text:
\section{Introduction}
\label{sec_intro}

There is a recent upsurge in studies of topological phases of matter~\cite{hasan10,
qi11, lukasz11, chen13, senthil15, chiu16}. These phases are robust against weak
perturbations due to the existence of a bulk gap, which does not vanish unless the
system crosses a gapless quantum critical point (QCP). In addition, a topological
phase is characterized by a topological invariant, which remains constant under
continuous variations of parameters as long as the system remains in the same phase
and becomes ill-defined at QCPs which separate different phases.

In this regard, the Kitaev chain of spinless fermions (a $p$-wave superconducting
system in one dimension) is a paradigmatic model that hosts symmetry protected
topologically non-trivial and
topologically trivial phases separated by a QCP~\cite{Kitaev01, laumann09}. The
topological properties of a Kitaev chain with periodic boundary conditions is
characterized by a topological invariant known as the winding number. The winding
number assumes non-zero integer-quantized values in the topologically non-trivial
phase and vanishes in the topologically trivial phase. For a system with open boundary
conditions, the topologically non-trivial phase of the model is manifested in the
existence of zero-energy Majorana modes localized at the edges; on the contrary, the
topologically trivial phase does not host Majorana edge modes. The exact solvability
of the model has been extensively exploited to understand its equilibrium as well as
out-of-equilibrium properties~\cite{Kitaev01, laumann09, DeGottardi11,
DeGottardi13, dsen13, trs_sen13, rajak14, dutta15, saha17, souvik_open20, souvik2021}.

Concerning the non-equilibrium dynamics of closed quantum systems, periodically
driven systems have been explored both in the context of
thermalization~\cite{russomanno12,tomka12, nag14, bukov15, sayak15, nag15, arnabsen16, mukherjee16, eckardt17, takashi19, sen_2021} and emergent topology ~\cite{kitagawa10, jiang11, gu11, trif12, dsen13, liu13, DeGottardi13, kundu13, wu13, tong13, andres13, lindner13, katan13, thakurathi14, asboth14, reichl14, perez15, adhip16, roy16, yao17, thakurathi17, saha17, vega18, tilen19, utso_2019, souvik2021} (for recent review
articles, see Refs.~\cite{bukov15, eckardt17, sen_2021, souvik2021}). For a
periodically driven Kitaev chain with open boundary conditions, it has been shown that Majorana
edge modes (zero and $\pi$-modes) can be dynamically generated~\cite{dsen13, saha17, souvik2021} even
though the instantaneous Hamiltonian
may remain topologically trivial at all times. In fact, it is the effective Floquet
Hamiltonian~\cite{floquet83} that determines the non-trivial topology (i.e., the
existence of zero-energy Majorana edge modes) of a driven chain. It has been
observed that the
number of such dynamical edge modes increases as the drive frequency is reduced.
Further, a strong (having a sufficiently large amplitude) periodic modulation of the
hopping parameter can produce some ``anomalous" edge modes with non-zero Floquet
quasienergies~\cite{saha17}. However, the anomalous edge modes are not Floquet Majorana modes. These modes have no topological
significance and topological invariants like the winding number miss them completely. Furthermore, as we elaborate in this work, these modes are not robust against
weak spatial disorder.

There have been several attempts to characterize the out-of-equilibrium topology of one-dimensional systems (e.g., the Kitaev chain and the Su-Schrieffer-Heeger chain) using the dynamical winding number calculated from the instantaneous wave function of the system~\cite{cooper18, souvik19, souvik2019}. In a periodically driven Kitaev chain, the corresponding winding number~\cite{dsen13} is calculated from the Floquet Hamiltonian (for a review, see Ref.~\cite{souvik2021}). This winding number correctly predicts the number of zero-energy Majorana modes for a Kitaev chain with a periodically driven chemical potential.
However, the dynamical winding number fails to detect the anomalous edge modes
which arise when the hopping parameter is driven strongly~\cite{saha17}.

Recently, the notion of a disconnected entanglement entropy (DEE)~\cite{fromholz20,
micallo20} has been introduced which plays a role similar to a topological invariant
in an equilibrium Kitaev chain with an open boundary condition.
It is worth noting that unlike the winding number, the DEE is not a bulk topological
invariant. Rather, it extracts the entanglement between the Majorana modes localized
at the edges. Although the DEE can take any real value by its construction, it turns
out to be integer-quantized for a short-ranged Kitaev chain in the topological
phase, where the integer is the total number of edge modes of the
system~\cite{fromholz20, micallo20, msaikat22}.

In this paper, we explore the efficacy of the DEE in detecting the dynamically
generated edge modes for a periodically driven Kitaev chain. We study the variation
of the DEE with
the drive frequency for three different types of periodic modulations of the chemical
potential, namely, $\delta$-pulses, (and also square pulse and sinusoidal variations). Our study
establishes that the DEE correctly predicts the number of edge modes. We also investigate the applicability of the DEE as a marker of anomalous
edge modes appearing due to a periodic modulation of the nearest-neighbor
hopping amplitude.

It is also noteworthy that the verification of topological properties of periodically driven
systems are experimentally more viable compared to undriven systems. Recently, the periodic driving protocol of a (kicked) transverse field Ising model has been implemented experimentally using an array of superconducting qubits~\cite{mi22}. It is important to note that this model can be mapped to a Kitaev chain through Jordan-Wigner transformations~\cite{lieb61} and thus this model can host Majorana edge modes. In the present work, we not only probe how these Floquet Majorana modes are manifested in the DEE, but also we illustrate the robustness of these modes against weak spatial disorder and temporal noise.

The rest of the paper is organized as follows: the conventional definition of the DEE is introduced in Sec.~\ref{sec_dee}. In Sec.~\ref{sec_srk}, we briefly recapitulate a short-ranged Kitaev chain of spinless fermions and its topological properties. The behavior of the DEE for a Kitaev chain with periodically modulated chemical potential is explored in Sec.~\ref{sec_drive}. We analyze the effects of spatial disorder and temporal noise in the periodic driving on the DEE in Sec.~\ref{sec_disorder}. In Sec.~\ref{sec_anomalous}, we study the situation where the nearest-neighbor hopping amplitude is periodically modulated and address the question of whether the DEE can detect the anomalous edge modes. Concluding remarks are presented in Section~\ref{sec_conclusion}. The definition of the winding number of a short-range (static) Kitaev chain is given in Appendix~\ref{sec_topology}. The methods used for computing the DEE from Floquet Hamiltonian are explained in Appendix~\ref{app_method}. We present the behavior of the DEE for periodic driving with a square pulse and a sinusoidal modulation in Appendix~\ref{sec_sq}. We then briefly compare the DEE with the dynamical winding number derived from the Floquet Hamiltonian for a periodic variation of the chemical potential in Appendix~\ref{sec_winding}. In Appendix~\ref{app_gap}, we provide an analytical derivation of the frequencies at which Floquet quasienergy gap closes, choosing the example of the periodic driving of the hopping amplitude.

\section{Disconnected entanglement entropy}
\label{sec_dee}

\begin{figure}
\centering
\includegraphics[scale=0.35]{partition.pdf}
\centering
\caption{Partitions of a chain with the disconnected partition $D =
\overline{A \cup B}$ and $2 L_{A} = 2 L_{B} = 4 L_{D} = L$. The subsystem $B$
consists of two partitions $A \cap B$ and $B \backslash A$, separated by the
disconnected partition $D$ (Ref.~\cite{msaikat22}).} \label{fig_partitions} \end{figure}

In this section, we briefly introduce the notion of disconnected entanglement
entropy (DEE)~\cite{fromholz20, micallo20}. To this end, we first consider a
composite system $\mathcal{S}$ that is in a pure state and is described by a density
matrix $\rho$. The reduced density matrix of a subsystem $A$ is obtained by tracing
over the degrees of freedom of the rest of the system $\overline{A}$ \cite{peschel03}:
\begin{equation}\label{eqn_rho_A}
\rho_{A} = \rm{Tr}_{\overline{A}} (\rho). \end{equation}
The entanglement entropy~\cite{vidal03, calabrese04, latorre09, calabrese09} of
subsystem $A$ is then defined in terms of the eigenvalues
$\alpha_i$ of the reduced density matrix $\rho_{A}$ as
\begin{equation}\label{eqn_SA}
S_{A} = - \rm{Tr}_{A} (\rho_{A} \ln (\rho_{A}) ) = - \sum _{i} \alpha_{i} \ln (\alpha_{i}).
\end{equation}
As the system $\mathcal{S}$ is in a pure state, it can be shown that
$S_{A} = S_{\overline{A}} $.

We now consider a configuration of the partitions $A$, $B$, $A \cap B$ and $A \cup B$
of the system $\mathcal{S}$, such that the subsystem $B$ consists of two parts $A \cap B$
and $B \backslash A$, separated by the disconnected partition $D=\overline{A \cup B}$, as
shown in Fig.~\ref{fig_partitions}. The DEE~\cite{fromholz20, micallo20, msaikat22}
is then defined as
\begin{equation}\label{eqn_SD}
S_{D} = S_{A} + S_{B} - S_{A \cup B} - S_{A \cap B}. \end{equation}

\section{Short-range Kitaev chain}
\label{sec_srk}

We recall the Hamiltonian of a Kitaev chain~\cite{Kitaev01, laumann09, DeGottardi11, DeGottardi13, dsen13} with short-ranged interactions given by
\begin{multline}\label{eqn_H}
H = - \gamma \sum_{n=1}^{L-1} (c_{n}^{\dagger} c_{n+1} + c_{n+1}^{\dagger} c_{n} ) - \mu \sum_{n=1}^{L} ( 2 c_{n}^{\dagger} c_{n} -1 ) \\
+ \Delta \sum_{n=1}^{L-1} (c_{n} c_{n+1} + c_{n+1}^{\dagger} c_{n}^{\dagger}),
\end{multline}
where $c_{n}$ ($c_{n}^{\dagger}$) is the annihilation (creation) operator for a spinless
fermion on the $n$-th site, $\gamma$ is the nearest-neighbor hopping parameter, $\Delta$
is the strength of the $p$-wave superconducting pairing, and $\mu$ is the on-site chemical
potential. The parameters $\gamma$, $\Delta$ and $\mu$ will be taken to be real unless
otherwise mentioned. Consequently, the Hamiltonian respects time-reversal symmetry
($\mathcal{T}$), particle-hole symmetry ($\mathcal{P}$) and sub-lattice$/$chiral symmetry
($\mathcal{C}$) and the system belongs to the BDI symmetry class. Definition of the
winding number and topological properties of a short-range Kitaev chain are briefly
discussed in Appendix~\ref{sec_topology}.

