text:
\section{Introduction}\label{sec_int}}
Quantum modular value is a concept that was proposed by Kedem and Vaidman in 2010 \cite{Kedem105}.  When a quantum system is prepared in an initial state $|\psi\rangle$ and post-selected in a final state $|\phi\rangle$, the modular value $(\hat{A})_{\rm m}$ of an observable $\hat{A}$ is defined to be the expectation value of the {\it dynamically evolved phase factor} $e^{-ig\hat A}$, and is expressed as
\begin{align}{\label{modular}}
(\hat{A})_{\rm m} = \dfrac{\langle\phi|e^{-ig\hat A}|\psi\rangle}{\langle\phi|\psi\rangle}\;,
\end{align}
where $g$ is the magnitude of the coupling.

Eq. (\ref{modular}) is derived, in relation to {\it non}-weak measurement, as follows \cite {Kedem105,Ho}. In between the preparation of $|\psi\rangle$ and the post-selection of $|\phi\rangle$ of the quantum system, a qubit pointer, which is prepared in state $\gamma |0\rangle + \bar\gamma |1\rangle$, is coupled to the system. Here we use the word ``pointer" instead of ``meter" since we use the subscript (and sometimes superscript) m to denote ``modular value", and then, we use p to denote ``qubit pointer" (=meter). Following the standard  von Neumann treatment \cite{vNm}, the interaction Hamiltonian is given by $ \hat H = g(t)\hat A\otimes\hat P$, where $g(t)$ is an arbitrary (possibly time dependence) coupling constant and $\hat P = |1\rangle\langle 1|$ is a projection operator of the qubit pointer. The final state of the qubit pointer after the interaction and post-selection on the system is calculated to be $ \langle \phi|\psi\rangle (\gamma |0\rangle +\bar\gamma(\hat{A})_{\rm m}|1\rangle)$, where  $(\hat{A})_{\rm m} \equiv  \langle\phi|\hat e^{-ig\hat A}|\psi\rangle/\langle\phi|\psi\rangle$, and is named ``modular value". Here, $g$ is the magnitude of the coupling defined as $g \equiv \int g(t) {\rm d}t$.

\sloppy
Apparently, a modular value of an observable is related to the corresponding weak value through $\langle \hat{A}\rangle_{\rm w} = i \left[ {\partial \over \partial g} (\hat{A})_{\rm m} \right]_{g = 0}$, where the weak value, denoted as $\langle \hat{A}\rangle_{\rm w}$, is defined to be the expectation value of the measured values of $\hat{A}$ through repeated weak measurements performed in-between the preparation and the post-selection, which was shown to be $\langle \hat{A}\rangle_{\rm w} = \langle\phi|\hat A|\psi\rangle / \langle\phi|\psi\rangle$ \cite{Aharonov60}. Interestingly, the modular value can be related to the weak value even for nonzero $g$'s \cite{Kedem105, Ho}.

Weak values can take values outside the range of eigenvalues of $\hat{A}$, and can even be complex. Although this strange property has been discussed for weak values in the context of probabilistic interpretation \cite{Hosoya43} or contextuality \cite{Pusey113}, and is considered to be  a suitable index to describe many intriguing quantum phenomena including quantum paradoxes \cite{Aharonov17,Hardy68,Aharonov301,Lundeen102,Yokota11,Aharonov15,Hasegawa5}, and even is  applied to amplification and precision metrology \cite{Pang113,Zhang114,Huang17,Nishizawa92,Susa92}, discussions on this kind of property are still missing in modular values. Furthermore, as also claimed by us in Ref. \cite{Ho}, modular values are sometimes more beneficial than weak values, in the sense that measuring a modular value is more efficient than measuring a weak value because the measurement coupling constant $g$ can be made large. From the experimental point of view, modular values are seemingly easier to measure because one can simply perform the tomography using binary outcomes in the qubit pointer \cite{Ho}. Therefore, it is necessary and meaningful to shed light on the study of quantum modular values. Specifically, we focus our study on the behavior of quantum modular values as complex numbers in relation with complex conditional probabilities in the present work.

Recently, Cormann et al. have proposed a new procedure to measure a quantum modular value \cite{Cormann}. They demonstrated directly the modulus and argument of the modular value as functions of the measurement strength. These observations require more detailed theory on the behavior of quantum modular values as complex numbers.

The main purpose of this work is to understand the complex behavior of quantum modular values. In contrast to the weak-value case, where the real and imaginary parts play a significant role each, what is more important is the modulus and argument in the modular-value case, as we show in this paper. To see this, we first relate the modular value to complex conditional probabilities as will be seen in Sec. \ref{sec_sta}. Then we derive the polar decomposition (modulus and argument) of the modular value, and relate them to some interesting concepts in Secs. \ref{sec_mod} and  \ref{sec_arg} as below.

We first derive that a modular value can be expressed as the average of a dynamic phase factor over all eigenvalues with complex conditional probabilities [Eq. \eqref{mv}].  Thus, the modular value is interpreted in the context of the complex conditional probabilities, which is analogous to the weak-value case [Eq. \eqref{Aw=sum_a a Pr(a|psi,phi)}]. In addition, the chain rule of modular values Eq. \eqref{modular_rule}, analogous to that for weak values Eq. \eqref{weak_rule}, is also derived. This implies that a modular value can be expressed by a set of intermediate weak values and modular values. These results will be described in Sec. \ref{sec_sta}.

In Secs. \ref{sec_mod} and  \ref{sec_arg}, we discuss the interpretation of the modulus and argument components of a modular value in the polar decomposition \cite{Botero44,BoteroArxiv}. Therein, in Sec. \ref{sec_mod}, we express the modulus of the modular value in relation to the relative change in the qubit pointer post-selection probabilities. We define {\it the relative change in the qubit pointer post-selection probabilities} (hereafter referred to as ``relative change" for short) as the ratio of the statistical frequency of finding the chosen final state $|1\rangle$ to that of $|0\rangle$ for the qubit pointer.
We show that the modulus of the modular value is proportional to the square root of the corresponding relative change. Using this theory, a qubit system is extensively examined, and  we also propose a way to experimentally determine the coupling constant $g$ (when it is unknown beforehand) by measuring this relative change.

In Sec. \ref{sec_arg}, we relate the argument of the modular value to the Pancharatnam relative phases \cite{Pancharatnam44} by considering the initial state, the evolved state, and the post-selected state of the system. In this work, we pay attention to two kinds of phase, that are, {\it the intrinsic phase} (the phase shift by the evolution of the state) and {\it the geometric phase} (the geometric phase associated with the three states). It is particularly shown that the argument of the modular value is expressed by the total Pancharatnam relative phases (the summation of the geometric phase and the intrinsic phase).
The Pancharatnam phase plays an important role for robust quantum gates in quantum information processing \cite{Sjoqvist}, and has applications to quantum information such as fault-tolerant quantum computation \cite{Zanardi264, Duan292} and weak measurement \cite{Tamate11}. So the study on modular values in connection with the Pancharatnam phases might open new possibilities for further studies.

Finally, we summarize the results of this paper in Sec. \ref{sec_con}.

{\section{Probabilistic interpretation of modular values}\label{sec_sta}}
In this section, we extend the previous studies of Hofmann about weak values in Refs. \cite{Hofmann13, Hofmann14} to probabilistic interpretation for modular values. We show that, analogous to weak values, modular values can be understood in the context of complex conditional probabilities.

Let us first give a brief summary to the previous studies. The ordinary expectation value, that is, the expectation value without the post-selection condition, can be interpreted as the average of weak values over all possible post-selection states as $\langle \hat{A}\rangle_{\psi} = \sum_\phi \langle \hat{A}\rangle_{\rm w} \text{Pr}(\phi|\psi)$, where $\text{Pr}(\phi | \psi)$ is the conditional probability of observing state $| \phi \rangle$ on condition that the prepared state is $| \psi\rangle$, and is, of course, equal to $| \langle \phi | \psi \rangle |^2$ \cite{Aharonov72,Tollaksen40,Shikano43,Hosoya43,Hosoya44}. Comparing this to $\bar x = \sum_x x\text{ Pr}(x)$ in standard statistics, the weak value can be treated as a
$|\phi\rangle$ dependent variable --- which can take complex values, but its expectation value is real with the real probability $\text{Pr}(\phi | \psi)$ \cite{Hosoya43}.

Interestingly, a weak value itself can be regarded as the average of conditional probabilities --- in this case, however, conditional probabilities themselves can take complex values \cite{Shikano43,Mitchison76,Hofmann13,Hofmann14}. In fact, using the spectral decomposition $\hat A = \sum_a a \ \hat{\Pi}_a$  $\left( \hat{\Pi}_a \equiv |a\rangle\langle a| \right)$, it is straightforward to obtain \cite{Hofmann13,Hofmann14}
\begin{align}{\label{Aw=sum_a a Pr(a|psi,phi)}}
\langle A\rangle_{\rm w} = \sum_a a \ \text {Pr} (a | \psi,\phi)\;.
\end{align}
Here,
\begin{align}{\label{complex_conditional_prob_1}}
\text{Pr} (a | \psi,\phi) = {\langle\phi | \hat{\Pi}_a | \psi\rangle \over \langle\phi|\psi\rangle} = \langle \hat{\Pi}_a \rangle_{\rm w} \;,
\end{align}
is known as the {\it complex conditional probability} \cite{Hofmann13,Hofmann14}, for the process: from the initially prepared state $|\psi\rangle$ to the finally post-selected state $|\phi\rangle$ via the intermediate state $|a\rangle$. Normally, the weak value of the projection operator $\hat A = |a\rangle\langle a|$ is the transition amplitude from the initial state to the final state via the intermediate state, the squared of its values which is known as the probability \cite{Hosoya43}. However, here we interpreted it as complex conditional probability in the scene that the state $|a\rangle$ is might not observed by projective measurements, for example  ``counter-factual probabilities" \cite{Dirac,Feynman,Hofmann81}.

Using this, the ordinary expectation value is expressed by the chain rule as
$\langle A\rangle_{\psi} = \sum_a a\sum_\phi \text {Pr} (a | \psi,\phi) \text{Pr}(\phi|\psi) $.
Here, $\text{Pr}(\phi|\psi)$ is real but $\text {Pr} (a | \psi,\phi)$, so to say a jointly conditioned probability, can be negative or even complex, and the finally obtained expectation value is real. Nevertheless, Hofmann also constructed quantum mechanics based on this generalized probability formalism, where  he called the properties of these generalized probabilities as {\it physical properties} \cite{Hofmann89, Hofmann91}, which provide the full framework of quantum mechanics, including quantum ergodicity \cite{Hofmann89}, and quantum paradoxes \cite{Hofmann91}.

