure a place on Hong Kong's first commercial electric double-decker bus today as it plied the busy 5B route between Causeway Bay and Kennedy Town.
One youngster at the head of the 250-strong queue said he arrived at the Hong Kong Stadium bus stop at 8am, four hours before the scheduled departure at noon, and that he had heard about the launch through the CityBus Facebook page.
Speaking before passengers embarked, Bravo Corporate Communications Manager Andy Tsang said the 5B route was chosen as it was relatively flat and offered a good testbed for the heavy double-decker.
Bravo's Corporate Communications Manager Andy Tsang (right) and CityBus and New World First Bus General Manager for Operations Roger Ma at the launch at Hong Kong Stadium this morning
Routes 20, 20A and 22M between Kai Tak and Tai Kok Tsui, Tsim Sha Tsui and To Kwan Wan should be in operation by 4 July, subject to approval from Transport Department, says the company.
According to Tsang, there are no charging stations en route, with the bus needing to return to the Chai Wan depot for charging. Tsang said he hoped regulators would soon approve charging stations built at Hong Kong Station.
In the meantime, Tsang said the bus could make three return trips of the 5B route between Hong Kong Stadium and Kennedy Town, giving it an effective range of around 80 km including the trips between route head and the Chai Wan depot.
Tsang also revealed the company's first hydrogen bus would be arrive "within weeks", and that the company would be testing both battery electric and hydrogen fuel-cell buses side by side. But he said the regulatory process was slow and the hydrogen bus wouldn't be ready for demonstration on public streets for "some time".
The 11.9km route took 51 minutes, with a moving time of 43 minutes and an average moving speed of 15.1 kph
Transit Jam followed the bus by bicycle, measuring an average moving speed at around 15.1 kph for a distance of 10.91 km and a total time of 51 minutes.
Aside from being much cooler and cleaner to approach from behind, there was no discernible difference in how the bus operated in terms of acceleration and braking.
Passengers enjoyed the ride, with one youngster in Kennedy Town claiming it had been "full of joy".
The driver noted the jam-packed bus had been "very heavy".
The bus packs around five tonnes of batteries which can charge in around three hours through a 150kW charger.
Earlier, bus expert Paul Bromley, managing director of Phoenix Consulting, had said the high-capacity battery design approach has "compromised the passenger carrying capacity" with, he said, around 11 fewer seats and 11 fewer standing passengers
Bravo executives, who had been seen showing Chief Executive Carrie Lam around the double-decker in April, were absent from the launch this morning, and staff present would not answer questions on the relationships between Bravo, investor Templewater and bus maker Wisdom. "You will have to ask Templewater," said Bravo's Tsang.
Categories: Transit
Tagged as: Andy Tsang, Bravo, CityBus, electric, electric double-decker, Paul Bromley, Templewater
MASSIVE ROAD BUILDING PLANS REVEALED AS LANTAU SUSTAINS "FUNDAMENTAL CHANGE TO FUNCTION"
"POSSIBLY FISHY": QUESTIONS RAISED OVER "BLOODY EMBARRASSING" JUMBO SINKING
Transit Jam is registered under Hong Kong's Registration of Local Newspapers Ordinance, Cap. 268. The proprietor and printer is Media Karma, PO Box 5885, GPO, Hong Kong


So here are a few more WIP shots for the Cauldron of Blood. I have added some candles and skulls etc around the cauldron and a pile of shredded bodies at the base. I think I'm almost there with the conversion now, time to give it a base coat and get some Hag attendants!
That is really cool. It is bigger than I thought and will probably suffer from LOS but when painted will be an epic centre piece.
Man this is amazing! Much better than the current Cauldron of Blood!