It is noteworthy that in a chain with short-ranged couplings and open boundary
conditions, the DEE, calculated in the ground state of static Hamiltonian, is an
integer multiple of $\ln(2)$, i.e., $S_{D}=p \ln(2)$, where $p$ is the total number
of modes at the edges of an open chain (see
Ref.~\cite{fromholz20, micallo20, msaikat22}). The total number of edge modes is
twice the number of modes at each edge. Therefore, the values of the DEE in
the topologically non-trivial ($-1<\mu<1$) and trivial ($|\mu| >1$) phases of a Kitaev chain are $2\ln(2)$ and
zero, respectively, and there is a discontinuous jump in the value of the DEE at the
QCP separating the two phases. Thus, the DEE plays a role equivalent to the
winding number for an open chain.

\section{DEE for a Kitaev chain with periodically modulated chemical potential}
\label{sec_drive}
\begin{figure*}
\centering
\subfigure[]{
\includegraphics[width=0.45\textwidth]{sd_delta.pdf}
\label{fig_dee_delta}}
\centering
\hspace{5mm}
\subfigure[]{
\includegraphics[width=0.45\textwidth]{majorana_delta.pdf}
\label{fig_no_delta}}
\caption{(a) DEE ($S_{D}$) in units of $\ln (2)$ and (b) total number of Majorana
edge modes $p$ as functions of driving frequency
$\omega$ (in the units of the hopping parameter $\gamma$, which is set equal to unity) for a Kitaev chain in which the chemical potential $\mu$ is periodically
modulated by $\delta$-pulses
(Eq.~\eqref{eq_delta}) having $\mu_{0}=2.5$ and $\mu_{1}=0.2$. We have taken $L=200$ and
$L_{D}=50$. The DEE assumes integer-quantized values except at low frequencies.
The number of dynamically generated edge Majorana modes increases as $\omega$ decreases.}
\label{fig_delta} \end{figure*}

In this section, we discuss the behavior of the DEE calculated in the ground state of the effective Floquet Hamiltonian for a Kitaev chain with a periodically modulated chemical potential.

We consider a Kitaev chain with an open boundary condition in which the
chemical potential is periodically modulated~\cite{dsen13}, such that $\mu (t) = \mu
(t+T)$, with $T=2\pi/\omega$, where $\omega$ is the driving frequency, so that
$H(t)$ in Eq.~\eqref{eqn_H} satisfies $H(t)=H(t+T)$.
For a time-periodic Hamiltonian $H(t)$, the stroboscopic time-evolution operator
(i.e., the Floquet operator) is defined as
\begin{multline}\label{eqn_U}
U_{F}=\mathbb{T} \exp \left(-i \int_{0}^{T} H (t) dt \right) = \exp(-iH_{F}T),
\end{multline}
where $H_{F}$ is the Floquet Hamiltonian and $\mathbb{T}$ denotes time-ordering.
(We will set $\hbar =1 $ in this paper).

We recall that due to the unitary nature of the Floquet operator $U_{F}$, its
eigenvalues
are phases. Further, these appear in complex conjugate pairs, $e^{i\theta}$ and
$e^{-i\theta}$ (see Appendix~\ref{app_method} for details). If present, Majorana edge modes correspond to the eigenvalues $+1$ and $-1$ of the Floquet operator ($U_{F}$). In other words, their corresponding Floquet quasienergies are $\epsilon_{F}=0$ and
$\epsilon_{F}=\pm \pi/T$, respectively. Thus, the number of Majorana
edge modes is given by the total number of eigenvalues $+1$ and $-1$ of $U_{F}$.

\begin{figure}
\centering
\includegraphics[scale=0.4]{low_freq_log.pdf}
\centering
\caption{DEE ($S_{D}$) in units of $\ln (2)$ as a function of the length $L$ (in log-log scale) of a
Kitaev chain (with $L_{D}=L/4$) in which the chemical potential $\mu$ is periodically modulated by $\delta$-pulses (Eq.~\eqref{eq_delta}) having $\mu_{0}=2.5$, $\mu_{1}=0.2$, and $\omega=1$. We
observe a saturation to an integer-quantized value as $L$ increases establishing that
the discrepancy observed for low $\omega$ in Fig.~\ref{fig_delta} is a finite-size
effect.} \label{fig_L} \end{figure}

We now consider the protocol in which the chemical potential $\mu$ is periodically
modulated by the application of $\delta$-pulses such that~\cite{dsen13, souvik2021}
\begin{equation}\label{eq_delta}
\mu (t) = \mu_{0} + \mu_{1} \sum_{m=-\infty}^{\infty} \delta ( t -m T ),
\end{equation}
where $T=2 \pi/ \omega$. For this driving protocol, the DEE is calculated in the ground state of the Floquet Hamiltonian $H_{F}$, where all the single-particle negative quasienergy states are filled and all the single-particle positive quasienergy states are empty. The methods used to calculate the DEE from the correlation matrix are explained in Appendix~\ref{app_method}. In this driving protocol, the DEE, calculated in the ground
state of the Floquet Hamiltonian, is equal to integer multiples of $\ln(2)$, as can
be seen from Fig.~\ref{fig_dee_delta}. Thus, $S_{D}=p\ln(2)$, where $p$ is the total number of Majorana edge modes (both zero and $\pi$-modes). It is also interesting to note that the DEE
generally increases
as the drive frequency $\omega$ decreases. Further, we have verified that the value of $S_{D}/\ln(2)$ is equal to the number of Majorana modes (see Fig.~\ref{fig_no_delta}) generated by the same
periodic driving of the Kitaev chain. We reiterate that the number of Majorana modes is counted from the total number of eigenvalues $+1$ and $-1$ of the Floquet operator $U_{F}$.

However, at low drive frequencies (i.e, when $\omega$ is of the order of the hopping parameter $\gamma$), the DEE is not integer-quantized and the value of $S_{D}/\ln(2)$ differs significantly from the number of Majorana end modes. This is however a finite-size effect, as shown in Fig.~\ref{fig_L}, which demonstrates that the DEE does saturate to an integer-quantized value for large system size $L$. The reason for the finite-size effect is that at low frequencies, the decay lengths of the Majorana edge modes increase and therefore the edge modes mix more and more with the bulk states. When the decay length is comparable to the size $L/4$ of the disconnected region $D$, the contribution of such end modes to the DEE deviates from integer multiples of $\ln (2)$. This leads to the reduction of the entanglement between the edge modes. On the other hand, at low frequencies, the bulk states become long-range entangled (as the effective range of couplings appearing in the Floquet Hamiltonian increases with decreasing drive frequency) and contribute to the DEE computed from the Floquet Hamiltonian. For small $\omega$, therefore, the deviation of the DEE from integer-quantized value occurs due to the competition between these two contradictory effects. As the length $L_{D}=L/4$ is increased, the bulk contribution to the DEE decreases. Also, with the increase of $L$, the dispersion of the edge modes to the bulk states decreases, even at low drive frequencies. Thus, for sufficiently large $L$ (and therefore sufficiently large $L_{D}=L/4$), the bulk contribution becomes negligibly small and the DEE only contains the integer-quantized contribution of the edge modes.

We also observe a similar behavior of the DEE for periodic modulation of the chemical potential with a square pulse and sinusoidal variation, as shown in Appendix~\ref{sec_sq}. Further, the DEE is equivalent to the dynamical (Floquet) winding number in counting the number of emergent Floquet Majorana modes; this is discussed in Appendix~\ref{sec_winding}.

\section{DEE for periodic modulation of chemical potential in presence of spatial disorder and temopral noise}\label{sec_disorder}

In this section, we discuss the behavior of the DEE for a periodically driven Kitaev chain in the presence of spatial disorder as well as temporal noise, and we establish that the Floquet Majorana modes are robust against weak spatial and temporal disorder.

\subsection{DEE for periodic driving in presence of spatial disorder}\label{sec_spatial}
\begin{figure}
\centering
\includegraphics[scale=0.45]{sd_spatial.pdf}
\centering
\caption{DEE ($S_{D}$) in units of $\ln(2)$ as a function of $\omega$ for the driving protocol in the presence of spatial disorder, as in Eq.~\eqref{eq_mu_spatial}. Here, we have chosen $\mu_{0}=2.5$, $r=0.2$, $L=200$ and $L_{D}=50$. $\beta_{n}$ assumes a random value in the range $[0,1]$. Here, $S_{D}$ has been calculated after taking average over a large number of configurations of random numbers.} \label{fig_spatial} \end{figure}

We consider a driving protocol where the on-site potentials $\mu_{n}(t)$ for different sites are driven with $\delta$-pulses of random amplitudes, such that the translational symmetry of the chain is explicitly broken. Therefore, we consider the following form of the chemical potential,
\begin{equation}\label{eq_mu_spatial}
\mu_{n} (t)= \mu_{0} + r \beta_{n} \sum_{m=-\infty}^{\infty} \delta(t-mT),
\end{equation}
where $n$ denotes the site number in the chain, $\mu_{0}$ and $r$ are independent of $n$, and $\beta_{n}$ can assume a random value in the range $[0,1]$.

After taking the average over a large number of configurations of random numbers, we find
that the value of the DEE, calculated in the ground state of the effective Floquet
Hamiltonian, remains perfectly  integer-quantized even in the presence of weak spatial disorder for high frequency (see
Fig.~\ref{fig_spatial}). This demonstrates the robustness of Floquet Majorana modes
(both zero and $\pi$-modes) against weak disorder. However, the deviation of the DEE from integer-quantized value at sufficiently low-frequency is due to the finiteness of the system, as we have elaborated  in Fig.~\ref{fig_L} for the driving protocol without spatial disorder.