Our main result of this section is to show that the modular value is the average of the dynamic phase factor $e^{-iga}$ over all eigenvalues with the complex conditional probability, which is expressed as
\begin{align}{\label{mv}}
(\hat{A})_{\rm m} = \sum_a e^{-iga} \text {Pr} (a | \psi,\phi)\;.
\end{align}
To show this, we use the spectral decomposition of an arbitrary function of operator $\hat{A} = \sum_a a |a\rangle\langle a |$, where all eigenvalues $\{|a\rangle\}$ form orthonormal bases. The spectral decomposition of $F(\hat{A})$, where $F$ is an any analytic function, is written as
\begin{align}{\label{f(A) = sum f(a) |a rangle langle a |}}
F(\hat A) = \sum_a F(a) |a\rangle\langle a | \;,
\end{align}
which is derived by the Taylor (Maclaurin) expansion of function $F(\hat A)$. Choosing $e^{-ig\hat A} $ as the function {$F(\hat{A})$,} Eq. (\ref{f(A) = sum f(a) |a rangle langle a |}) immediately leads to
\begin{align}{\label{SpectralDecompositionForExp(-igA)}}
e^{-ig\hat A} = \sum_a e^{-iga} |a\rangle\langle a|\;.
\end{align}
Putting this into Eq. (\ref{modular}) and using Eq. (\ref{complex_conditional_prob_1}), we obtain Eq. (\ref{mv}).

Next, we discuss chain rules. We fix the initial state $|\psi\rangle$ and the final state $|\phi\rangle$, and consider the case that the intermediate state is found to be $|a\rangle$, assuming that there is another intermediate measurement that randomly projects the state onto one of the orthonormal states $|x\rangle$'s. In this case, the chain rule describing the process of taking route $|\psi\rangle\rightarrow|a\rangle\rightarrow|\phi\rangle$ is the summation over all possible $|x\rangle$'s with proper conditional probabilities. Therein, the process of taking route $|\psi\rangle\rightarrow|a\rangle\rightarrow|x\rangle\rightarrow|\phi\rangle$ for each $|x\rangle$ is the product of $\text{Pr}(x|\psi,\phi)$, which is the process of taking $|\psi\rangle\rightarrow|x\rangle\rightarrow|\phi\rangle$ conditioned by the initial $|\psi\rangle$ and the final $|\phi\rangle$, and $\text{Pr}(a|\psi,x)$, which is the process of taking $|\psi\rangle\rightarrow|a\rangle\rightarrow|x\rangle$ conditioned by  $|\psi\rangle$ and $|x\rangle$. Thus  the chain rule  becomes \cite{Hofmann89}
\begin{align}{\label{Bayes-like}}
 \text{Pr}(a|\psi,\phi) &= \sum_x \text{Pr}(a|\psi,x) \text{Pr}(x|\psi,\phi) \;.
\end{align}
Substituting Eq. \eqref{Bayes-like} into Eq. \eqref{Aw=sum_a a Pr(a|psi,phi)}, and using $\text{Pr} (x | \psi,\phi)  = \langle \hat{\Pi}_x \rangle_{\rm w}$ with $ \hat{\Pi}_x \equiv |x\rangle\langle x|$, we obtain
\begin{align}{\label{weak_rule}}
{_\phi\langle \hat{A}\rangle_\psi^{\rm w}} = \sum_x  {_x\langle A\rangle_\psi^{\rm w}} \cdot {_\phi\langle \hat{\Pi}_x\rangle_\psi^{\rm w}} \;,
\end{align}
where ${_f\langle \cdot\rangle_i^{\rm w}}$ denotes the weak value between pre- and post- selection states $|i\rangle$ and $\langle f|$, respectively.

In this paper, we obtain a chain rule  for the modular value in a similar way.  In fact, substituting Eq. \eqref{Bayes-like} into Eq. \eqref{mv}, we obtain
\begin{align}{\label{modular_rule}}
{_\phi(\hat{A})_\psi^{\rm m}} = \sum_x  {_x(\hat{A})_\psi^{\rm m}}\cdot{_\phi\langle \hat{\Pi}_x\rangle_\psi^{\rm w}}\;,
\end{align}
where ${_f(\cdot)_i^{\rm m}}$ denotes the modular value between pre- and post- selection states $|i\rangle$ and $\langle f|$, respectively. We can also generalize the expression if we define
\begin{align}{\label{generalized_modular}}
(\hat{A})_{\rm F} \equiv \dfrac{\langle\phi| F(\hat{A}) |\psi\rangle}{\langle\phi|\psi\rangle}
= \sum_a F(a) \text {Pr} (a | \psi,\phi)\;,
\end{align}
where function $F$ can be any analytic function.
Substituting Eq. \eqref{Bayes-like} into Eq. \eqref{generalized_modular}, we also obtain the chain rule:
\begin{align}{\label{generalized_modular_rule}}
{_\phi(\hat{A})_\psi^{\rm F}} = \sum_x  {_x(\hat{A})_\psi^{\rm F}} \cdot{_\phi\langle \hat{\Pi}_x\rangle_\psi^{\rm w}}\;.
\end{align}
When $F(a) = a$, it leads to the weak value, and when $F(a) = e^{-iga}$, it leads to the modular value.

\bigskip

{\section{The modulus of modular values}\label{sec_mod}}
We consider the system-pointer interaction Hamiltonian $\hat{H}$, and assume that the interaction is not weak but  can be arbitrarily large. Initially, the quantum system is prepared in $|\psi\rangle$ and the pointer is prepared in $|\xi\rangle$. Following the standard von Neumann treatment, the unitary evolution $\hat U(g)$ for the measurement is assumed to be $\hat U(g) = e^{-ig\hat A^{\rm s}\otimes\hat P^{\rm p}}$, where $\hat A^{\rm s}$ is an operator in the system Hilbert space $\mathcal H^{\rm s}$ and $\hat P^{\rm p} \equiv |\eta \rangle \langle \eta |$ ($|\eta\rangle$ is one of the orthonormal bases of the pointer) is a selected projection operator in the pointer Hilbert space $\mathcal H^{\rm p}$. The role of $|\eta\rangle$ is the same as $|1\rangle$ in the qubit pointer in Sec. \ref{sec_int}, which means that we generalize the qubit pointer to qudit pointer (i.e., the dimension of the pointer Hilbert space is arbitrary but finite.) Now we can calculate the joint transitional probability to find the pointer in $|\mu\rangle$ ($|\mu\rangle$ can be any of the bases, which might or might not be equal to $|\eta\rangle$) and the system in the final state $|\phi\rangle$. We write this conditional joint probability as  ${\rm Pr}_g(\mu,\phi|\xi,\psi)$,  where $\mu$ and $\phi$ are obtained outcomes indicating that the pointer is found in the state $|\mu\rangle$ and the system in $|\phi\rangle$, respectively.   Similarly, $\xi$ and $\psi$ are the observed indicators corresponding to the preparation of the pointer in $|\xi\rangle$ and the system in $|\psi\rangle$, respectively.  The conditional joint probability is calculated to be
\begin{align}{\label{joint_pro}}
{\rm Pr}_g(\mu,\phi|\xi,\psi) = \text{Tr} (\hat M_\mu^\dagger \hat \Pi_f \hat M_\mu \hat \rho_i)\;,
\end{align}
where $\hat \Pi_f = |\phi\rangle\langle\phi|$ and $\hat\rho_i = |\psi\rangle\langle\psi|$, respectively, and the subscript $g$ means that the probability is $g$ dependent. The operator $\hat M_\mu\equiv \langle\mu| e^{-ig\hat A^{\rm s}\otimes\hat P^{\rm p}}|\xi\rangle =  \langle\mu|\xi\rangle e^{-ig\hat A^{\rm s}\delta_{\mu\eta}}$ is known as the {\it Kraus operator}, which is acting on the system Hilbert space $\mathcal H^{\rm s}$. It is easy to check that $\sum_\mu \hat M_\mu^\dagger  \hat M_\mu = \hat I^{\rm s}$. Then, the straightforward calculation of the joint transitional probability \eqref{joint_pro} leads to ${\rm Pr}_g(\mu,\phi|\xi,\psi) = |\langle\mu|\xi\rangle|^2\cdot |\langle\phi|e^{-ig\hat A^{\rm s}\delta_{\mu\eta}}|\psi\rangle|^2 \;.$

Now, let us show that this formalism is useful when we try to measure the modular value experimentally. We consider the case that the pointer is a qubit with the initial state $|\xi\rangle = \gamma|0\rangle + \bar\gamma|1\rangle$, where $\gamma$ and $\bar \gamma$ are assumed to be real, satisfying $\gamma^2+\bar\gamma^2=1$. The projection operator $\hat P^{\rm p}$ is chosen to be $|1\rangle\langle 1|$, that is, $|\eta\rangle = |1\rangle$. Then it is straightforward to calculate the joint probability for the cases $\mu = 0$ and 1, that is, for the cases that we find the qubit pointer in $|\mu\rangle = |0\rangle$ and $|1\rangle$, respectively. The results become
\begin{align}{\label{P_g(0)}}
{\rm Pr}_g(0,\phi|\xi,\psi) = \gamma^2|\langle\phi|\psi\rangle|^2 \quad {\rm for} \ \mu = 0 \;,
\end{align}
and
\begin{align}{\label{P_g(1)}}
{\rm Pr}_g(1,\phi|\xi,\psi) = \bar\gamma^2|\langle\phi|e^{-ig\hat A^{\rm s}}|\psi\rangle|^2 \quad {\rm for} \ \mu = 1\;.
\end{align}
Now we introduce the ratio of ${\rm Pr}_g(1,\phi|\xi,\psi)$ to ${\rm Pr}_g(0,\phi|\xi,\psi)$, which we denote by $\chi$.
Then, using Eqs. (\ref{P_g(0)}) and  (\ref{P_g(1)}), we obtain
\begin{align}{\label{modulus_99}}
\chi \equiv {{\rm Pr}_g(1,\phi|\xi,\psi) \over {\rm Pr}_g(0,\phi|\xi,\psi)} = \left| \dfrac{\bar{\gamma}}{\gamma} \right|^2 \cdot \dfrac{|\langle\phi|e^{-ig\hat A^{\rm s}}|\psi\rangle|^2 }{|\langle\phi|\psi\rangle|^2} \;.
\end{align}
This equation is interesting in the sense that the right-hand side means the relative change in the post-selection probabilities  of finite $g$ case to the $g=0$ case for the system, whereas the definition of $\chi$ is the ratio of the statistical frequency of finding $\mu = 1$ to that of $\mu = 0$ for the pointer. For this reason, we will simply refer to $\chi$ as ^^ ^^ relative change", hereafter.

