DENVER—Senators from Colorado, Wyoming and South Dakota are encouraging federal officials to use the timber industry to help thin forests prone to wildfires, like ones that raged across their states this summer.
In a letter Thursday to Agriculture Secretary Tom Vilsack, the senators said overgrown forests, drought, vast stretches of trees killed by beetles, and more people living in fire zones have left the West at a critical juncture. They expressed support for thinning more acres near critical infrastructure and in areas where urban areas are up against forests. The senators also urged Vilsack to prioritize timber sales.
The letter was signed by Sens. Mark Udall and Michael Bennet of Colorado; Mike Enzi and John Barrasso of Wyoming; and Tim Johnson and John Thune of South Dakota.


Indeed, there are several ways to consider what AI is. The first – and the most common – is to look at the sought-after outcome of AI research: roughly speaking, either the "creation and study of machines that behave in a way that denotes intelligence (note: whatever 'behave' may mean)" or "the creation and study of machines that think (note: whatever 'think' may mean)".
Indeed, this definition is not far from the concepts of Artificial General Intelligence (or strong AI or full AI) and Artificial Super Intelligence (or superintelligence), of which the examples abound in the works of science fiction. They designate generalist systems that would respectively match or exceed the capabilities of humans – that is, that would combine all the components we just listed.
One of the most popular sports among AI commentators today is thus trying to guess when Skynet will take over. If you notice a wide variation among predictions about Artificial General Intelligence and Artificial Super Intelligence, it's perfectly normal – really hard to say if such forecasts are under- or overestimated, and if such levels of machine intelligence are even achievable.
In the first approach, you program rules, solving a problem through a tree of steps – the pioneers of artificial intelligence, many of them logicians, were fond of this method. It culminated in the 1980s with the rise of expert systems, programs that intended to encapsulate a knowledge base and decision engine taken from specialists of narrow fields, in order for instance to help organic chemists identify unknown molecules.
The problem is that with such systems, you have to start from scratch when developing a new model – handwritten, specific rules are by nature very difficult or utterly impossible to generalize from one problem to the next, say from speech recognition to medical diagnosis.
In the second approach, you program a general model, but it's the computer that adjusts the model's parameters using the data you provide it with. It's the most popular approach these days.
If you've heard about a current deep learning frenzy, it's because this type of ANNs, made up of a large number of layers – hence "deep" – has yielded significant results in tasks such as identifying objects in images.
Supervised learning: you feed your model with labeled data – e.g. a stereotypical cat image comes with an explicit "cat" tag attached.
Unsupervised learning: you feed your model with unlabeled data, and let it recognize patterns on its own. Since data is usually not labeled – think about all the photos accumulated in your smartphone – and the labeling process takes time, the unsupervised learning approach is harder / less developed and looks more promising than the supervised one.
Reinforcement learning: at the end of each iteration of your model, you simply give it a "grade". Let's take the example of DeepMind, which trained a model to play old Atari games: there, the grade was the score displayed by the games, and the model progressively learned to maximize it. The reinforcement learning approach is probably the least developed of the 3, but the recent accomplishments of DeepMind's algorithms have shed new light on this effort.
Artificial intelligence is not a tree… it's a bush!
So, when you combine the problems tackled by AI research, its various "schools of thought", these schools' own branches, various goals and sources of inspiration… you understand why the attempts at well-organized classifications of the field are always flawed. Take a look at this one – do you see the problem?
Putting "machine learning" and "speech" at the same level is inaccurate, because you can use machine learning models to solve speech issues – they're not parallel branches, but rather different ways to classify AI that can get entangled.
Hence, the difficulty – and beauty – of the artificial intelligence field is that it's certainly not an orderly tree – it's a bush. One branch grows faster than another and is in the limelight, then it's another one's turn, and so on… Some of those branches have crossed, others have not, some have been cut and new ones will appear.
Hence our essential piece of advice is: Never forget the big picture or you'll get lost!
Interested in receiving every week a new episode on Artificial Intelligence first Season by FABERNOVEL?


I am a hobby baker and self taught cake decorator who just started baking cakes for my children, then grandchildren. I got the "bug" to try to improve my caking skills when I started watching cake shows on tv. Then I looked on the internet and youtube and watched lots of videos, and tutorials. Got some supplies......and here I am. Enjoying my hobby immensely and I love making people happy with cakes.
Thank you for checking out my cakes Jan14grands (I like the name). Do you have 14 grandchildren?
Oh my goodness that is amazing! How many children do you have? I only have three grandchildren (4, 2 &1), but they keep this grandma pretty busy as I babysit them 10 hours a day while their parents work.
We have 4 daughters. I am busy for sure as 11 of them live close to me. The youngest is 1 and the oldest is 21. Oops, I may have just given away my age :) Wow, you babysit 3 little ones 10 hours a day? I give you so much credit. I know how hard that is. My 37 yr. old daughter who has 4 kids – ages 3-12, found out she had breast cancer last year and has undergone chemo, and reconstruction. So I filled in the gap and it was very hard. She is doing so well now.
I'm so glad your daughter is doing well now! Cancer is such a scary thing! Your cakes are all so lovely! Cake making is only a hobby for me also. It is so much fun to make beautiful creations for friends and family!
thanks you – it sure is scary. I appreciate you liking my cakes – I enjoy it so much.