\subsection{DEE for periodic driving in presence of temporal noise}\label{sec_noise}
\begin{figure}
\centering
\includegraphics[scale=0.45]{sd_noise.pdf}
\centering
\caption{DEE ($S_{D}$) in units of $\ln(2)$ as a function of $\omega$ for the driving protocol in the presence of temporal noise, as in Eq.~\eqref{eq_mu_noise}. Here, we have chosen $\mu_{0}=2.5$, $\mu_{1}=0.2$, $r=0.2$, $L=200$ and $L_{D}=50$. $f(t)$ assumes a random value in the range $[-1,1]$ at any time $t$.} \label{fig_noise} \end{figure}

We now consider a driving protocol where the chemical potential $\mu(t)$ is spatially uniform, but is driven with $\delta$-pulses in the presence of a random noise $f(t)$ of sufficiently small amplitude $r$. We consider the following form of the chemical potential,
\begin{equation}\label{eq_mu_noise}
\mu (t)= \mu_{0} + \mu_{1} \sum_{n=-\infty}^{\infty} \delta(t-nT) + r f(t),
\end{equation}
where the function $f(t)$ assumes a random value between $[-1,1]$ at any time $t$.

For this driving protocol with the temporal noise, we find that the value of the DEE remains
invariant as shown in Fig.~\ref{fig_noise}. This indicates
the robustness of the dynamically generated Floquet Majorana modes against a
weak temporal noise in the driving.

\section{Detection of the anomalous edge modes with periodically modulated hopping parameter through DEE}
\label{sec_anomalous}

\begin{figure*}
\centering
\subfigure[]{
\includegraphics[width=0.45\textwidth]{spec_sym.pdf}
\label{fig_sp_a1_sym}}
\centering
\hspace{5mm}
\subfigure[]{
\includegraphics[width=0.45\textwidth]{ipr_sym.pdf}
\label{fig_ipr_a1_sym}}
\subfigure[]{
\includegraphics[width=0.45\textwidth]{prob_sym.pdf}
\label{fig_prob_a1_sym}}
\subfigure[]{
\includegraphics[width=0.45\textwidth]{sd_sym.pdf}
\label{fig_sd_sym}}
\caption{(a) Floquet quasienergies $\theta$ as a function of the drive frequency
$\omega$ (the two isolated lines seen near the top and bottom in the
frequency range of about $[1.4,2.2]$ correspond to anomalous end modes. The two isolated lines seen near the top and bottom in the
frequency range of about $[1.1,1.4]$ correspond to Majorana $\pi$ modes.)
(b) Inverse participation ratio (IPR) as a function of the real part of
the eigenvalue of the Floquet operator ($U_{F}$) at $\omega=1.6$ and for $L=200$. The modes with the real part of eigenvalue $+1$ of the Floquet operator are Majorana zero modes and the modes with the minimum real part of eigenvalue (if it is not equal to $-1$) of the Floquet operator are anomalous modes. There are four anomalous modes and two zero-energy modes. (c) Probability as a function of the site number for two anomalous modes with the eigenvalues $-0.7412 \pm 0.6713i$ of the Floquet operator $U_{F}$ at $\omega=1.6$. (d) DEE ($S_{D}$) in units of $\ln (2)$
as a function of $\omega$ for $L=400$ and $L_{D}=100$. For all the plots, the amplitude of the hopping parameter is periodically modulated (see Eq.~\eqref{eq_sym}) with $a=1.0$. We have taken $\mu=0$, $\Delta=0.8$ and
$\gamma_{0}=1.0$.} \label{fig_a1_sym} \end{figure*}

We now consider the periodic driving of the hopping parameter $\gamma$, which may
be complex in general, so that the Hamiltonian in \eqref{eqn_H} is modified to
\begin{multline}\label{eqn_H_trs}
H (t) = - \sum_{n=1}^{L-1} ( \gamma (t) c_{n}^{\dagger} c_{n+1} + \gamma^{\star} (t) c_{n+1}^{\dagger} c_{n} ) \\ - \mu \sum_{n=1}^{L} ( 2 c_{n}^{\dagger} c_{n} -1 ) + \sum_{n=1}^{L-1} \Delta ( c_{n} c_{n+1} + c_{n+1}^{\dagger} c_{n}^{\dagger}).
\end{multline}

 It has been established that for this type of driving protocol, modes localized
 at the edges with the eigenvalues of the Floquet operator away from $\pm 1$ (referred to as anomalous
 modes) can dynamically emerge~\cite{saha17}. We address here the question of whether
 the DEE can detect these anomalous modes.

\subsection{Periodic driving of the amplitude of the hopping parameter}
\label{subsec_sym}

We consider the following form of the hopping parameter,
\begin{equation}\label{eq_sym}
\gamma(t)= \gamma_{0} \left( 1+ a \cos (\omega t) \right), \end{equation}
where $\omega=2\pi/T$, and $a$ determines the strength of the modulation of the hopping amplitude.
Since the hopping parameter is chosen to be real, the time-reversal symmetry of the
Hamiltonian $H(t)$ is preserved, and the periodically driven chain belongs to the BDI
(Floquet) symmetry class.

To see if there are emergent anomalous modes, we plot the Floquet quasienergies $\theta$ as a
function of $\omega$ for $a=1$ in Fig.~\ref{fig_sp_a1_sym}. Evidently, for $1.5<\omega<2.0$, the
extreme values (near the top and bottom) of the Floquet quasienergies are separated by finite gaps
from the other quasienergies. The modes with these isolated values of Floquet quasienergies are
known as anomalous modes~\cite{saha17} since the corresponding eigenvalues of the Floquet operator
differ from $\pm 1$.

In Fig.~\ref{fig_ipr_a1_sym}, the variation of the inverse participation ratio (IPR) is plotted against the real part of the corresponding eigenvalues of the Floquet operator for $\omega=1.7$. (For a normalized wave function $\psi_j (n)$, where $j$ labels the wave function and $n$ denotes the site index, the IPR is defined as $\sum_n |\psi_j (n)|^4$. It is known that as the system size $L$ is taken to infinity, the IPRs of modes which are extended in the bulk go to zero while the IPRs of modes localized at the ends remain finite. Hence a plot of the IPR versus $j$ provides an easy way to identify the edge modes). From this figure, it can clearly be seen that the anomalous modes [which have the minimum real part (not equal to $-1$) of the eigenvalues of the Floquet operator] have relatively large IPRs, compared to the other modes having non-zero Floquet quasienergies. We note here that the IPRs of the anomalous modes are almost comparable to that of the zero-energy Majorana modes (with the eigenvalue of the Floquet operator being equal to $+1$). Fig.~\ref{fig_prob_a1_sym} further confirms that these anomalous modes, despite having non-zero Floquet quasienergies, are localized at the edges of the chain~\cite{saha17}.

In Fig.~\ref{fig_sd_sym}, the DEE ($S_{D}$) is plotted as a function of the
drive frequency $\omega$ to find the contribution of both the anomalous modes and the zero-energy modes to the
DEE. As is evident from Fig.~\ref{fig_sd_sym}, in the approximate range of frequencies between $[1.6,1.8]$, the non-zero and integer-quantized
contribution of the anomalous modes and the zero-energy modes to the DEE enables us to detect these edge
modes. In this range of frequencies, there are four anomalous modes and two Floquet zero-energy Majorana modes (two zero-energy Majorana modes are generated at $\omega=2$ for $\gamma_{0}=1$, as can be seen from the analytical calculation provided in Appendix~\ref{app_gap}) and the DEE is nearly equal to $6\ln(2)$. Thus, we observe that $S_{D}/\ln(2)$ matches
exactly with the total number of edge modes (the zero-energy Majorana modes as well as the anomalous modes) for $1.6 \lesssim \omega \lesssim 1.8$. In this range of frequency, the DEE is able to detect the anomalous modes and zero-energy Majorana modes. Subsequently,
we will illustrate in Sec.~\ref{sec_an_disorder} that the zero-energy Floquet Majorana modes are robust against weak spatial disorder while the anomalous modes are not.

\subsection{Periodic driving of the phase of the complex hopping parameter}
\label{subsec_brk}

Now we consider the hopping parameter to be complex~\cite{saha17}, with the form
\begin{equation}\label{eq_brk}
\gamma(t)= \gamma_{0} \exp \left[ i a \cos (\omega t) \right], \end{equation}
where $\omega=2\pi/T$, and the parameter $a$ determines the strength of the
modulation of the phase of the hopping parameter. The complex hopping parameter in
Eq.~\eqref{eq_brk} explicitly breaks the time-reversal symmetry of
the Hamiltonian $H(t)$~\cite{trs_sen13,saha17}. Therefore, a chain periodically driven with this protocol belongs to the D (Floquet) symmetry class. For this driving protocol, similar to the protocol discussed in Sec.~\ref{subsec_sym}, zero-energy Floquet Majorana modes and anomalous modes appear. However, we find that the DEE, calculated using the methods provided in Appendix~\ref{app_method}, is not able to count the anomalous edge modes and zero-energy Majorana modes correctly for this driving protocol.

\subsection{Effect of spatial disorder on the DEE for periodic driving of hopping parameter}\label{sec_an_disorder}

\begin{figure}
\centering
\includegraphics[width=0.45\textwidth]{sym_disorder.pdf}
\caption{DEE ($S_{D}$) in units of $\ln (2)$ as a function of drive-frequency ($\omega$) for periodic driving of the amplitude of the hopping parameter in the presence of spatial disorder (see Eq.~\eqref{eq_sym_disorder}). We have taken $L=200$, $L_{D}=50$, $\Delta=0.8$, $\mu=0$, $\gamma_{0}=1.0$ and $a=1.0$. For this protocol, $\nu_{n}$ assumes a random value in the range $[0,1]$ at each site $n$. The DEE has been calculated after taking the average over a large number of configurations of random numbers.} \label{fig_sym_disorder}	 \end{figure}

In this section, we investigate whether the dynamical zero-energy Majorana modes and the anomalous modes discussed in Sec.~\ref{subsec_sym} survive in the presence of weak spatial disorder. To this
end, we explore the effects of disorder on the DEE for a periodic driving of the nearest-neighbor hopping amplitude.