Using Eqs. (\ref{modular}) and (\ref{modulus_99}), we obtain the relation between $\chi$ and the modular value, as
\begin{align}{\label{modulus_98}}
\left |(\hat{A}^{\rm s})_{\rm m}\right| = \left| \dfrac{\gamma}{\bar\gamma} \right| \sqrt{\chi}
\;.
\end{align}
The value $\chi$ is easily obtained experimentally because $\chi$ is the average of a series of measurement results for the qubits pointer, and each measurement is done after separating the system and the pointer, and thus, we can use a strong and destructive measurement each time.
In this way, the modulus of a modular value of the system can be obtained from measurements of the qubits pointer.

It is worth to note that our definition about the relative change $\chi$ is slightly different from that of the Dressel et al. approach, where the authors supposedly defined the relative change as the ratio in between the changing transitional probability induced by the system-pointer interaction and the initial transitional probability without the interaction for weak coupling strength \cite{Dressel86,Dressel91} . With $\gamma =\bar\gamma = 1/\sqrt{2}$, however, our $\chi$ becomes equivalent to the Dressel's one.

Furthermore, in the Dressel et al. works, the authors have shown that for the constant $g$ is small enough, the Taylor series expansion gives the {\it linear dependence} of $\chi$ as $\chi_{\rm w} = 1+ 2g \ \text{Im}\langle \hat{A}\rangle_{\rm w}$ \cite{Dressel86}. Here, we used subscript w for $\chi$ because it is expressed by the weak value. This expression is valid only in the {\it weak interaction regime}, where the higher order terms can be neglected and thus the following requirements are satisfied: (i) the relative change $\chi_{\rm w} $ should be close to one, and (ii) the first order term should be large compared to the sum of all higher order corrections (see Ref. \cite{Dressel86} and Ref. \cite{Duck40} and references therein). The above linear expression of $\chi_{\rm w}$ can be used  for experimental estimation in two ways. One is to estimate the magnitude of $g$ when $g$ is not known but $\chi_{\rm w}$ and the imaginary part of $\langle \hat A \rangle_{\rm w}$ are experimentally obtainable. Another is the indirect estimation of the observable using only the detector statistics \cite{Dressel91}. In both cases, however, we can use $\chi_{\rm w}$ only when $g$ is small enough.

For arbitrary values of $g$, however, our ``relative change" gives the exact relation to the modulus of modular values. Therefore, we can rigorously write $\chi_{\rm m} = \dfrac{\bar\gamma^2}{\gamma^2}\left|(\hat A^s)_{\rm m}\right|^2$, where we use the subscript m for $\chi$ as well since the relative change, in this case, is induced by the modular value rather than the weak value.  So, $\chi_{\rm m}$ enlarges the usage of the ^^ ^^ relative change" much more than $\chi_{\rm w}$. Of course, this expression of $\chi_{\rm m}$ is exact for small $g$ including $g=0$. When we increase $g$, however, $\chi_{\rm m}$ clearly shows its nonlinear dependence on $g$.

As an illustration, let us consider a polarization qubit ($|0\rangle = |{\rm H}\rangle$: horizontally polarized photon, $|1\rangle = |{\rm V}\rangle$: vertically polarized photon), and assume the initial and final qubit states, following \cite{Dressel86}, to be
\begin{align}{\label{state}}
|\psi\rangle = \dfrac{|{\rm H}\rangle -e^{i\varphi}|{\rm V}\rangle}{\sqrt{2}}; \hspace {0.25cm} |\phi\rangle = \cos \frac{\theta}{2}|{\rm H}\rangle + \sin\dfrac{\theta}{2}|{\rm V}\rangle\;,
\end{align}
where, $\varphi$ is the lateral angle for the prepared state, and $\theta$ is the azimuthal angle for the post-selected state on the Bloch (Poncar\'e) sphere (see Fig. \ref{fig1}). The evolution of the qubit is generated by $\hat{A}^s = \hat{S}$, where $\hat S \equiv |{\rm H}\rangle\langle {\rm H}| - |{\rm V}\rangle\langle {\rm V}|$ is the Stokes polarization operator, whose eigenvectors are $|{\rm H}\rangle$ and $|{\rm V}\rangle$ with the corresponding eigenvalues $1$ and $-1$, respectively.

\begin{figure} [t!]
\centering
\includegraphics[width=6.5cm]{fig1.eps}
\caption{
(color online) A schematic drawing of the Bloch (Poncar\'e) sphere exhibiting the qubit states. The lateral angle $\varphi$ of the initial state $|\psi\rangle$ is fixed constant and the final state $|\phi\rangle$ can be rotated by changing $\theta$ from 0 to 2$\pi$. The polarization states of the qubit are represented on the sphere, where $|H\rangle$: horizontal, $|V\rangle$: vertical, $|D\rangle = \frac{1}{\sqrt{2}}(|H\rangle+|V\rangle)$: diagonal, $|A\rangle = \frac{1}{\sqrt{2}}(|H\rangle-|V\rangle)$: anti-diagonal, $|L\rangle = \frac{1}{\sqrt{2}}(|H\rangle+i|V\rangle)$: left circular, $|R\rangle = \frac{1}{\sqrt{2}}(|H\rangle-i|V\rangle)$: right circular.
}
\label{fig1}
\end{figure}

The joint transitional probabilities ${\rm Pr}_g(\mu,\phi|\xi,\psi)$ corresponding to the outcomes $\mu = $ H and V are calculated as (in the present example, we use Pr(H) and Pr(V) for short)
\begin{align}
{\rm Pr}(H) &= \gamma^2(1-\cos\varphi\sin\theta)/2\;,\label{p0}\\
\text{Pr}(V) &=\bar\gamma^2\bigl(1-\cos(2g+\varphi)\sin\theta\bigr)/2\;.\label{pm}
\end{align}
Then, using Eqs.\eqref{modulus_99} and \eqref{modulus_98},  the modulus of the modular value is calculated as

\begin{align}{\label{pmdp}}
\left|(\hat{S})_{\rm m}\right| = \biggl[\dfrac{1-\cos(2g+\varphi)\sin\theta}{1-\cos\varphi\sin\theta}\biggr]^{1/2}\;.
\end{align}

As a numerical calculation, we fix the value of the lateral angle $\varphi$ of the initial state to be a constant, say, $\varphi = -0.2 \pi$, and assume $\gamma=\bar\gamma=1/\sqrt{2}$. Then we calculate the $\theta$ dependence of the joint transitional probabilities for several values of $g$ and $g$ dependence of the modulus of modular values for several values of $\theta$. Fig. \ref{fig2}(a) shows the $\theta$ dependence of the joint transitional probabilities for $g$ ranging from 0 to 0.25$\pi$. The $\theta$ dependence is sinusoidal both for Pr(H) and Pr(V), but the amplitude depends on $g$ for Pr(V) as is shown by the green area while it does not depend on $g$ for Pr(H) as is shown by the single black curve.
This black curve also expresses Pr(V) for $g=0$.   By increasing $g$ from 0, Pr(V) gradually deviates  from Pr(H), the deviation becomes maximum at $g=0.1\pi$, and then it comes back to the Pr(H) curve when $g$ reaches to 0.2$\pi$,
which is shown again by the black curve.

\begin{figure} [t!]
\centering
\includegraphics[width=8.4cm]{fig2.eps}
\caption{
(color online) (a)  Main figure: Plot of the joint transitional probabilities as functions of $\theta$ for various values of $g$ from 0 to 0.25$\pi$. The black solid curve is the Pr(H) and also denotes the Pr(V) with $g = 0$, and $0.2\pi$. The value of $\varphi$ is assumed to be -0.2$\pi$ and $\gamma=\bar\gamma=1/\sqrt{2}$ in all of the plots in (a) and (b). Inset: The $g$ dependence of the relative changes, $\chi_{\rm w}$ (red solid line) and $\chi_{\rm m}$ (blue dash-dotted curve) for $\theta=3\pi/2$. The value 1 is shown by the black dotted horizontal line, which makes it easy to see that $\chi_{\rm m}$ deviates from 1 as $g$ is increased from 0 and then it comes back to 1 again.  The point where this occurs is indicated by the small black arrow, which corresponds to $g = 0.2\pi$ $(= - \varphi)$.
(b) The $g$ dependence of the modulus of the modular value, $|(S)_{\rm m}|$,  for $\theta = \pi/2$ (blue solid curve) and $\theta=3\pi/2$ (blue dotted curve). The modulus of weak values are constants and shown as the black dotted horizontal lines.}
\label{fig2}
\end{figure}

We can see this by plotting $g$ dependence of the relative change $\chi$. The inset of Fig. 2(a) shows the $g$ dependence of the relative changes $\chi_{\rm w}$ and $\chi_{\rm m}$ for $\theta=3\pi/2$. The red line shows the {\it linear} dependence of $\chi_{\rm w}$ to $g$, and therefore, its value takes 1 only when $g$ is 0. On the other hand, the blue dash-dotted curve ($\chi_{\rm m}$) behaves as the {\it sine function} with respects to $g$. The intersections of the black dotted horizontal line (= 1) and $\chi_{\rm m}$ make one easy to see that $\chi_{\rm m}$ deviates from 1 as $g$ is increased from 0 and then comes back to 1 again. This means that the joint transitional probability Pr(V) comes back to the same value as that of the joint transitional probability Pr(H), and its first come-back occurs when $g$ is set to be $g = -\varphi$ ($= 0.2\pi$ in this example), which is indicated by the small black arrow. In addition, whenever the relative change becomes 1, $\chi$ does not change from its original value at all. This no-change points are shown by the intersections between the horizontal line and $\chi_{\rm m}$ (see the inset of Fig. 2a). Interestingly, this no-change-point appears periodically with the period $\pi$. Mathematically, it can be explained by solving the equation Pr(H) - Pr(V) = 0, with respects to $g$. The solution is straightforwardly calculated as follows:
\begin{align}{\label{solu}}
\notag&-\cos(2g+\varphi)\sin\theta+\cos\varphi\sin\theta = 0\\
&\Rightarrow g =
\left [
	\begin{array}{l}
		k\pi  \\
		-\varphi+k\pi
	\end{array}
\right.
k \in \mathbb N\;.
\end{align}

We next analyze the $g$-dependence of the modulus of the modular value $|(S)_{\rm m}|$ shown in Fig. 2(b) for $\theta = \pi/2$ (blue solid curve) and $\theta=3\pi/2$ (blue dashed curve). Here, again, $\varphi$ is chosen to be $\varphi = -0.2\pi$.  The corresponding modulus of the weak values are shown by the black dotted horizontal lines. Obviously, the modulus of the modular value explicitly depends on the coupling constant $g$ and deviates from unity as $g$ is increased from 0.