Let us consider the driving protocol where the amplitude of the nearest-neighbor hopping parameter $\gamma_{n}(t)$ for the $n$-th site is periodically modulated in
the presence of spatial disorder. Therefore, this is the same driving protocol as in Eq.~\eqref{eq_sym}, but in the presence of spatial disorder. For this driving protocol, $\gamma_{n}(t)$ is given by,
\begin{equation}\label{eq_sym_disorder}
\gamma_{n}(t)=\gamma_{0} (1+ a \nu_{n} \cos(\omega t)),
\end{equation}
where $\gamma_{0}$ and the modulation strength $a$ are independent of site index $n$, and $\nu_{n}$ assumes random value in the range $[0,1]$ for each site $n$. From Fig.~\ref{fig_sym_disorder}, it can clearly be seen that for $1.6 \lesssim \omega \lesssim 1.8$, the DEE is almost constant and equal to $2\ln(2)$ in the presence of spatial disorder. On the other hand, in the absence of disorder, the DEE is equal to $6\ln(2)$ (as there are four anomalous modes and two zero-energy modes) in the same range of $\omega$ (see Fig.~\ref{fig_sd_sym}). From this observation, we infer that the two zero-energy modes remain robust against spatial disorder, whereas the four anomalous edge modes disappear in the presence of spatial disorder.\\

\section{Conclusions}
\label{sec_conclusion}

In this paper, we have shown that for the periodic driving protocol of the
chemical potential, the DEE, calculated in the ground state of the Floquet
Hamiltonian, is integer-quantized, with the integer being equal to the total number of
dynamically generated Floquet Majorana edge modes. Thus, it can be inferred that
similar to the static situation, the DEE can act as a marker of Majorana edge modes
even for a periodically driven Kitaev chain.
At low frequencies, there is an apparent discrepancy and the value of $S_{D}/\ln(2)$
differs significantly from the number of Majorana end modes. However, this is an
artefact of the finite size of the system, and we have established
that the DEE saturates to an integer-quantized value at large system size $L$, even
at low drive frequencies ($\omega$ of the order of the hopping amplitude $\gamma$).
Thus, in a periodically driven chain with open boundary conditions, the DEE
counts the number of edge Majorana modes correctly and therefore plays a role similar
to that played by the winding number derived from the Floquet Hamiltonian in the
corresponding system with periodic boundary conditions.

If the amplitude of the nearest-neighbor hopping in the
Kitaev chain is periodically modulated (see the protocol in Eq.~\eqref{eq_sym}), such that the Floquet Hamiltonian remains in the BDI symmetry class, then
``anomalous" edge modes (with Floquet quasienergies not equal to zero or $\pi$) can be
dynamically generated. Although these anomalous edge modes do not have a topological
origin and are not associated with a winding number, we find that the DEE is
able to detect the existence of the anomalous edge modes
for certain ranges of driving frequencies. Furthermore, we illustrate that the anomalous edge modes are not robust against weak spatial disorder, and they disappear in that situation while the zero-energy Majorana modes survive.

The dynamical generation of anomalous edge modes is also possible with the periodic modulation of the phase of the complex hopping parameter (see the driving protocol in Eq.~\eqref{eq_brk}, where the system belongs to Floquet D symmetry class). However, for this driving protocol, the DEE fails to detect them properly. Further, we have checked that one cannot infer conclusively
the effects of disorder on both zero-energy and anomalous modes in the presence of spatial disorder. Why the DEE fails to detect edge modes of both types when the Floquet Hamiltonian is in the symmetry class D is an unresolved question at the moment that requires further investigation.

We conclude by noting that recently the topological entanglement entropy has been measured experimentally for a two-dimensional toric code model \cite{satzinger21}; the quantity has been measured experimentally using simulated anyon interferometry and extracting the braiding statistics of emergent excitation~\cite{satzinger21}. On the other hand, in the present work, we have computed the DEE for one-dimensional Kitaev model where anyons do not exist. We are also not aware of an equivalent of the DEE in two-dimensional
situations.
This experiment however provides a motivation
for an experimental measurement of the DEE for one-dimensional topological systems and a possible generalization of the DEE for two-dimensional systems.

In conclusion, we note that it would be interesting to investigate out-of-equilibrium behavior of the DEE in Kitaev chains with more complicated interactions, like
next-nearest-neighbor hopping and superconducting pairing~\cite{trs_sen13, bsourav18}.

\begin{acknowledgments}
S.M. acknowledges financial support from PMRF fellowship, MHRD, India. D.S. thanks SERB, India for funding through Project No. JBR/2020/000043. A.D. acknowledges support from SPARC program, MHRD, India and SERB, DST, New Delhi, India. We acknowledge Souvik Bandyopadhyay and Sourav Bhattacharjee for comments.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Q: What is a good strategy for handling Complex Right Outer Joins in LINQ / EF I have this Model

My goal is to retrieve all resources for a user except for resources that share a restricted role with that user.
This is not too hard in straight SQL (6BA60C09-2873-46A5-BAFB-5996A6C6482B is the userid)
SELECT distinct r.Name
FROM  dbo.Resources xr
INNER JOIN [dbo].[x_Resource_RestrictedRole] rr ON  xr.Id = rr.ResourceId
INNER JOIN [dbo].[aspnet_UsersInRoles] ur ON ur.RoleId = rr.RoleId
    AND ur.UserId = '6BA60C09-2873-46A5-BAFB-5996A6C6482B'
RIGHT JOIN dbo.Resources r on r.id = xr.id
WHERE xr.id IS NULL

I can't figure out a good strategy for this in EF because I don't have access to the association tables.
Can this be done in LINQ or lambda expression?

A: You have some sort of question but I will try to answer about your query
var y = (from xr in context.Resources
         join rr in context.x_Resource_RestrictedRole on xr.Id equals rr.ResourceId
         join ur in context.aspnet_UsersInRoles on rr.RoleId  equals ur.RoleId
         join r in context.Resources on xr.id equals r.id into rJoin
         from r2 in rJoin.DefaultIfEmpty()
         where xr.id == null && ur.UserId = "6BA60C09-2873-46A5-BAFB-5996A6C6482B"
         select new { r.Name }).Distinct(c => c.Name).ToList();

redpajama_set_name: RedPajamaStackExchange


text:
Keywords: demolition; environmental impact; evaluation; materials; overheads; recycling; transport
URL: http://etheses.whiterose.ac.uk/15041/
There are many important environmental issues involved in the construction and use of buildings which are either undergoing or require further research. The lack of detailed embodied energy assessments models has been identified and limits possible environmental analysis. This study examines the current state of research into the environmental impact of frame materials, assesses the quality and range of data available, sets up a new framework for evaluation of materials and uses several example structures to assess the environmental impact This has been achieved by, firstly, studying the environment related literature available concerning the frame of the building, separate from other considerations, to provide a clear understanding of the processes involved. Second, data is extracted from the literature and processed to provide a homogenous approach and level field from which frame analysis can take place. Gaps in the available data are identified. Third, the identified gaps are filled using data derived from sources ranging from manufacturers' literature to direct analysis of on site activities. Fourth, a model has been created to assess the environmental impact of the building frame. The factors assessed within the remit of environmental impact are: embodied energy, embodied CO2 and transportation hours. The embodied energy includes the primary energy for all raw materials, transportation, office overheads and contractor operations. These are calculated from the winning of raw materials, through manufacture, to demolition and recycling. Embodied CO2 encompasses the same range of data, but with respect to the CO2 transportation hours estimate the time spend on the road by vehicles involved in the embodied energy and CO2 calculations. Finally data from several buildings has been used, to evaluated the environmental merits of each with respect to each other and to other buildings for which calculations have been performed. Conclusions have been draw and. further work suggested.
Cho, C, Kim, K, Park, J and Cho, Y K (2018)

redpajama_set_name: RedPajamaCommonCrawl


A Dual Weighting System lowers of the Center of Gravity (CG) and increases the Moment of Inertia (MOI) for improved performance and forgiveness. A sculpted sole facilitates solid contact through the impact area from virtually any lie. Constructed of a 17-4 stainless steel body and 465 maraging steel face for maximum initial ball velocity and distance. A brushed steel top-line encourages a square alignment.


text:
Previous / Team ORECA-Matmut LMP2 Prepare For 24 Hours Of Le Mans Next / Peugeot Aims For Le Mans 24 Hour Victory
Johnny Mowlem Prepared For Le Mans 24 Hour
La Sarthe Circuit
LOTUS RETURNS TO THE FAMOUS LE MANS 24 HOURS, MOWLEM PREPARES.
It's a busy time of year for globe-trotting racing drivers with the biggest and most important race of the sports car season looming large.
Still, its normal procedure for those among the best drivers in the world: Take part in a number of 24-hour race simulations as a team prepares as well as possible for the gruelling prospect of 24 hours non-stop action behind the wheel.
#65 Lotus Jetalliance Lotus Evora: Jonathan Hirschi, James Rossiter, Johnny Mowlem
Photo by: Lucien Harmegnies
The 24 Hours of Le Mans is next up for Britain's Johnny Mowlem.
For the new Lotus Ever GTE race car there is one last 24 hour test on May 28-29. Before that Mowlem will be commentating for SKY Television for the famous Indy 500 race, then he drives straight up to the Lotus test facility to conduct the two-day test. Mowlem gets three days at home before a zip across the Channel from his home in England to France for an official inspection of the Lotus Evora GTE car on June 5. Then there is practice and qualifying on the 8th and 9th of June, the famous drivers parade around the town of Le Mans on the 10th June and finally, on June 11, the start of one of the world's toughest races.
Mowlem, who is a Lotus factory driver, and his teammates James Rossiter and Jonathan Hirschi, will pilot the Jet Alliance Lotus Evora. This is the first time in nearly two decades that Lotus will be racing at Le Mans, and everyone is focused on making the return a successful one.
"We've done a great deal of work on this car, but it is really still in the development stage," Mowlem said. "It's a tribute to the company and everyone involved and their determination to succeed that we have come so far in such a short amount of time. Le Mans will be the biggest test yet for the car, and having done this race quite a few times already, I know what a huge test Le Mans can be! The race will all be about us against the circuit. If we can run cleanly and reliably, the opposition can take care of themselves, and then who knows what might happen!"
Mowlem has seven Le Mans starts, including a class podium as well as another top 10 overall finish.
The race begins on June 11.
-source: johnnymowlem.com.
Team ORECA-Matmut LMP2 Prepare For 24 Hours Of Le Mans
Peugeot Aims For Le Mans 24 Hour Victory
Jonathan Hirschi
Manor hit with seven-minute penalty for Nurburgring race
Porsche completes driver lineup with Hartley and Lieb
3 Hours of Paul Ricard: Murphy Prototypes race winners with the ORECA 03
Peugeot must race at Sebring or Spa for Le Mans 24 Hours entry
Esports Esports
Champions sign up for 24 Hours of Le Mans Virtual by Motorsport Games
What could have been: When Carlos Sainz's Le Mans debut was scuppered
Third Toyota at Le Mans for Ogier "an option" for 2023
What we've learned from the Le Mans 24 Hours so far
The new dawn for the FIA World Endurance Championship has arrived at Le Mans, as Hypercars prepare to duel for victory in the world's oldest endurance race. Motorsport.com picks out the 10 things we have learned in the build up to the race.
Le Mans 2021: The team-by-team guide
After a two-month delay due to the ongoing impact of the COVID-19 pandemic, the 2021 Le Mans 24 Hours is set to get underway with the start of the Hypercar era at the Circuit de la Sarthe.
The ex-F1 drivers making a name for themselves in LMP2 at Le Mans
Kevin Magnussen will make his Le Mans 24 Hours debut this weekend alongside father Jan in LMP2. But the Danes won't be the only ex-F1 drivers to appear in the hotly contested category this year.
Can Toyota's #7 crew break its Le Mans curse?
One Toyota, normally with the number 7 on the side, always seems to attract the bad luck in the Le Mans 24 Hours. Mike Conway, Kamui Kobayashi and Jose Maria Lopez are hoping for a change in fortune this time around, but face significantly more unknowns than in recent years
How to prepare an amateur for Le Mans sensory overload
By Marco Seefried
The 23-car GTE Am field promises to be one of the most open in this year's Le Mans 24 Hours, with the added jeopardy of managing the enthusiasm of amateur drivers to boot, as Absolute Racing Porsche driver Marco Seefried explains