The interesting thing is that, as is discussed above, $\chi_{\rm m}$ comes back to 1, and we can find specific values of $g$ $(\ne 0)$ that realizes $\chi_{\rm m} = 1$ again [see example in the inset of Fig. \ref{fig2}(a)]. This
property of $\chi_{\rm m}$ can be used in the experimental tuning of the value of $g$ to the desired value (such as for preparing the interaction strength in a modular-value measurement). In the following, we show how to do this tuning. Assume that one wants to realize $g=0.3\pi$ by adjusting an uncalibrated experimental set-up. The first thing to do is to prepare the initial state $|\psi\rangle$ of Eq. (\ref{state}) with $\varphi = -0.3\pi$. Starting from no interaction ($g=0$), increase $g$ (not calibrated experimentally yet), and plot $\chi_{\rm m}$ with a certain value of $\theta$. $\theta$ should be chosen so that the deviation of $\chi_{\rm m}$ from 1 is clearly seen. Then, like the inset of Fig. \ref{fig2}(a), $\chi_{\rm m}$ comes back to 1 again. At the very moment when $\chi_{\rm m}=1$ is realized, the set-up is appropriately adjusted to give $g = 0.3\pi$.

\begin{figure}[t!]
\includegraphics[width=8.6cm]{fig3.eps}
\caption{
(color online) A schematically set-up of a reference system to determine the value of $g$. At first, the system and qubit pointer states ($|\psi\rangle$, and $|\xi\rangle$) are injected into Device $\widetilde g$, where the interaction is implemented. The system then post-selected onto the final state $|\phi\rangle$, whereas, the qubit pointer output state are passed through the Polarized Beamsplitter (PBS) in order to measure the corresponding probabilities of the Horizontal polarization beam Pr($H,\phi|\xi,\psi$) and the Vertical polarization beam Pr($V,\phi|\xi,\psi$).
}
\label{fig3}
\end{figure}

To be more concrete, let us consider a reference system as shown in Fig. \ref{fig3}, where Device $\widetilde g$ implements the interaction between a quantum system and a qubit pointer with an uncalibrated but controllable coupling. Prepare a photon in a polarization state $|\psi\rangle$ with the desired value of $\varphi$, and postselect it onto $|\phi\rangle$ as in Eq. \eqref{state}. The initial state of the qubit pointer is $|\xi\rangle = \frac{1}{\sqrt{2}}(|{\rm H}\rangle + |{\rm V}\rangle$). The unitary evolution is $\hat U(g) = e^{-ig\hat S\otimes\hat P}$, where $\hat P\equiv$ $|{\rm V}\rangle\langle {\rm V}|$ denotes the projection operator. In order to determine the value of $g$, one can experimentally change $g$ so that the outcome joint transitional probability $\text{Pr}(H,\phi|\xi,\psi)$ equals to $\text{Pr}(V,\phi|\xi,\psi)$. Then it is guaranteed that the value of $g$ is calibrated to be $-\varphi$.

{\section{The argument of modular values}\label{sec_arg}}
As was discussed by Cormann et al., the argument of a modular value can be measured by the phase in a quantum eraser interference experiment \cite{Cormann}. Here, we analyze the argument of modular values more in detail, and
we show that it is expressed by the Pancharatnam phases.

In 1956, Pancharatnam considered the interference of two optical states, say $|A\rangle$ and $|B\rangle$, that are not orthogonal to each other in polarization \cite{Pancharatnam44}. The Pancharatnam relative phase associated with two states, written as $\delta(A, B)$, is defined by the argument of the inner product of the two states, so, $\delta(A,B) \equiv {\rm arg}[\langle A|B\rangle]$. This is also known as the intrinsic phase \cite{Tamate11}. States $|A\rangle$ and $|B\rangle$ are said to be ``in phase" if the absolute value of the inner product is maximum, i.e. $\delta(A,B)=0$.

This phase does not satisfy the transitive rule, that is, even if both $\delta(A,B)$ and $\delta(B,C)$ are in phase, the relative phase $\delta(A,C)$, in general, is not in phase. This nontransitive property can be seen by considering the three pure states --- ``three" is the smallest nontrivial entity. The Pancharatnam relative phase associated with three states, written as $\Delta( A,B,C)$, is defined by the following equation \cite{Erik359}:
\begin{align}{\label{phase_define}}
\Delta( A,B,C)  \equiv  \text{arg} \Big[\langle A| C\rangle \langle C| B\rangle \langle B| A\rangle \Big]\;.
\end{align}
This phase, which is also known as the geometric phase, is gauge invariant because the local phase factor, which might be independently chosen for each quantum state,  always appears with its complex conjugate due to a couple of bra and ket vectors, and thus all the local phases are canceled. For example in qubit case, this geometric phase is well understood by considering the Bloch (or Poincar\'e) sphere, on which we can draw a geodesic triangle having three vertices, $|A\rangle, |B\rangle$, and $|C\rangle$. It is well established that the geometric phase is expressed by the solid angle $\Omega$ of the geodesic triangle as $\Delta(A,B,C) = -\Omega / 2$. \cite{Pancharatnam44,Ramaseshan55,Berry34}.

As  was discussed in Ref. \cite{Cormann}, the phase in the modular value is an intrinsic property of the quantum system in the sense that the evolution $e^{-ig\hat{A}}$ in the modular value solely depends on the system evolution but not on the measurement apparatus or environments. In this paper, we show that the argument of a modular value is expressed by the summation of an intrinsic phase and a geometric phase, as is shown in the following.

Let us consider the following state-evolution process: an initial state, i.e., pre-selected $|\psi\rangle$, evolves
under the evolution operator $e^{-ig\hat A}$, then we project the resultant state $|\psi(g)\rangle \equiv e^{-ig\hat A} |\psi\rangle$ onto the post-selection state $|\phi\rangle$ that we selected. The final state (after post-selection) is given by $|\psi_\phi(g)\rangle\equiv|\phi\rangle \langle\phi|e^{-ig\hat A}|\psi\rangle$ (not normalized). The phase difference between this final state and the initial state is calculated to be
\begin{align}{\label{phase_1_rew}}
\notag{\rm arg}[\langle\psi|\psi_\phi(g)\rangle] &= {\rm arg}[\langle\psi|\phi\rangle \langle\phi|e^{-ig\hat A}|\psi\rangle] \\
&={\rm arg}[(A)_{\rm m}].
\end{align}
This is one interpretation of the meaning of the (argument of the) modular value.  Next, we relate this to the geometric phase among $|\psi\rangle, |\psi(g) \rangle$ and $|\phi\rangle$, which is calculated from Eq. \eqref{phase_define} by replacing $|A\rangle, |B\rangle$ and $|C\rangle$ by
$|A\rangle=|\psi\rangle$, $|B\rangle= |\psi(g)\rangle$ and $|C\rangle=|\phi\rangle$ \cite{Erik359, Berry34,Mukunda228}, as
\begin{align}{\label{phase1}}
\Delta (\psi,\psi(g), \phi) = \text{arg} \Big[\langle \psi|\phi\rangle \langle \phi|\psi(g)\rangle \langle \psi(g)|\psi\rangle\Big]\;.
\end{align}
The meaning of this equation is that this phase shift is induced by the closed-loop projection, $|\psi\rangle \rightarrow |\psi(g)\rangle \rightarrow |\phi\rangle \rightarrow |\psi\rangle$. Using this, the argument of the modular value is calculated to be
\begin{align}{\label{phase_1}}
\notag{\rm arg}[(A)_{\rm m}] &= {\rm arg}\Bigl[\dfrac{\langle\phi|e^{-ig\hat A}|\psi\rangle}{\langle\phi|\psi\rangle}\Bigr]\\
\notag&= {\rm arg}\Bigl[\dfrac{\langle \psi|\phi\rangle \langle\phi|\psi(g)\rangle\langle\psi(g)|\psi\rangle}{|\langle\psi|\phi\rangle|^2\langle\psi(g)|\psi\rangle}\Bigr]\\
\notag&= {\rm arg}\Big[\langle \psi|\phi\rangle \langle \phi|\psi(g)\rangle \langle \psi(g)|\psi\rangle\Big]-\text{arg}[\langle\psi(g)|\psi\rangle]\\
&= \Delta (\psi,\psi(g), \phi) + \delta(\psi,\psi(g))\;.
\end{align}
\begin{figure} [t!]
\centering
\includegraphics[width=8.6cm]{fig4.eps}
\caption{
(color online) The argument of a modular value is the total phase shift of a state-evolution process that starting from an initial state, evolve onto an intermediate state, then project onto a final state and finally project back onto the initial state. This total phase shift corresponds to the summation of the geometric phase and the intrinsic phase.
}
\label{fig4}
\end{figure}
Although $|\psi(g)\rangle$ is the result of the evolution induced by $e^{-ig\hat A}$,
$\Delta$ does not carry any phase shift by this evolution since the bra and ket vectors cancel out this phase shift.
So, only the pre-post-projections yield the geometric phase $\Delta$ but the evolution does not.
The evolution phase shift is solely carried by $\delta$.
In both cases ($\Delta$ and $\delta$), one needs to project the final state onto the initial state to compare the phase shift directly. We illustrate this situation in Fig. \ref{fig4}. Interestingly, as we show here, by picking up a point in the evolution path, the argument of modular value now becomes the summation of the geometric phase $\Delta$ of a geodesic triangle having three vertices $|\psi\rangle$, $|\psi(g)\rangle$, and $|\phi\rangle$, and the intrinsic phase $\delta$ between the initial state and the intermediate state $|\psi(g)\rangle$. This is the main result of this section.

Particularly, when the coupling constant $g$ is sufficiently small, we can take the first order of the Taylor series expansion of the exponential term and obtain
\begin{align}{\label{phase_1_gsmall}}
\notag{\rm arg}[(A)_{\rm m}] \big |_{g\to 0}  &\approx {\rm arg}\Bigl[\dfrac{\langle\phi|(\hat I -ig\hat A)|\psi\rangle}{\langle\phi|\psi\rangle}\Bigr]\\
\notag&= {\rm arg}\Bigl[1-ig\langle A\rangle_{\rm w}\Bigr]\\
\notag&\approx {\rm arg}\Big[e^{-ig\langle A\rangle_{\rm w}}\Big]\\
&= -g{\rm Re}\langle A\rangle_{\rm w}\;.
\end{align}
We emphasize that for small $g$, the argument of the modular value does not reduce to the argument of the weak value, instead, it is proportional to the real part of the weak value.

To show the difference and advantage of the argument of modular values, we will compare with the more familiar weak-value case. We consider the weak value of the projection operator $\hat A = |a\rangle\langle a|$, then the argument of the weak value reduces to the geometric phase as:
\begin{align}{\label{phase_weak}}
{\rm arg}[\langle A\rangle_w]=\Delta (\psi,a, \phi) = \text{arg} \big[\langle \psi|\phi\rangle \langle \phi|a\rangle \langle a|\psi\rangle\big],
\end{align}
as is written in \cite{Erik359} and can be measured by the shift in position and momentum of the pointer. This means that, when the process is such a one that the initial state $|\psi\rangle$ is projected onto an intermediate state $|a\rangle$, successively projected onto $|\phi\rangle$, and finally projected onto the initial state $|\psi\rangle$, then the total phase shift is expressed by the geometric phase $\Delta(\psi,a,\phi)$. This process is different from the state-evolution process above.

\bigskip

{\section{Conclusions}\label{sec_con}}
The main purpose of this work is to examine the property of quantum modular values as complex numbers by using the spectral decomposition and the polar decomposition. We interpreted the complex modular value in connection with the complex conditional probability and expressed the modulus component of the quantum modular value by the relative change in the qubit pointer post-selection probabilities, and also the argument component of the quantum modular value by the relation to the Pancharatnam phases.

First, we have considered the chain rule of conditional probabilities in the situation that the system is initially prepared as $|\psi\rangle$, evolves into ${\rm e}^{-{\rm i}g\hat{A}}|\psi\rangle$ ($\hat{A} \equiv \sum_i^N a_i |a_i\rangle\langle a_i|$), is then weakly measured on $\hat{A}$, is then weakly measured on $\hat{X} \equiv \sum_j^N x_j|x_j\rangle\langle x_j|$, and  is finally projected on $|\phi\rangle$. The result is Eq. (\ref{modular_rule}), which means that the modular value is the sum of the products {over $j$}, each of which is the product of the modular value of $\hat{A}$ sandwiched by $\langle\psi|$ and $|x_j\rangle$ and the weak value of $|x_j\rangle\langle x_j|$ sandwiched by $\langle\psi|$ and $|\phi\rangle$. This is a generalization of the weak-value chain rule, Eq. (\ref{weak_rule}). The most generalized expression is also given as Eq. (\ref{generalized_modular_rule}), where $F(a) = a$ gives the weak-value chain rule, and $F(a) = {\rm e}^{-{\rm i}ga}$ gives the modular-value chain rule. In this sense, the modular value, like the weak value, plays the role of complex conditional probability.

Next, we have investigated the modulus of modular values, and obtained an expression that describes $|(A)_{\rm m}|$ being proportional to the square root of the ratio of the joint transitional probabilities of the qubit pointer, which we refer to as the relative change in the qubit pointer post-selection probabilities, $\chi$, as is described in Sec. \ref{sec_mod}.  Focus on this relation, we can see that, for small $g$ case (i.e., small evolution case), $\chi$ deviates from 1 linearly as we increase $g$ from 0. We have shown that, however, $\chi$ shows the nonlinear behavior to $g$, and in some particular cases, such as $\gamma=\bar\gamma=1/\sqrt{2}$, $\chi$ comes back to 1 at some points of the value $g=g'$. Using this value $g'$,  especially for the qubit systems, we can experimentally calibrate the coupling parameter $g$ by watching the shift of the relative change in the joint transitional probabilities.

Finally, we have obtained a relation that connects the argument of modular values to the summation of the geometric phase of a closed triangle on the Bloch (Poincar\'e) sphere spanned by $|\psi\rangle$, ${\rm e}^{-{\rm i}g\hat{A}}|\psi\rangle$, and $|\phi\rangle$, and the intrinsic phase spanned by $|\psi\rangle$, and ${\rm e}^{-{\rm i}g\hat{A}}|\psi\rangle$, as is described in Sec. \ref{sec_arg}.

Since the modulus of the modular value is related to the relative change in the joint transitional probabilities (Sec. \ref{sec_mod}), and the argument of the modular value is related to the Pancharatnam intrinsic phase and the geometric phase (Sec. \ref{sec_arg}), both the modulus and the argument components of the modular value are connected to the experimentally obtainable quantities.

\bigskip

\begin{acknowledgments}
This work was supported by JSPS Grant-in-Aid for Scientific Research(A) JP16H02214.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Trump Gives Scientific American No Choice
Wed., Sep. 16, 2020
By Kevin McCauley
Hats off to Donald Trump for finally getting the gang at Scientific American to gather the gumption to endorse a presidential candidate. It's their first endorsement in the magazine's 175 years.
The endorsement though isn't for the tweeter-in-chief who has "badly damaged the U.S. and its people—because he rejects evidence and science," according to SA.
The editorial board wants Joe Biden in the White House because of his "fact-based plans to improve the nation's health, economy and environment."
It rips Trump for his "dishonest and inept response" to the COVID-19 pandemic that has cost the lives of more than 190K Americans and for attacking environmental protections, medical care, researchers and public science agencies that help this country prepare for its greatest challenges.
The SA editors write:
"Trump repeatedly lied to the public about the deadly threat of the disease, saying it was not a serious concern and "this is like a flu" when he knew it was more lethal and highly transmissible, according to his taped statements to journalist Bob Woodward. His lies encouraged people to engage in risky behavior, spreading the virus further, and have driven wedges between Americans who take the threat seriously and those who believe Trump's falsehoods. The White House even produced a memo attacking the expertise of the nation's leading infectious disease physician, Anthony Fauci, in a despicable attempt to sow further distrust."
The president's reaction to America's worst public health crisis in a century has been to say "I don't take responsibility at all."
Instead he blamed other countries and his White House predecessor, who left office three years before the pandemic began."
Trump has repeatedly tried to get rid of the Affordable Care Act while offering no alternative, proposed billion-dollar cuts to the National Institutes of Health, the National Science Foundation, and the Centers for Disease Control and Prevention and want the US out of the World Health Organization.
The president keeps pushing to eliminate health rules from the Environmental Protection Agency and replacing replaced scientists on agency advisory boards with industry representatives.
SA editors write: "In his ongoing denial of reality, Trump has hobbled U.S. preparations for climate change, falsely claiming that it does not exist and pulling out of international agreements to mitigate it. The changing climate is already causing a rise in heat-related deaths and an increase in severe storms, wildfires and extreme flooding."
Though Trump and his cronies are trying to create obstacles that prevent voters from casting their ballots, SA urges Americans to overcome all challenges and vote.
"It's time to move Trump out and elect Biden, who has a record of following the data and being guided by science," concludes the editorial.
Will the president retaliate by cancelling his sub to SA?
Category: PR Commentary
Return to Sep. 16, 2020 News

redpajama_set_name: RedPajamaCommonCrawl


1. Hillary Clinton is elected president.
2. Democrats take over the Senate and reduce the Republican margin in the House to just three votes.
3. Elizabeth Warren announces she'll challenge Hillary in the 2020 Democratic primaries if Hillary isn't sufficiently progressive and bold during her first term.
4. The Democratic National Committee issues new rules eliminating "superdelegates" and requiring open primaries.
6. President Hillary Clinton nominates Barack Obama to the Supreme Court, who immediately pledges to reverse "Citizens United." Senate Democrats make a rule change that allows Obama to be confirmed with 51 Senate votes. He is.
7. President Clinton nominates Bernie Sanders for Treasury Secretary and Michelle Obama for Attorney General. Both are immediately confirmed.
8. The chairman of the Republican Party officially repudiates Donald Trump, saying "shame on us for having nominated him." Mitch McConnell, Newt Gingrich, Rudy Giuliani and Mike Pence appear in a joint news conference in which they apologize for having ever supported Trump.
9. With Trump disgraced and his brand in tatters, the value of his properties drops 80 percent. His creditors demand that his personal assets — homes, planes, furniture, all he possesses — be liquidated to pay his bills.
10. Rupert Murdoch fires Sean Hannity from Fox News.


text:
package com.devopsbuddy.backend.persistence.domain.backend;

import com.devopsbuddy.backend.persistence.converters.LocalDateTimeAttributeConverter;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;

import javax.persistence.*;
import java.io.Serializable;
import java.time.LocalDateTime;

/**
 * Created by tedonema on 10/04/2016.
 */
@Entity
public class PasswordResetToken implements Serializable {

    /** The Serial Version UID for Serializable classes. */
    private static final long serialVersionUID = 1L;

    /** The application logger */
    private static final Logger LOG = LoggerFactory.getLogger(PasswordResetToken.class);

    private final static int DEFAULT_TOKEN_LENGTH_IN_MINUTES = 120;

    @Id
    @GeneratedValue(strategy = GenerationType.AUTO)
    private long id;

    @Column(unique = true)
    private String token;

    @ManyToOne(fetch = FetchType.EAGER)
    @JoinColumn(name = "user_id")
    private User user;

    @Column(name = "expiry_date")
    @Convert(converter = LocalDateTimeAttributeConverter.class)
    private LocalDateTime expiryDate;