Satire, a humorous attack or criticism aimed at political leaders, celebrities, institutions or the media, has had a global resurgence during the past decades. In the United States, The Daily Show, The Colbert Report, Last Week Tonight with Jon Oliver and Full Frontal with Samantha Bee became some of the most influential political shows on cable TV. While all of these shows have a strong online presence, some found on the internet their main venue. Online comedy shows, such as Between-Two-Ferns, from websites like Funny or Die, College Humor, and Comedy Central, have developed critical humor for the millennial generation. This is, of course, a global phenomenon. Latin American YouTubers and digital savvy comedians have also targeted the social and political tensions of their countries through digital videos.
Here are ten online satiric TV shows from Latin America that you need to know.
Created by feminist comedian Malena Pichot, Cualca (2012-2015) was an Argentinean satiric sketch show focused on sexism and gender issues. The name of Cualca comes from a colloquialism that loosely means "whatever." It was initially included as a segment of the TV show Duro de Domar, but its viral videos became popular online throughout the region.
Argentinian Federico Simonetti turned from stand-up to satire when he started País de Boludos in 2017. This weekly online show tackles various controversial topics affecting Argentina, from abuse of the indigenous by corporations, to protests for women's rights.
Greg News is a late night talk show on HBO Brazil airing since 2017. The host, Gregório Duvivier, was a star on and co-creator of the hit online channel Porta dos Fundos. Inspired by Last Week Tonight with John Oliver, Duvivier uses satire to engage with Brazilian and international news alike.
Porta Dos Fundos is a Brazilian YouTube channel started in 2012 which satirizes social and cultural issues of contemporary urban Brazil. From Whatsapp to the Ten Commandments, there are few topics Porta Dos Fundos, which translates to "back door", leaves untouched.
María Paulina Baena is the host of La Pulla, a video column put out by El Espectador, Colombia's oldest newspaper. Her videos have been a hit, particularly with the millennial generation. Her no-nonsense style has enabled La Pulla to tackle issues from abuse of domestic employees in Colombia to the political situation in Venezuela.
Like La Pulla, Las Igualadas is a video column put out by El Espectador, Colombia's oldest newspaper. Las Igualadas, hosted by Mariángela Urbina, specializes in gender issues in Colombia. The name takes ownership of colloquialism used to describe women who are deemed disrespectful or ignorant of authority.
El Pulso de la República is a popular online show developed and hosted by Chumel Torres. A mechanical engineer by training, Chumel was inspired to create a Mexican version of the late night satirical news shows so popular in the US. Since 2012, his program has identified and criticized the peculiarities of Mexican news and politics.
Gerardo García, better known as 'El Juan' or 'El Cacash', is a Peruvian YouTuber who has been making satirical videos since 2012. His videos even come with a disclaimer, preparing one for El Juan's tell-all style and El Cacash's street-style humor.
GCU (Gente como Uno) was a digital satiric TV show released from 2014-2017 through Utero.pe, a popular news and entertainment portal based in Lima. GCU's fictional host (a hyper-conservative, bigoted, and ignorant interviewer) parodied and took to the extreme some of the most prevalent social prejudices in Peru shown daily in national TV and the press.


Howdy, we are continually improving our help center with new helpful content and excellent howtos. Please write to us if you have any issue not covered in this documentation center and we would be happy to assist you. We usually answer within 3-12 hours.


Research Statement: Our research interests are in the origin and evolution of new gene function focusing on genes that are involved in Diabetes.
Origin and evolution of new gene function. We have studies a number of genes that have acquired novel functions in vertebrates. An example is the proglucagon gene. To understand the evolution of proglucagon genes we have both cloned and characterized proglucagon genes from diverse vertebrate species as well as mined these sequences from diverge molecular sequence databases. We then analyze these sequences suing a variety of molecular evolutionary tools to better understand changes in their sequences and their potential function. Similar studies have been conducted on genes associated with proglucagon function (e.g., receptors).
We are involved in a number of collaborations (Peking University, East China Normal University, and the Kunming Institute of Zoology, Chinese Academy of Sciences) on genes involved with cancer, diabetes and evolution of new physiological functions.
Dr. David M. Irwin is a Professor in the Departments of Laboratory Medicine and Pathobiology and Ecology and Evolutionary Biology at the University of Toronto, Canada. He is also a member of the Banting and Best Diabetes Centre at the University of Toronto.
Dr. Irwin obtained his Ph.D. in Genetics from the University of British Columbia, Vancouver, Canada, in 1986, and then completed a post-doctoral fellowship in the Department of Molecular and Cellular Biology, University of California, Berkley. He joined the University of Toronto in 1991 as Assistant Professor in the Department of Clinical Biochemistry. He was promoted to full Professor in 2006.
Diversification of the functions of proglucagon and glucagon receptor genes in fish.
Multiple specialised goose-type lysozymes potentially compensate for an exceptional lack of chicken-type lysozymes in Atlantic cod.
Seppola M, Bakkemo KR, Mikkelsen H, Myrnes B, Helland R, Irwin DM, Nilsen IW.
Sci Rep. 2016 Jun 21;6:28318. doi: 10.1038/srep28318.
Bats: Body mass index, forearm mass index, blood glucose levels and SLC2A2 genes for diabetes.
Meng F, Zhu L, Huang W, Irwin DM, Zhang S.
Sci Rep. 2016 Jul 21;6:29960. doi: 10.1038/srep29960.
Genomic analysis of snub-nosed monkeys (Rhinopithecus) identifies genes and processes related to high-altitude adaptation.
Yu L, Wang GD, Ruan J, Chen YB, Yang CP, Cao X, Wu H, Liu YH, Du ZL, Wang XP, Yang J, Cheng SC, Zhong L, Wang L, Wang X, Hu JY, Fang L, Bai B, Wang KL, Yuan N, Wu SF, Li BG, Zhang JG, Yang YQ, Zhang CL, Long YC, Li HS, Yang JY, Irwin DM, Ryder OA, Li Y, Wu CI, Zhang YP.
Nat Genet. 2016 Aug;48(8):947-52. doi: 10.1038/ng.3615. Epub 2016 Jul 11.


Arriving at University of Limerick was so nerve-racking. I didn't know anyone or where anything was. Even after orientation week, I was still confused on where to go and what to do; I had so much information thrown at me that I couldn't keep it all straight. Despite knowing people from my home school that studied abroad in Limerick last spring, I completely forgot the advice they gave me. I was so overwhelmed and excited to be here. I wanted to provide a quick crash course on adjusting to life at the University of Limerick!
A student Leap Card is used for the Bus Éireann buses that go into the Limerick City Center and other places around Ireland. The regular price for a one-way ticket into the city is €2.40. If you get the Leap Card, you get discounted fares and the price goes down to €1.70.
I worked out my class schedule so that I have Thursdays and Fridays off. This way, when I have free time, I can take the bus into the city to get lunch or go shopping. The buses are really helpful and can take you to several places around Limerick. They run about every 15-20 minutes and stop at three places on campus, so you'll always be able to catch it to go somewhere! Buses usually run until about midnight, so if you go out during the evening you can still take the buses back.
The International Society is kind of self-explanatory. but it's a club on campus for all the international students. They offer great trips around Ireland, fun activities during the week and have their own dedicated night at the on campus pub.
The trips they take you on are all over the Emerald Isle. Some trips are just for the day and others are for a whole weekend. I went on a few and they were so fun! I got to meet new people and see the beautiful views that Ireland has to offer. I went to Glendalough, Dingle, Kenmare and a few other towns. The day trips cost about €12-20, which is a fair price considering the amazing places you get to see.
On Friday nights at the on-campus pub, Stables, you are able to get in for free as a member of the International Society before a certain time. Each Friday has its own theme, some being "wear your country colors," "decades night," and "stoplight party." The International Society is a great way to get to make friends and meet people from all over the world!
There are certain classes that are only offered to the international students at the University of Limerick. They are the classes that are about Ireland, Celtic history, folklore and other things relating to the Irish culture.
This semester I am enrolled in Irish Music and Dance. We have a lecture where we learn about both, and then we got to chose which of the two we wanted to learn in a more hands-on way. The options were the tin whistle, the bodhrán (a drum), song or dance. My friends and I chose dance, even though we have absolutely no dance experience.
I definitely recommend this class to anyone who is looking to learn about the history of Irish music and dance, but and wants to learn in a hands-on way. At the end of the semester, the whole class puts on a performance and anyone is welcome to come!
The Shack is an amazing donut shop. It's right in the City Center and there are banners outside so you can't miss it! They have deals for student and loyalty cards. If you get a loyalty card, you have to buy 8 donuts and the 9th is free. Let me tell you, its very easy to get those 8 donuts so quickly. On Wednesdays, they have a BOGO deal for students; I recommend taking advantage of that. Another great deal they have is 3 donuts for €8 euro. Each donut is €3 so if you and 2 friends are looking for a snack, go to The Shack.
This post was contributed by Laura Prioletti, a student from St. John Fisher College who is spending her spring semester studying abroad with AIFS in Limerick, Ireland.


text:
Mohammed "Moa" Abdellaoue, född 23 oktober 1985 i Oslo, är en norsk före detta fotbollsspelare (anfallare) av marockansk härkomst. Han spelade under sin karriär för det norska landslaget. Hans yngre bror Mostafa Abdellaoue, känd som "Mos", är också en fotbollsspelare.