    /**
     * Default constructor.
     */
    public PasswordResetToken() {

    }

    /**
     * Full constructor.
     * @param token The user token. It must not be null.
     * @param user The user for which the token should be created It must not be null.
     * @param creationDateTime The date time when this request was created. It must not be null.
     * @param expirationInMinutes The length, in minutes, for which this token will be valid. If zero, it will be
     *                            assigned a default value of 120 (2 hours)
     * @throws IllegalArgumentException If the token, user or creation date time are null
     */
    public PasswordResetToken(String token, User user, LocalDateTime creationDateTime, int expirationInMinutes) {
        if ((null == token) || (null == user) || (null == creationDateTime)) {
            throw new IllegalArgumentException("token, user and creation date time can't be null");
        }
        if (expirationInMinutes == 0) {
            LOG.warn("The token expiration length in minutes is zero. Assigning the default value {} ", DEFAULT_TOKEN_LENGTH_IN_MINUTES);
            expirationInMinutes = DEFAULT_TOKEN_LENGTH_IN_MINUTES;
        }
        this.token = token;
        this.user = user;
        expiryDate = creationDateTime.plusMinutes(expirationInMinutes);
    }

    public long getId() {
        return id;
    }

    public void setId(long id) {
        this.id = id;
    }

    public String getToken() {
        return token;
    }

    public void setToken(String token) {
        this.token = token;
    }

    public User getUser() {
        return user;
    }

    public void setUser(User user) {
        this.user = user;
    }

    public LocalDateTime getExpiryDate() {
        return expiryDate;
    }

    public void setExpiryDate(LocalDateTime expiryDate) {
        this.expiryDate = expiryDate;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;

        PasswordResetToken that = (PasswordResetToken) o;

        return id == that.id;

    }

    @Override
    public int hashCode() {
        return (int) (id ^ (id >>> 32));
    }
}

redpajama_set_name: RedPajamaGithub


text:
TWICE Has Been Dubbed "Charity Angels" For 7 Months Straight (and Counting!), Here's Why
ONCEs are seriously the sweetest!
ONCEs don't just use their love of TWICE to support the group, but to also help those in need!
K-Pop media company myloveidol recently announced that TWICE had won the title of "charity angels" for the month of January 2019.
Certificate noting that 500,000 won (~$450 USD) has been donated in TWICE's name
What this means is that this month, the company will donate 500,000 won (~$450 USD) to a charity in the group's name.
In this specific case, the charity supported is the Kids & Future Foundation .
So how did ONCEs help?
Well, in the myloveidol app, users can do various in-app activities to boost their fave's rankings. At the end of the month, myloveidol donates money to charity in the the "winning" idol/group's name – and also dubs them a "Charity Angel" for the month.
Due to the sheer power of ONCEs, TWICE has held onto the "Charity Angel" title for 7 straight months, which is insane (in a good way!)
Due to TWICE's stronghold on the top spot, myloveidol has so far donated about 5 million won ($4,480 USD) in the group's name.
Funnily enough, Tzuyu has also held the individual title of female title of "Charity Angel" for the same amount of time – and also having money donated in her name.
All together, ONCEs have helped donate about 10 million won ($8,960 USD) in TWICE's name.
ONCEs are seriously amazing, and we're sure TWICE is proud of them as well!
Source: @myloveidol_kpop


Share your belief in Christ with this pretty design! Add it to a Bible cover or tote to carry to church. Easy Embroidery is happy to present Christ Jesus machine embroidery design which has 7533 stitches and is [82.16 mm x 101.60 mm] large. If you would like to view more embroidery patterns please search on our embroidery designs page.


First, allow me to clarify: I'm using the term "Pop Music" to reference music produced by the mainstream music industry. Stuff like Justin Bieber, Kanye, Britney Spears and their ilk are what I'm talking about with this headline.
Secondly, allow me to cite the primary inspiration for this headline; Guy Forsyth made an excellent observation of popular music, and that observation has prompted this expression.
Allow me to paraphrase: Popular radio and music works because it is designed to appeal to the greatest number of people. It isn't there to offend. It's manufactured to be acceptable to a wide variety of listeners, rather than explore new horizons and touch on great ideas.
Mine, as well as Guy's points are that we should look toward the nooks and crannies of the music industry for true music. Find the art in music again. Find something that truly inspires, brings your mind someplace amazing, and makes you feel passionate. Turn on an independent radio station and you'll hear countless breathes of life into a seemingly lifeless modern music machine.
I'm getting off track, however. My point about pop music can be easily made with just a few links.
Britney Spears and lip syncing. Kanye West ruins Bohemian Rhapsody. Of course, there is also the great book by Moses Avalon, "Confessions of a Record Producer".
The major music industry is a machine designed to churn out what I'd describe as something akin to buying "art" at Walmart. Pieces that are designed to have mass appeal, and sell quickly and easily. The largest issue I have with such things are that it devalues the work of truly creative, unique artists who are constantly reinventing themselves and the music world itself.
Take a moment to visit a common music store, and browse the selection. Pick 10 random CDs, and look at the record label. I'll bet most of what you look at was put out by one of the big three.
Sure, looking for good music takes effort.. Or does it? We've got the Internet, a vast resource for everything creative. Here's just one of many resources to find indie music. You can also easily ask a person for new music, or check out Pandora.
Don't forget to join me in sharing the headline "Pop Music Isn't Music"! Either download & print the temporary tattoo (my logo is optional), or share this post with your friends.


England and India will clash in a series of five Test matches.
England and India will play the first Test of the five-matches explosive series at the Edgbaston, Birmingham. This will also be the 1000th Test match for England, who will become the first team to reach this milestone.
British media has been constantly reminding the Indian team of their tours to England in 2011 and 2014; yet what they don't realize is that this is the new look Indian team under the captaincy of the more aggressive Virat Kohli. England, on the other hand, also have a new captain in Joe Root and thanks to the condition in England, namely the drought and high temperatures, the pitches and conditions are expected to suit the visitors more than the home side.
This even led England to call Adil Rashid out of red ball retirement and include him in the playing XI for this Test match. India on the other side is dealing with the headache of finding a good opener to partner M Vijay. They will also have the trouble of choosing which two spinners or which lone spinner would get to play in the final XI.
England will be banking on their swing bowlers in James Anderson and Sam Curran since they believe to have some swing at Edgbaston.
The team winning the first Test will definitely have the upper hand when it comes to moving forward to the next Test in the series.


We had sun yesterday, it was a delight. We gathered ourselves up and went for a walk. Just down the road from our house we are blessed with National Forest, and a lot of natural walking trails. So, Fur Ball, ready to run and chase, my son. in shorts, my husband in his sandals and winter hat, my daughter and I properly dressed for a spring walk, headed out. Fur Ball was elated to run up and down the trail until he had to stop to rest, panting in exhaustion. Our children, had to scout out all the rocks, only wishing to find the best ones in which to climb. Our son was willing to tromp through the snow even if it meant getting his bare legs ice cold. My husband, forgetting his age, decided to walk the barricade, and show off for the family his amazing skills. Our daughter worked very hard to keep up with her brother, and did a good job of it. I just took pictures and kept everyone in line!
It was a very nice day and a great walk, with the people I love. I am thankful for this. God does bring adventure into my life all the time, how could He not? Look at the people He has blessed me with!
Say That Again, Jesus, I went on a Country Walk and in one hour I experienced so much of Your love through this adventure. My children climbing through the snow and up the rocks. My husband balancing on a bar and being silly. And, my dog running around like a crazy dog....laughter, love, fun, and joy. I felt Your warmth, and saw Your nature, I heard You speak. Jesus, Say that Again, You will be with me on my Country Walk always!


text:
PROTECT ME FROM WHAT I WANT
Drew Pettifer
Drew Pettifer, Untitled (Selfportrait going down), 2013
Drew Pettifer, Untitled (Lachlan BJ), 2015
Drew Pettifer, Untitled (Ass licker), 2015
Drew Pettifer, Untitled (Andre on top), 2012
Drew Pettifer, Untitled (Kieran going down on Mia), 2011
Drew Pettifer, Untitled (Hotel liaison), 2015
Drew Pettifer, Untitled (Cumshot), 2013
Drew Pettifer, Untitled (Selfportrait holding him), 2012
Artists and institutions are increasingly self-censoring provocative and subversive work to secure audiences and funding while dodging protests and controversy. To avoid having to respond to attacks on freedom of expression from broader society, it appears that artists and institutions are sidestepping the issue altogether by choosing not to put these works before the public.
Artists are constantly making editorial decisions as they navigate their practice. What they choose to exclude from the public sphere is invariable determined by factors that might be as simple as the accessibility of materials, or based on complex theoretical considerations. Once the work is made, the artist must consider how it will be encountered. So, artists are constantly making editorial decisions about what is excised and what remains. Indeed, this process of refinement and resolution is often thought of as a necessary process for producing 'good' art.
But this does not occur within a vacuum. The social, political and economic context in which a work is produced and in which it is displayed will no doubt influence these judgments. That is not to say that artists are doomed to replicate the hegemonic norms of any given society; historically, many artists have used their art to challenge dominant ideologies. Art both reflects and influences the dominant culture within which it operates. . An artist's response to these conditions will also be informed by the prevailing conditions of the time, at both the societal level and within the 'art world'.
In spite of the many progressive developments that have occurred in recent decades, I can't help but feel that we live in a more conservative cultural climate than existed even a generation ago. On the other hand, it could be argued that our society is more polarised than it has been for some time, with the gap between 'left' and 'right' or 'progressive' and 'conservative' ever increasing. The difference now being that these conservative forces wield significantly more power in our contemporary culture, and openly call on the state to back their positions. From the court case involving Paul Yore to the formation of the National Program for the Excellence in the Arts to the furore around Bill Henson's work we need not look far to find examples of state intervention into freedom of expression within the arts. These are not the catalysts in themselves, but rather the symptoms of a bigger cultural and political shift.
Self-censorship is one such chilling effect that arises from this prevailing cultural condition. The following images are works that I was willing to produce, but which I have not been willing to show until now. These are works that I have censored due to their sexual nature. My work is of a sexual nature. These are the images that I have deemed too explicit, confronting or 'pornographic' even for an eroticised practice like my own.' I carefully consider and contextualise the images of nudity and sexuality that I exhibit to encourage a particular kind of reading. However there is no way to ensure that the viewer reaches this reading, or agree with it when they get there.
In the contemporary Australian context the nude figure has become increasingly linked to the sexualised body, so exhibiting a nude of any kind could be read as eroticised. I don't believe that this link is universal – it is contextual. I've had people openly respond to my nudes in Australian galleries before with disgust or avoidance, but I'm not certain that it would receive this kind of response in art galleries in many other countries.
In Australia images exploring sex and desire are commonly seen as pornographic, even when they appear in artworks clearly intended for artistic contexts. This point was driven home for me when an image of one of my works appeared without my knowledge on an erotic website. I was searching for a reference to my work in a publication, and Google revealed that the work in question had also appeared on a Tumblr page full of pornographic images of young men. Through this recontextualisation, I too could see how the image could be read in as pornographic. The Internet can be a problematic space; it can decontextualize provocative or subversive images and thus redefine them. We arguably see more art online these days than we do in gallery spaces, so the solution isn't to limit the visibility of these works on the Internet, but to develop a sensitivity to the original context in which a work was intentionally exhibited.
If someone disapproves of my work when viewed or understood in an appropriate context such as an art gallery then I take no issue with their critique. Rather than try to shut it down or have it censored, in this context it is possible to enter into a discourse about the work: explain what you don't like about it. Discuss where you think the work fell short or went wrong. Express your disapproval. Unless it is a breach of law, leave the State out of it. The threat of state censorship is often one of the greatest incitements to artistic self-censorship, which is a much more insidious form of censorship. When the state silences a voice, there is often evidence of this process of censorship on public record. As the practice of self-censorship becomes more and more widespread there will be few traces to show that the shift ever occurred.
My final reason for not exhibiting or publishing these works until now comes from a desire to remain able to function within the contemporary gallery system. I want to continue to exhibit my work, and risk-averse contemporary galleries are not going to stage an exhibition that could threaten their funding sources or upset key stakeholders. This system, as it stands, encourages artistic self-censorship, and a significant sociopolitical shift will be needed for this to change.
Born Shepparton, Victoria. Lives and works between Kyabram, Victoria and Melbourne, Victoria.
Drew Pettifer is an artist and academic who currently lectures in Art History and Theory and Print Imaging Practice at RMIT University. He is scheduled to complete his doctorate in fine art (photomedia) at Monash University in early 2016. Drew's art practice explores themes of intimacy, gender, sexuality and the politics of desire using photography, video, installation and performance. Recent exhibitions of his work include: Less than Lovers (solo), Utrecht, Tokyo (2015); Territorial Pissings (solo), Bus Projects, Melbourne (2015); Turnintensive, Kunstraum Tapir, Berlin (2014); Melbourne Now, National Gallery of Victoria (2013-14); Mapping the interior: In search of an inland sea (solo), Margaret Lawrence Gallery, Melbourne (2013); and, Androgyne (solo), Nellie Castan Gallery, Melbourne (2013). Drew is currently a member of the Shepparton Art Museum Foundation Board of Directors and until early 2015 served for 6 years as a director of Bus Projects. He is also a qualified solicitor and works from time to time as an independent curator and writer. His work is held in various collections, including the National Gallery of Victoria, Monash Gallery of Art, Horsham Regional Art Gallery and Shepparton Art Museum, as well as private collections nationally and internationally.
www.drewpettifer.com