Externa länkar

 Mohammed Abdellaoue på ESPNsoccernet
 Mohammed Abdellaoue på uefa.com

Norska fotbollsspelare
Norska landslagsspelare i fotboll
Spelare i Skeid Fotball
Spelare i Vålerenga IF Fotball
Spelare i Hannover 96
Spelare i VfB Stuttgart
Spelare i Tippeligaen
Spelare i Fußball-Bundesliga
Födda 1985
Levande personer
Män
Idrottare från Oslo

redpajama_set_name: RedPajamaWikipedia


A lavishly illustrated book that offers an in-depth look at the cultural practices surrounding the tradition of collecting ancient bronzes in China during the 18th and 19th centuries.
An unprecedented in-depth guide to one of the world's most spectacular collections of ancient chess and games pieces.
One of the world's leading anthropologists assesses the work of the founder of structural anthropology.
Die Ausstellung untersucht den Einfluß der japanischen Kunst auf das Schaffen der impressionistischen und postimpressionistischen Künstler von 1860 bis in die Anfänge des 20. Jahrhunderts.
This sumptuously illustrated volume examines the impact of indian art and culture on Rembrandt in the late 1650s.
Through a series of essays, photographs, and archival content, this book highlights the diverse young and old diaspora communities of the Middle East and North Africa (MENA) around the world.
In this precious and delightful book, Felice,Beato and his outstanding photos transport the reader to the world of fascination and mystery of 19th-century Japan.
A beautiful book that presents nearly four centuries of artistic creation from one of the largest former princely states in India, the kingdom of Marwar-Jodhpur in southwestern Rajasthan.
Now available in a new edition, this gorgeously illustrated book showcases botanical masterpieces by Alexander von Humboldt, one of history's great scientists and explorers.


In parallel, additional workshops, forums, information events and tours provide a platform for innovative ideas and solutions that will transform the market. A further highlight of the exhibition is the Intersolar AWARD Ceremony.
Your exhibition ticket enables you to attend the ees Europe, Power2Drive Europe and EM-Power.


What's special about this network cabling tester?
The LAN Cable Tester is a great instrument for verifying the pin configurations for patch cords and cable installations quickly and easily. This compact tool can perform the job of many without taking up too much space or requiring you to carry around a lot of equipment.
- This basic Local Area Network tester is designed to test 8P8C network cables, but can also test RJ11 four or six pin connections.


SARA portends to disrupt the world's current understanding of and consumption of radio and mobile audio. The universally standard system that serves what will be interactive radio will also generate a host of beneficiaries. In targeting the most pervasive handset technology on the planet to reach all peoples, SARA will drive considerably more traffic to cellular networks and introduce opportunities to dramatically increase wireless revenues for all carriers and content providers.
Consider radio. People listen longer. Their consumption is not transactional; it is driven by desirable content pushed to a largely passive audience satisfied to delegate to a broadcaster the active involvement with selecting audio. Now consider this: radio is not portable. That's right. Radio is trapped in our cars; radio is built into our home theaters and our bedside alarm clocks. But even though radio waves are all around us, radio is not portable. Radio hasn't been portable since the beginning of this century when it became clear that there's only room in our pockets for one device. Nobody carries a transistor radio. Everybody carries a phone. And those phones can go everywhere radio goes as well as everywhere radio cannot.
Over the past twenty years radio broadcasters have lost a major share of audience. They don't realize this because weekly tune-in to AM/FM is still enormous. But this vast listenership might listen even more to radio if it was truly as portable as cell phones. After all, most audio is consumed on-the-go.
This puts carriers in a position to leapfrog broadcast radio. Their networks are completely cohesive; every radio listener also has a cell phone so a wireless audience is already out there and proven. And carriers can deliver the killer app: interactivity. Carrier network traffic has historically been transmissions of brief one-to-one exchanges of information – voice calls. Much of this traffic now moves in the form of lower cost texts and email, and carriers increasingly rely on data subscriptions to drive revenue. The cohesive voice infrastructure goes under-monetized and unnoticed as a platform ripe for infotainment-centric audio content delivery, a platform for Radio 2.0.
Telephones today are no longer mere conduits for two-way conversation. With cognitive computing, interactivity enables the delivery of personalized audio streaming that rivals what smartphone apps deliver. Interactivity also enables instant purchasing and transacting with advertising and content. All on a platform as pervasive as radio, and with a national, not localized, presence. Moving radio consumption to carrier networks drives traffic, extended usage, and creates access to transactional and other new income streams. Carriers can dramatically increase wireless revenues while revolutionizing radio and mobile audio streaming for a one-to-one relationship with each subscriber/listener.
Mobile audio apps don't generate incremental income to carriers. Mobile audio apps compete with social, games and video on what is not a level playing field – and they are losing the competition for consumer interest. That's the insurmountable dilemma for any app maker contending with the consumption-limiting mobile data user's hierarchy of needs. But what seems like a dire situation actually teaches the path for carriers to increase wireless revenues and ARPU while simultaneously casting a survival lifeline to audio providers. Adoption of the voice line to deliver mobile audio content dramatically increases usage of underutilized cohesive infrastructure and presents opportunities to monetize that consumption and increase wireless revenues with an interactive location-aware service superior to today's radio.
The most successful and entrenched platform for mobile audio remains radio. Compatible devices are pervasive and radio network infrastructure nearly as so, though regionally fragmented. Not television or home-based Internet coverage rivals the reach and universal adoption of radio. But wireless telephony does. And the cohesive infrastructure that supports wireless telephony also enables seamless national coverage and reach of a radio alternative.
Radio is still massively successful because of fundamental factors that any audio provider would be wise to emulate, but most importantly, radio is pervasive, standardized, universal and simple to use – just like telephones. Today's generation of mobile audio apps are none of these things.
Wouldn't the most logical platform for mobile consumer audio be the one with a device penetration that rivals radio and requires no learning curve to adoption and use? Wireless carriers have already built-out the cohesive networks that combined exceed terrestrial radio's coverage while enhancing service with distinctive features including interactivity and personalization. Carriers can dramatically increase wireless revenues by monetizing their already built-out networks as conduit for mobile audio.
Diverting audio consumption to the voice line creates an access point to interactive audio for subscribers using feature phones or smartphones on metered service or without data plans – essentially doubling-to-tripling the immediate prospective audience available to discover mobile streaming audio for the first time. Instead of mobile audio being relegated to a small segment of smartphone users, it can be immediately accessible to anybody with a phone.
Carriers don't need to compete with radio or audio streaming services to reap financial rewards. Carrier networks can be leveraged to extend the reach of current providers and enable enhanced services through interactivity. That was the original intention of the current generation of apps from the likes of SiriusXM and iHeartRadio.


text:
Ponam is an Austronesian language spoken on Ponam Island, just off Manus Island in Papua New Guinea.

References

Manus languages
Languages of Manus Province


text:
Q: How to redirect user to login page in JSF I use JSF 2.0 and facelets. I want to login check at each page and redirect to loginpage if it fails...
<%
HttpSession sess = request.getSession(true);

if (sess.getAttribute("userName") == null ) {
%>
<jsp:forward page="/login.xhtml"/>
<%
return;
} else {
    // some code
%>
    <%-- some other code --%>
<%
}
%>

When I write this code, Netbeans IDE won't let me.
How can I use this.
Thanks.

A: I would suggest using a filter instead of jsp. Then, define it as one of the first filters in web.xml.
public class DirectAccessBlockFilter implements Filter {

    private String loginPage = "login.xhtml";

    @Override
    public void doFilter(ServletRequest request, ServletResponse response,
        FilterChain chain) throws IOException, ServletException {
        HttpServletRequest httpRequest = (HttpServletRequest) request;
        HttpSession session = httpRequest.getSession(false);

        if(session.getAttribute("userName") == null && !httpRequest.getServletPath().contains(loginPage)) {
            RequestDispatcher dispatcher = request.getRequestDispatcher(loginPage);
            dispatcher.forward(request, response);
            return;
        }

        chain.doFilter(request, response);
    }

}

A: You cannot do that. It's completely impossible, because facelets are not JSPs. Scriptlets don't exists.
Besides, this kind of thing should be implemented in a servlet filter, not on individual pages. Furthermore, you should not do it yourself but use one of the freely available mature implementations:

*

*Apache Shiro

*Spring Security

A: Don't do it. Facelets is the default view for a reason.
The login check should instead be done in either of the following:

*

*javax.servlet.Filter

*javax.faces.event.PhaseListener

A: Like the others mentioned, you should absolutely not do it this way, even if it was possible.
Facelets is a pure XML document that's parsed by an XML parser for the sole reason of creating the component tree. As such it's only used for component layouting. There is no facility whatsoever to include any kind of scriptlet.
Technically there are a few tricks which more or less would give you the (wrong) idiom you're after. E.g. you could put that code fragment in a backing bean and call it via an EL expression at the start of each page. You could also create a Java based custom component and place that at the start of each page. Finally you could define your own custom EL function containing that code and call that.
But I can't stress enough however that such an approach is plain wrong. Use the filter or phaselistener suggested by mmanco and Bozho. If you can't live with this, then maybe JSF and Facelets is just not the best technology for you and you'll be better off programming in JSP or PHP.


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This page describes the structure of the game's source code, as found in the official SVN repository. For instructions on getting the code and building on your particular platform see Build Instructions.
binaries : Contains the game's data, scripts, and Windows executables.
build : Tools for generating the workspaces needed to build the game.
docs : Placeholder for documentation.
libraries : Libraries (third-party software) needed to build the game.
source : Source code for the engine and associated tools.
All these are covered in more depth below.
This directory contains everything that gets released to the end-user. This is the only part that an artist or designer needs to modify. The game is run from within this directory and it includes prebuilt executables for Windows users. Custom builds also end up here for Windows, Linux and OS X.
In Windows, the game is run by opening pyrogenesis.exe and the Atlas scenario editor is with Atlas.bat (which invokes "pyrogenesis.exe -editor"). These files can be found in the binaries\system\ directory and are regularly updated on SVN as the game engine changes.
This directory contains data distributed to all users of the game. However, data created during games is stored in separate locations, depending on the user's OS, see GameDataPaths for those locations.
Contains the default configuration file default.cfg, a simple text file containing pairs of key = value entries. To make changes to the configuration, use in-game options or create/modify local.cfg in the user data directory (see Manual_Settings). The presence of dev.cfg indicates a developer version of the game, not a release package, which changes how mods are handled.
keys.txt is a list of hotkey definitions which can be used in the config system.
Internationalization and Localization files for the engine.
This contains the game data and is of primary interest to the game's artists, developers and the modding community. The official mod is in the public directory. Mods may be placed in a .zip archive or left as loose files. They can be selectively loaded by users, for a different game experience.
See the mod layout page for details.
Contains some non-mod data and scripts used by the test suite.
Some data associated with tools separate from the engine itself, like Atlas and font builder.
Binaries and required libraries for the game are found here. For Windows users, the game's executables (EXEs) and libraries (DLLs) can be found here along with the game's tools. Similarly for developers building the game themselves, the binaries will end up here.
This directory is most useful for developers wishing to build the game themselves. This section will briefly describe the directory, see Build Instructions for more details on building the game for your OS.
Some utilities for the build process.
Some analysis scripts for Dehydra, a tool for custom static analysis of C++ code.
A tool for generating the error and exception codes used in the game.
Building the game is eased by an automated tool called Premake, which creates platform-specific workspaces for developers. Premake uses scripts written in Lua. Windows, Linux, and OS X are the supported environments, as are a few major IDEs (namely Visual C++ and Xcode).
Icons and data files for the game's installer.
Utility for outputting the current game build's revision number.
These are the third-party libraries currently stored in the repository, organized roughly by OS; they are not necessarily used in the final game. Here are some descriptions of the libraries and where they can be downloaded.
Contains a script for building OS X dependencies, see BuildInstructions#OSX.
Source code of modified libraries and some that may not be available in package managers. It is shared for OS X, Windows, and *nix.
Headers and prebuild static libs for win32 developers. Not used for *nix or OS X.
iconv: iconv is a computer program and a standardized application programming interface (API) used to convert between different character encodings.
This directory contains the source code of the engine and associated tools. It is almost exclusively written in C/C++. It should be noted that our convention is to place both header/include files (.h) and source files (.c/.cpp) in the same directory (see also: Coding conventions).
As there are many subdirectories, they will not all be listed here. However this may serve as a brief introduction to the codebase.
Libraries to convert COLLADA assets to the engine's proprietary format. COLLADA is the format for adding new 3D models and animations to the game and is supported by a number of free and commercial 3D modeling programs. See Art Design for more details.
Defines classes for maintaining data about what the user sees in the game world, such as objects, textures, terrain, shaders, and particles. Also includes map handling.
Internationalization and Localization support for the engine.
Low-level code for the engine, including abstractions of specific systems by OS and architecture.
Contains code to support using the XmPP-based multiplayer lobby.
Defines classes for typical mathematical operations.
Contains code related to the cxxtest suite.
Defines classes for supporting multiplayer, networked games with a server-client architecture.
Precompiled headers for faster compilation of the game.
Defines classes for rendering 3D things during the game. These are the implementations used in the rendering loop.
Contains code from third party libraries that are built as part of 0 A.D. Unlike the rest of source/ they are not written by WFG and may have different (but compatible) licensing.
This directory contains a number of tools which are to be considered largely separate of the game engine. Of these Atlas is the most useful to modders and developers.
Atlas is the name of the Scenario Editor used to create maps for the game. Atlas is not merely a data editor but uses the engine for rendering and simulation, to accurately reproduce the way maps will be handled in the game. As such the Atlas UI runs in a separate thread from the engine, messages are passed between threads to synchronize behavior.
AtlasFrontends: Contains a few stand-alone tools based on Atlas, the most useful of which is Actor Editor.
AtlasObject: Defines some helper classes for manipulating XML and JSON data in Atlas.
AtlasScript: Defines a minimal interface for scripting in Atlas, using SpiderMonkey.
AtlasUI: Define classes for the Atlas UI, which will be run in its own thread.
DatafileIO: Old code used by the AoE3Ed tool.
GameInterface: Defines the message passing and handling behavior of Atlas.
Tools for packaging the game.
Some entity tools, the most useful is checkrefs.pl, which scans a lot of game data for duplicate and missing references.
This utility builds the font textures seen in the game's UI, from font style definitions and a list of characters to include. The source fonts are located in binaries\data\tools\fontbuilder\.
Tools for Internationalization and Localization.
Scripts for opening the logs folder on Windows.
Web client for the game's built-in profiler.
Extracts profiling data from replays, for graphing purposes. See EngineProfiling.
Generates basic square and circle selection overlay textures by parsing all the entity XML files and reading their Footprint components (see script for details).
Utility to sort the component definitions of entity templates into alphabetical order.
Scripts for the multiplayer lobby.


text:
Kent Justice, Anchor/reporter
Eric Wallace, Senior Producer, I-TEAM
Published: July 17, 2016, 10:56 pm
Tags: News, Politics, Republican National Convention
Security plans in place as RNC begins
Thousands expected to descend on Cleveland this week
CLEVELAND – As 50,000 people descend on Cleveland this week for the Republican National Convention, security is one of the main topics on the minds of organizers, attendees, and Cleveland residents, amid concerns over the potential for protests and violent clashes.
Sunday afternoon, before the start of the convention, numerous streets around Cleveland's Quicken Loans Arena, the site of the convention, were blocked off to traffic. An estimated 3,000 police officers, 500 of them from Cleveland, are on hand to secure the city. Some came from elsewhere in Ohio, others came from as far away as the California Highway Patrol.
More than 4,000 U.S. government personnel will also be on hand, representing agencies including the Secret Service, the Transportation Security Administration, the FBI, the Department of Homeland Security, and the Coast Guard.
Cleveland officials have faced criticism that the city's police force is not properly trained or equipped to keep the peace.
"We have planned, we have 'what-if'ed,' we have table-topped this from day one to yesterday, and everything that can and will happen we have planned for," Cleveland Police Chief Calvin Williams said last week. But authorities have been tight-lipped about preparations, with Williams declining to elaborate, citing their "sensitive" nature.
News4Jax crime and safety analyst Gil Smith, who grew up in Cleveland, and has friends in the city's police department, says lots of planning has gone into security for such a large and high-profile event. His contacts indicate quiet concern among law enforcement, some of that due to insurance considerations for out-of-area officers, some of whom had come from California.
"They're telling me they do have a unique set of problems here," Smith said, "because you have a large convention here, so many people are for the candidate Trump and so many people are against."
Smith also referred to the potential dangers, following recent attacks on police across the country.
"You're going to have large numbers of police in areas, where the shooter in Dallas was able to shoot several police officers together, and there's no way to avoid that," Smith said.
The preparations seemed to put Cleveland residents at ease, as delegates, party activists, journalists, and others descended on their city.
"A lot of law enforcement, so I think we feel safe," said Henry Williams. "We're from here, this is our hometown and we feel good about it. We just want to impress the rest of the country and let everybody know, Cleveland is open for business."
Randy Bishop, an elected alternate delegate from Michigan, felt the convention could be a potential target for terror attacks, but felt safe, given the security measures.
"I think the police presence and the way they've coordinated the efforts are very good, I feel very secure here," Bishop said. "Haven't noticed any protesters, no incidents at all."
The convention formally begins Monday at 1 p.m. News4JAX will be speaking with members of the Florida delegation Monday and throughout the week, with live reports throughout the day as well as updates on News4JAX.com.
Kent Justice
Kent Justice co-anchors News4Jax 10 p.m. and 11 p.m. newscasts weeknights, reports on government and politics. He also hosts "This Week in Jacksonville," Channel 4's hot topics and politics public affairs show each Sunday morning at 9 a.m.