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text:
lemon law - lemon law information, lemon law state statutes
Washington D.C Lemon Law
Washington D.C. Code, 40-1301 to 40-1310
40-1301 Definitions
For the purposes of this chapter, the term:
(1) "Board" means the Board of Consumer Claims Arbitration for the District of Columbia established by § 40-1303.
(2) "Consumer" means the purchaser, other than for purposes of resale, of a motor vehicle; any person to whom the motor vehicle is leased or otherwise transferred during the duration of a warranty applicable to the motor vehicle; and any other person entitled to enforce the obligations of the warranty. For the purposes of § 40-1303, the term "consumer" means any natural person who does or would purchase, lease, or receive consumer goods or services. The term "consumer" includes any natural person who purchases insurance coverage in the District of Columbia.
(3) "Council" means the Council of the District of Columbia.
(4) "Court" means the Superior Court of the District of Columbia.
(5) "District" means the District of Columbia.
(6) "Known" means, for the purposes of § 40-1305, that a dealer or the dealer's agent or employee has obtained facts or information about the condition of a motor vehicle which would lead a reasonable person in similar circumstances to believe that the motor vehicle contained 1 or more material mechanical defects. The term "known" encompasses knowledge obtained through an inspection, from a previous owner, from the salesperson at an auction, or through other means.
(7) "Material mechanical defect" means any defect, failure, or malfunction of the mechanical system of a motor vehicle, including, but not limited to, the engine, transmission and drive shaft, differential, cooling system, electrical system, fuel system, or accessories, which significantly impairs the operation, safety, performance, or value of the motor vehicle.
(8) "Mayor" means the Mayor of the District of Columbia.
(9) "Motor vehicle" means a motor vehicle which is manufactured for sale, offered for sale, sold, or registered in the District and which is designed for the primary purpose of transporting a driver and 1 or more passengers on streets, roads, or highways. The term "motor vehicle" shall not include buses sold for public transportation, motorcycles, motor homes, or motorized recreational vehicles.
(10) "New motor vehicle" means a motor vehicle which is in the period of the first 18,000 miles of operation or the first 2 years after the date of delivery to the original purchaser, whichever is earlier.
(11) "Safety-related defect" means an impairment which reduces the operator's ability to control the motor vehicle in normal operation or which creates a risk of fire, explosion, or other life-threatening malfunction.
(12) "Significantly impair" means to render the motor vehicle unreliable or unsafe for normal operation or to reduce its resale value below the average resale value for comparable motor vehicles.
(13) "Used motor vehicle" means a motor vehicle which is offered for sale in the District and which is not within the period of the first 18,000 miles of operation or the first 2 years after the date of delivery to the original purchaser, whichever is earlier; but it does not mean a motor vehicle sold only for scrap or parts.
(14) "Warranty" means the written or implied warranty of the manufacturer of a motor vehicle.
40-1302 Consumer's remedy for defective vehicles
(a) If a new motor vehicle does not conform to all warranties during the first 18,000 miles of operation or during the period of 2 years following the date of delivery of the motor vehicle to the original purchaser, whichever is the earlier date, the consumer shall during that period report the nonconformity, defect, or condition to the manufacturer, its agent, or its authorized dealer. If the notification is received by the manufacturer's agent or authorized dealer, the agent or dealer shall within 7 days forward written notice thereof to the manufacturer by certified mail, return receipt requested. The manufacturer, its agent, or its authorized dealer shall correct the of the first 18,000-mile period of operation or the 2-year period.
(b) If, after a reasonable number of attempts, the manufacturer, its agent, or authorized dealer is unable to repair or correct any nonconformity, defect, or condition which results in significant impairment of the motor vehicle, the manufacturer, at the option of the consumer, shall replace the motor vehicle with a comparable motor vehicle, or accept return of the motor vehicle from the consumer and refund to the consumer the full purchase price, including all sales tax, license fees, registration fees, and any similar governmental charges. In calculating a refund, the manufacturer may deduct from the consumer's full purchase price a reasonable allowance not to exceed 10 cents per mile for the consumer's use of the motor vehicle in excess of the first 12,000 miles of operation, and a reasonable allowance for any damage not attributable to normal wear or to the nonconformity, defect, or condition which significantly impaired the motor vehicle. Refunds shall be made to the consumer, and the lien holder, if any, as their interests may appear on the records of ownership kept by the Department of Public Works.
(c) Each of the following circumstances shall be an affirmative defense to any claim under this section:
(1) The nonconformity, defect, or condition does not significantly impair the vehicle.
(2) The nonconformity, defect, or condition is the result of abuse, neglect, or unauthorized modifications or alterations of the motor vehicle.
(d) It shall be presumed that a reasonable number of attempts have been made to conform a motor vehicle to the warranties, if:
(1) The same nonconformity, defect, or condition, if it is not safety- related, has been subject to repair 4 or more times by the manufacturer, its agent, or authorized dealer after notification by the consumer within the first 18,000 miles of operation or during the period of 2 years following the date of original delivery of the motor vehicle to a consumer, whichever is the earlier date, but the nonconformity, defect, or condition continues to exist;
(2) The same nonconformity, defect, or condition, if it is safety-related, has been subject to repair 1 or more times by the manufacturer, its agents, or authorized dealers after notification by the consumer within the first 18,000 miles of operation or during the period of 2 years following the date of original delivery of the motor vehicle to a consumer, whichever is the earlier date, but the nonconformity, defect, or condition continues to exist; or
(3) The motor vehicle is out of service by reason of repair of any nonconformities, defects, or conditions which significantly impair the vehicle, on a cumulative total of 30 days or more during either period, whichever is the earlier date.
(e) The 30-day out-of-service period shall be extended by any time during which repair services are not available to the consumer because of a war, invasion, strike, fire, flood, or other natural disaster.
(f) The consumer, in order to seek the refund or replacement provided by this section, shall first submit a claim to the Board of Consumer Claims Arbitration established pursuant to § 40-1303. If the Board rejects the case for arbitration, or if the claim is arbitrated and the consumer rejects the arbitration decision, the consumer may then bring an action in court to seek the remedies provided by this section.
(g)(1) If a motor vehicle is returned to a manufacturer, its agent, or authorized dealer pursuant to this section, the manufacturer, its agent, or authorized dealer shall notify the Department of Public Works that the motor vehicle was returned.
(2) The Department of Public Works shall note the fact that the motor vehicle was returned pursuant to this chapter on any certificate of title issued for the motor vehicle.
(3) A motor vehicle dealer shall state the fact that the motor vehicle was returned pursuant to this chapter in any sales contract for the motor vehicle prior to the signing of the contract by a prospective purchaser.
40-1303 Arbitration
(a) There is established in the Department of Consumer and Regulatory Affairs a Board of Consumer Claims Arbitration for the District of Columbia. The Board shall consist of 7 members who shall be appointed by the Mayor.
(b) The members shall be at least 18 years of age and residents of the District.
(c) Two members shall be attorneys admitted to the practice of law in the District, 1 of whom shall be designated by the Mayor as chairperson of the Board. Two members shall have training and experience in arbitration and mediation. One member shall be the Director of the Department of Consumer and Regulatory Affairs or his or her designee. One member shall have experience or training in representing the interests of consumers. One member shall have experience or training in the manufacture or wholesale or retail sales of consumer goods.
(d) The Mayor shall appoint the initial Board members within 60 days of March 14, 1985. Of the members first appointed, the chairperson and 1 other member shall be appointed for terms of 3 years; 2 members shall be appointed for terms of 2 years; 1 member shall be appointed for a term of 2 years; and 1 member shall be appointed for a term of 1 year. Subsequent appointments shall be for terms of 3 years. This subsection shall not apply to the representative of the Department of Consumer and Regulatory Affairs.
(e) Members of the Board shall be compensated pursuant to § 1-612.8.
(f) The Mayor shall issue, and may amend from time to time, rules and regulations to implement the provisions of this section and may establish reasonable fees for the filing of complaints.
(g) The Board, in accordance with the rules and regulations issued pursuant to subsection (f) of this section, shall provide arbitration for claims filed by consumers against manufacturers, their agents, or dealers pursuant to §§ 40-1302 and 40-1305; for claims voluntarily filed by consumers against the provider of any consumer goods or services, who agrees to arbitration, pursuant to rules and regulations issued by the Mayor; and for claims filed pursuant to § 35-2105 by parties agreeing to arbitration pursuant to rules and regulations issued by the Mayor.
(h) Consumers may submit claims to the Board by completing forms which shall be approved by the Mayor.
(i) Upon receipt of a written claim filed by a consumer, the Board shall within 5 business days determine whether the claim qualifies for arbitration pursuant to this chapter and notify the opposing party.
(j) The Board shall develop and maintain a roster of persons who are residents of the District, at least 18 years of age, and experienced in arbitration techniques who may be employed to serve as arbitrators for specific cases.
(k) The Board shall assign cases for arbitration according to the following provisions:
(1) A case may be assigned to a single arbitrator if the Board first informs all parties to the case of the identity and background of the arbitrator and obtains their consent. When a case is assigned to a single arbitrator, the arbitrator must be an attorney-member of the Board or another attorney admitted to the practice of law in the District and chosen from the roster of arbitrators maintained by the Board.
(2) All cases not assigned to single arbitrators shall be assigned to a panel of 3 arbitrators, 1 of whom must be a member of the Board and 1 of whom must be an attorney admitted to the practice of law in the District. Participation on the panel by an attorney-member of the Board shall satisfy both requirements. The Board shall inform all parties to the case of the identity and background of the arbitrators tentatively selected for the panel and shall obtain the consent of both parties to the choice of arbitrators. The decision of the panel shall be by majority vote.
(l) The Board is authorized to reject for arbitration consumer claims which are determined by a majority of the Board to be frivolous, fraudulent, or beyond the legal authority of the Board.
(m) The Board shall promptly assign all cases accepted for arbitration to an arbitrator or arbitrators who shall appoint a time and place for a hearing and notify the parties personally or by registered mail not less than 5 days prior to the hearing. Hearings shall be public and shall be recorded electronically.
(n) At all arbitration hearings, the parties are entitled to present oral and written testimony, to present witnesses and evidence relevant to the controversy, to cross-examine witnesses, and to be represented by counsel.
(o) The Board may issue subpoenas for the attendance of witnesses and for the production of books, records, documents, and other evidence. The Board or arbitrators designated by the Board shall have the power to administer oaths and affirmations and take acknowledgements.
(p) Upon application by any party to an arbitration proceeding, or upon its own motion, an arbitrator or arbitration panel may retain independent technical experts as needed to determine the facts in the case. The arbitrator or arbitration panel may assign the costs of the technical experts to 1 or both parties to the case.
(q)(1) The arbitrator or arbitration panel shall determine whether the defendant is liable to the claimant and, if so, shall award the claimant relief.
(2) The arbitrator or arbitration panel may award the claimant the relief provided by this chapter, any relief available under any other law, and reasonable attorneys' fees. The defendant may be assessed the costs of arbitration as part of any award rendered by the arbitrator or arbitration panel.
(3) Decisions of an arbitrator or arbitration panel shall be in writing and shall be entered by and in the name of the Board.
(4) Decisions shall be entered no later than 60 days from the date the Board accepts a case for arbitration.
(5) The decision shall state the relief granted, if any, and shall specify a time limit for compliance.
(6) The board shall promptly provide a copy of the decision to each party.
(r) The Board or any party to a case may petition the court to issue an order compelling compliance with a decision by the Board.
(s)(1) Any party to a case may, within 20 days after receipt of the Board's decision, petition the court to vacate the decision and grant a trial de novo.
(2) Upon receipt of a petition, the court shall first determine the validity of the arbitration proceeding and shall vacate an arbitration award upon a finding that:
(A) The award was procured by corruption, fraud, or other misconduct in violation of law;
(B) The arbitrator or arbitration panel exceeded its powers;
(C) The arbitrator or arbitration panel failed to conform to the rules and regulations issued pursuant to this chapter, and the failure to conform prejudiced the rights of a party to the complaint; or
(D) The award is based on a numerical error or other error of fact which the Board has failed to correct.
(3) If the court determines the arbitration process was valid but grants the petition for a trial de novo on other grounds, the decision of the Board shall be admissible as evidence and shall be presumed correct.
40-1304 Disclosure of rights
(a) The manufacturer, its agent, or authorized dealer shall provide written notification to the prospective consumer of any motor vehicle to be sold or registered in the District of the rights provided to the consumer by this chapter.
(b) The Mayor shall issue rules and regulations prescribing the form and content of the notification required by this section.
(c) Any agreement entered into by a consumer for the purchase of a motor vehicle which waives, limits, or disclaims the rights set forth in this chapter shall be void. These rights shall inure to a subsequent transferee of the motor vehicle.
40-1305 Disclosure of damages or defects in used motor vehicles; violations; penalties
(a) No motor vehicle dealer may offer for sale any used motor vehicle without first providing:
(1) Written notice to the prospective consumer of any material mechanical defect in the motor vehicle and any damage sustained by the motor vehicle due to fire, water, collision, or other causes for which the cost of repairs exceeded $1,000, when the defect or damage was known to the dealer; and
(2) Written notice to the prospective consumer whether the dealer has conducted any inspection of the motor vehicle to determine known defects or damage.
(b) A motor vehicle dealer who fails to provide the notices required by this section or who provides false or misleading notices shall, upon conviction, be subject to the following penalties:
(1) A fine of not less than $300 or more than $1,000 for a first offense; and
(2) A fine of not less than $1,000 or more than $5,000, or suspension or revocation of the license issued pursuant to § 300 of the Vehicles and Traffic Regulations (18 DCMR 300.1 et seq.), or both, for a second or subsequent offense.
(c) The purchaser of a used motor vehicle shall have a right of action against a used motor vehicle dealer for damages or injuries sustained as a result of the dealer's failure to comply with the requirements of this section. The purchaser, in order to seek the remedies provided by this section, shall first submit a claim to the Board. If the Board rejects the case for arbitration, or if the claim is arbitrated and the purchaser rejects the arbitration decision, the purchaser may then bring an action in court to seek the remedies provided by this section.
(d) Violations of this section shall be prosecuted in the name of the District of Columbia by the Corporation Counsel of the District of Columbia.
(e) Civil fines, penalties, and fees may be imposed as alternative sanctions for any infraction of the provisions of this chapter, or the rules or regulations issued under the authority of this chapter, pursuant to subchapters I through III of Chapter 27 of Title 6. Adjudication of any infraction shall be pursuant to subchapters I through III of Chapter 27 of Title 6.
40-1306 Listing of odometer readings
The Department of Public Works shall list the odometer readings at the time of registration or transfer of registration on the title of all motor vehicles registered in the District.
40-1307 Other rights or remedies; limitations on actions
(a) Nothing in this chapter shall in any way limit the rights or remedies which are otherwise available to a consumer under any other law.
(b) Any action brought pursuant to this chapter shall be commenced within 4 years of the date of original delivery of the motor vehicle to the consumer.
40-1308 Rules and regulations
The Mayor shall issue, and may amend from time to time, rules and regulations to implement the provisions of this chapter.
40-1309 Provision for alternative arbitration system.
If the arbitration system established pursuant to § 40-1303 cannot consistently handle complaints during the 60-day period as required by § 40- 1303(q)(4), and if the administration of the arbitration system results in expenditures beyond the sums budgeted annually for the program, the Mayor may certify an alternative arbitration system that complies with this chapter and rules issued to implement this chapter.
40-1310 Suspension of enforcement.
Notwithstanding any other provision of District law, enforcement of this chapter by the Department of Consumer and Regulatory Affairs is suspended until October 1, 2000.


text:
Home Caxton US$2 billion in damages awarded in Roundup cancer trial
US$2 billion in damages awarded in Roundup cancer trial
By Elizabeth Schroeder
A jury in the San Francisco Superior Court in the US has awarded more than $2 billion (about R28 billion) to a couple who claimed that the Bayer AG glyphosate-based Roundup herbicide gave them cancer.
READ France bans widely-used herbicide
A total of US$2 billion was awarded in punitive damages and a further US$55 million (R782 million) in compensatory damages.
The jury determined that the company was liable for the non-Hodgkin's lymphoma that was contracted by the plaintiffs Alva and Alberta Pilliod.
Glyphosate, a broad-spectrum systemic herbicide and crop desiccant used extensively in agriculture and horticulture to combat weeds, is often sprayed as a pre-harvest treatment on some food crops and is also used in parks, on lawns and in gardens.
This has been the third consecutive verdict against the company since litigation started over the chemical.
Roundup was acquired by Bayer as part of its US$63 billion (R895 billion) acquisition of Monsanto last year.
READ How to apply herbicides
The jury in the latest case found that Roundup had been "defectively designed", and that the company failed to warn of the herbicide's cancer risk and therefore acted negligently.
The German chemical giant faces more than 13 400 lawsuits in the US over the herbicide's alleged cancer risk.
The next trial in the glyphosate litigation is scheduled for August.
In a statement Bayer stated that it was a disappointing verdict and that the company would appeal it. A spokesperson called the jury's decision "excessive and unjustifiable".
According to the statement, decades of studies by the company and independent scientists had shown glyphosate and Roundup to be safe for human use.
READ Weeds: the biggest threat to SA's crop production
However, the plaintiffs alleged that Monsanto had known about the cancer risk associated with the herbicide for decades, but chose not to warn consumers about the risk and instead influenced scientists and regulators to give favourable assessments of its products.
These allegations were denied by Bayer.
The lawsuits were largely based on a 2015 conclusion by the World Health Organization's cancer arm, which classified glyphosate as "probably carcinogenic to humans".
However, health authorities in the EU had subsequently claimed that: "Experts, with only one exception, concluded that glyphosate is unlikely to pose a carcinogenic hazard to humans and the evidence does not support classification with regard to its carcinogenic potential".
Brazilian cotton farmers sue Bayer for US$151 million
Ceres growers help drought-stricken Karoo farmers