text:
Testing the test: How reliable are risk model backtesting results?
BankUnderground	Financial Markets, Financial Stability, New Methodologies	 15 January 2016 22 August 2016 7 Minutes
Emmanouil Karimalis, Paul Alexander & Fernando Cerezetti.
All models, including those which model financial risk, are in some sense "wrong" – they aim to "approximate" the real word but cannot possibly recreate it. Consequently, in a world in which risk models are used to calculate and exchange vast sums of capital and margin, the need for reliable tests is of paramount importance. The Kupiec-POF test represents the most widely-used test for assessing the reliability of these risk models (typically Value-at-Risk (VaR) models) – a process known as backtesting. As with all forms of testing, the Kupiec-POF test has a degree of error associated with its use and under certain circumstances these errors may be substantial.
Given the clear systemic risk implications of employing an erroneous model, regulators and risk managers are often concerned with so-called "Type-II" errors (i.e. the non-rejection of an incorrectly specified model). This blog reveals that the distributional nature of the profit and loss (P&L) distribution being modelled can have a significant impact upon the previously known factors driving Type-II errors.
What we already know about backtesting and the Kupiec-POF test
Risk models are not expected to produce reliable and robust risk estimates 100% of the time. Indeed when specifying a model, users build-in expectations around its accuracy often defined by the number of breaches it produces (i.e. occasions whereby the P&L of a portfolio is greater than that predicted by the model). The Kupiec-POF test therefore attempts to assess model performance by comparing the amount of breaches a user would expect a model to produce with the actual amount it does. The test is used by a range of financial institutions and has the following characteristics:
It involves hypothesis testing – i.e. it has statistical foundations.
It is two-tailed – i.e. it will fail a model if it has too few or too many breaches for a specific confidence level.
Previous research has highlighted several key relationships between the assumptions and performance of the Kupiec-POF test. In general, the likelihood of observing a Type-II error increases as:
The size of the backtesting sample falls;
The confidence interval of the risk model increases;
The Kupiec-POF test confidence level increases.
Our analysis, based upon a simulation based exercise, validates these relationships but also suggests that the test statistic underlying the Kupiec-POF test and the characteristics of the P&L distribution being modelled can have a sizeable impact on its performance.
The distribution of the Kupiec-POF test statistic
The test statistic of the Kupiec-POF test is assumed to follow a chi-squared distribution. A simple inspection of the test statistic's non-rejection area, which essentially determines whether or not the model has passed or failed, can prove to be very informative for users of the test.
Figure 1 below shows the test's relevant p-values on the y-axis and associated VaR model breaches on the x-axis at 99.5% (top panels) and 99% VaR confidence levels (bottom panels) using two sample sizes: 250 and 1000 days' worth of P&L returns. The red-shaded region denotes the non-rejection area corresponding to a 95% significance level.
Figure 1: Kupiec-POF test's p-values and non-rejection areas
The charts reveal two key observations:
As the backtesting sample size increases or the VaR confidence level declines the shape of the non-rejection area becomes "tighter" and more symmetric. This implies that if a user were to do either, the likelihood of experiencing a type II error would be lower.
Perhaps more interestingly, when the sample size is small (e.g. 250 days) or the VaR confidence level is high (e.g. 99.5%) the shape of the non-rejection area is skewed and bounded to the left. This indicates that the test will struggle to reject a risk model producing zero breaches even if the test has been designed to do so.
These findings suggest that the previously-known limitations of the Kupiec-POF test are, in fact, partly attributable to its statistical foundations.
Interesting results from our simulation-based analysis
One method of assessing the performance of any type of test is to create an artificial environment in which the model's accuracy is known by its user before the test is undertaken. This provides the user with perfect ex-ante understanding of a model's performance which also enables sensitivity analysis to be undertaken.
Applying this approach to the Kupiec-POF test, we generate a specific, pre-defined, P&L return distribution and then calibrate a VaR model such that it represents as close to a "perfect" fit as possible. To ensure similarity to real-world financial returns we employ three types of models and P&L distributions: Normal; Standardised Student-t; and a Standardised Skewed Student-t distribution.
In each case, the standard deviation or volatility of the "correct" model, which is set equal to one, is deliberately misspecified using a range of values between 0.7 and 1.3. Here, the model will over-estimate (under-estimate) volatility if its standard deviation is higher (lower) than one, by a maximum of 30%.
Figure 2 below shows Kupiec-POF test rejection rates under a number of different scenarios, with the key assumption that the underlying P&L returns follow a Normal distribution. In each chart, rejection rates and the model's volatility are displayed on the vertical and horizontal axes respectively. Coloured lines therefore denote the rejection rate for a given rate of volatility using a specific backtesting sample size. The "better" the test, the quicker the rejection rate should rise towards 100% as volatility is misspecified. The top two graphs show the results for the test at the 99% significance level and the bottom graphs show the results for a significance level of 95%. Additionally, graphs on the left and right hand sides represent results for the 99.5% and 99% VaR confidence levels.
Figure 2: Rejection rates for a Normal model
A simple visual inspection of these charts supports our previous expectation that the probability of experiencing a type II error is asymmetric around the correctly specified volatility. In particular, our results suggest that the Kupiec-POF test is in fact less likely to fail a VaR model which over-estimates volatility when compared to one that under-estimates volatility. Interestingly, this phenomenon worsens as the VaR/test confidence interval increases or the sample size is reduced.
Whilst insightful, our analysis has so far relied upon an assumption of normality for the underlying P&L distribution and extensive research has shown that this is unrepresentative for the majority of financial variables (e.g Fama (1963); Fama (1965); Mandelbrot (1963)); which are often skewed and exhibit excess kurtosis (i.e. fatter tails). With this in mind, it's worth exploring how our initial results might change as we assess the Kupiec-POF test using more representative P&L return distributions.
The figures below therefore show results for the same experiment, now based on a Student-t distribution with three and nine degrees of freedom (red and blue lines respectively) across different sample sizes and model/test confidence intervals. Here, lower degrees of freedom represent a more "fat-tailed" distribution.
Figure 3: Rejection rates for a standardised Student-t model
Interestingly, we can see that as the distribution of the P&L returns becomes more fat-tailed the likelihood of a type II error increases substantially. This is evidenced by analysing the difference between the blue and red lines above. The graphs also reinforce the phenomenon of asymmetry, as explained previously. Again, reducing the backtesting sample size or increasing the VaR/test confidence interval worsens both of these effects.
Extending our analysis to P&L returns which are both fat-tailed and skewed brings us even closer to real-world financial returns. To do so we utilise a standardised skewed Student-t distribution. The figure below presents results for a fat-tailed distribution (three degrees of freedom) with both negative and positive skew – i.e. 0.7 and 1.3 skew parameters, respectively.
Figure 4: Rejection rates for a standardised Skew-t model
Again, the results support previous analysis regarding backtesting sample sizes, model confidence intervals and the existence of asymmetry. However, it's also clear that these effects now become much more pronounced when the P&L distribution is more "fat-tailed" and negatively skewed (as the blue lines are always above their red counterparts).
In conclusion, our simulation based analysis has added to existing research on Kupiec-POF test performance by demonstrating that the impact of small backtesting sample sizes and/or high confidence intervals depends crucially upon the characteristics of the underlying P&L distribution.
How can users of the Kupiec-POF test use our findings to improve decision-making?
In practice, many factors affecting Kupiec-POF test performance are difficult to control – e.g. using a large backtesting sample size might not be possible for relatively new contracts or portfolios. That said, it goes without saying that in order to reduce Type-II errors users should favour longer sample sizes and resist the temptation to utilise low VaR model or test confidence intervals. Our analysis also suggests that one particularly important method of becoming more comfortable with Kupiec-POF test results is the user's assessment of the underlying P&L distribution's characteristics (i.e. kurtosis, skewness and tests for normality). By requesting such information, regulators and end-users might ultimately feel less circumspect with a relatively small backtesting sample size if the P&L returns appear normally distributed or alternatively request the use of a much larger backtesting sample size if they are highly skewed and fat-tailed.
Emmanouil Karimalis, Paul Alexander & Fernando Cerezetti work in the Bank's Risk, Research and CCP Policy Division.
If you want to get in touch, please email us at bankunderground@bankofengland.co.uk. You are also welcome to leave a comment below. Comments are moderated and will not appear until they have been approved.
Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.
Kupiec-POF test
Type-II error
Value-at-risk
Published 15 January 2016 22 August 2016
Previous Post Extracting insight from complexity
Next Post The cheque republic: money in a modern economy with no banks.
One thought on "Testing the test: How reliable are risk model backtesting results?"
Michael Harris (@mikeharrisNY) says:
"regulators and risk managers are often concerned with so-called "Type-II" errors (i.e. the non-rejection of an incorrectly specified model)."
AFAIK, the null hypothesis is that a model is random or unprofitable in the sense that its returns are drawn from a distribution with 0 mean return.
In that case, we are more interested in false positives, or Type-I errors.


text:
Sustainability in the UK art & design university curriculum: the how and the why
Houghton, Nicholas (2016) Sustainability in the UK art & design university curriculum: the how and the why. Revista Diálogos com a arte (6). pp. 73-84. ISSN 2183-1726
4249:105305
Sustainability in the UK art & design university curriculum: the how and the why - Nicholas Houghton (955kB)
Houghton, Nicholas
Sustainability is about ensuring everyone's basic needs are being met and can continue to be met in the future. It has two main areas: the social and the environmental. Some include a third: economic. There is a requirement in the UK for universities to implement and promote sustainability, including in the curriculum. This paper concentrates on how this is affecting learning and teaching in art and design. Sustainability in the curriculum has been resisted by those who cling onto an essentialist, formalist curriculum. However, the majority have a broader view of the curriculum in line with changes which took place in the professional sphere from the 1960s. These changes force artists and designers to consider such things as socio-cultural context. In the 1970s, this led to a gradual unfolding of a new curriculum, which has now become widespread. But even within this framework, teachers often find engaging with sustainability in their teaching to be challenging. It forces everyone to reassess their ways of working and living and even their fundamental beliefs and is sometimes considered an irrelevant initiative of management, or government. It can be seen as being in opposition to many of the practices of unfettered capitalism and neo-liberalism; more likely, it exposes some of the contradictions inherent in that ideology. But sustainability can also be considered a dogma in its own right, or even a set of uncomfortable truths people prefer to ignore. Some artists and designers embrace a social practice, but others prefer to indulge in a much more private way of working. Just as some universities wholeheartedly embrace sustainability while others do little more than play lip service to it, so some teachers are enthusiastic and others not. This paper discusses some of the ways sustainability has been introduced into the art and design curriculum, illustrated through case studies. It concludes that it works well if there is a faculty member who champions this way of working, but works best when embraced by most teachers and, in particular, students.
http://docs.wixstatic.com/ugd/6d6107_b259b70998024...
Uncontrolled Keywords or tags :
sustainability, art & design curriculum, higher education
School of Further Education
http://www.ese.ipvc.pt/revistadialogosco...
Dr Nicholas Houghton


Uninor launched a new service for its customers in Bihar and Jharkhand. Pre-paid users can now avail the Talk Time Transfer service and can transfer as well as ask for talk-time from their family and friends even if the user has no/zero balance.
Transfer balance amounts can be anything from Rs. 5 to Rs. 50 and a maximum of 7 transactions per day can be done. A charge of Rs. 2 will be deducted as the fee from the amount of transaction. Subscriber has to do minimum of two recharges while being there in Uninor network, before being able to use the balance transfer functionality.
Is Vodafone over charging you for data while other Vodafone users get more for less?


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The Canadian General Standards Board exam fees are not included in tuition/supply fees.
Courses in ND1130 Material and Process and MA1081 Math Fundamentals in NDT must be successfully completed prior to applying for national qualification exams.
Magnetic particle Inspection (MPI) trains students to use small magnetic particles (i.e. iron filings) to detect flaws in components. For this method to be used the component must be made of ferromagnetic material such as iron, nickel, cobalt, or some of their alloys.
Liquid Penetrant Inspection (LPI) trains students to recognize surface flaws in components that appear as a result of capillary action. Flaws become apparent when a colored or fluorescent dye bleeds out of the component to reveal a crack in its surface.
Ultrasonic Testing (UT) trains students to use high frequency sound energy to conduct examinations and make measurements in materials to determine surface or internal cracks or flaws in the materials.
Radiography Testing (RT) trains students to send radioactive energy through a material enabling a negative (Photo) to be produced for that material illustrating internal flaws or cracks.
Demonstrate knowledge of Quality Assurance, Control Documentation and Reporting Systems for various industrial sectors.
Develop attitudes conducive to the successful application of skills on the job.
Develop an awareness and concern for good safety practices in the work place.
Develop academic skills and knowledge in mathematics, communications and science.
Distinguish among various properties of metals with respect to their impact on NDT methods.
Time will be split between practical applications and the classroom throughout the program to assist the trainees in developing self-confidence/skills to carry out Non-Destructive Testing certification exams.