text:
package gov.samhsa.consent2share.domain.account;

import org.springframework.data.jpa.repository.JpaRepository;
import org.springframework.data.jpa.repository.JpaSpecificationExecutor;
import org.springframework.stereotype.Repository;

/**
 * The Interface EmailTokenRepository.
 */
@Repository
public interface EmailTokenRepository extends JpaRepository<EmailToken, Long>, JpaSpecificationExecutor<EmailToken> {

	/**
	 * Find by token.
	 *
	 * @param token the token
	 * @return the email token
	 */
	public EmailToken findByToken(String token);
}

redpajama_set_name: RedPajamaGithub


As nearly everyone knows, Israel's political system is parliamentary democracy taken to a lunatic degree. I had hopes a month back that somehow the Likud with Bibi Netanyahu at its head, Kadima with Tsipi Livni as its leader, and Labor spearheaded by Ehud Barak would be able to forge a political alliance that was Zionist and secular, egalitarian and capitalist, alert to its enemies and open to peace. This last dyad is the most essential. But much of it hinges on the Palestinians and, despite all of the frantic diplomacy in the Middle East, nothing good is happening among them.
The last piece of news on which the powers are trying to put a nice twist is actually disastrous. It is the resignation of Salam Fayyad as prime minister of the Palestinian Authority in order to smooth the way for a reunion of Fatah and Hamas. Fayyad was the one person you could trust with money in the Palestinian galaxy. So that is gone, just as a big load of international cash is scheduled to arrive. And what is really expected from the hudna--if there is a hudna--between Ramallah and Gaza? Let's pick odds. My (informed) guess: more intra-Arab carnage within a few weeks of the proclamation of the truce.
Anyway, the trio I had hoped for is kaput. And Netanyahu, a reasonable man open to compromise, is stuck with a coalition that won't coalesce. His most distasteful partner is Yisrael Beiteinu whose leader is Avigdor Lieberman, under investigation by the police for what, alas, has come to be quite common in the Jewish state: corruption at the top, sort of like with Arabs. What can one say good about Lieberman? Well, he is not a fascist or even exactly a neo-fascist. Still, the content and form of his politics are, well, Putinesque. The Palestinians are to Lieberman what the Chechens are to Putin. So if we can deal with Putin, and we seem to be very eager to deal with Putin, we can also deal with Lieberman. But I would want to be the one pouring the vodka. Actually, I'd prefer to be out of the room. On the other hand, Lieberman and his band of cossacks are also not murderers or terrorists, which is something you can't say about many of the Palestinians who are being enticed to the table.
What's also not widely known about Lieberman is that he has already been sitting in Ehud Olmert's peace-seeking government for several years, and did not rock the boat. But, yes, when he speaks about Arabs he is sometimes disgusting, although last week he announced that he'd leave his home in a West Bank settlement for peace with the Palestinians.
Lieberman's signature issue is not the Arabs but the cause of a completely secular society in Israel. Since his electoral base rests on immigrants from Russia and other countries in the former Soviet Union whose status as Jews may not quite be religiously up-to-snuff, his party is the most reliable on issues of civil marriage, pork products everywhere including the army, Sabbath observance and orthodox intrusions wherever and everywhere they intrude. On these matters, he and his party are even more trustworthy than the deep-into-decline left-wing parliamentary faction Meretz.
The third party that will anchor but not permanently stabilize Netanyahu's government is Shas, a group made up of ultra-orthodox Jews who mostly descend from countries in the Arab world. They tend to be poor and therefore dependent on government hand-outs for large families (which also helps the Palestinians, of course. This is the binding currency of the coalition, and it drives the Likud nuts. Shas is also blase about the territories, which does not especially endear it to its partners.
Shas also has amulets and magic trinkets in its basket, and reveres wonder rabbis both dead and alive. The most alive (at 88) is Basra-born Ovadia Yosef who has uttered much nonsense in his career. During the campaign he put an interdict on votes for Yisrael Beiteinu and labeled Lieberman "Satan." This is rough stuff. How his adepts will sit at cabinet meetings with Lieberman without being spooked... that's a problem for them to work out by themselves.
And so let me write about Netanyahu. Bibi's desire to form a government with Ehud Barak and Tsipi Livni tells you much more about him than the dour circumstance in which he finds himself and his party now. Yes, he is on the moderate right in economic matters. But his successors--Barak and Olmert--were not enthusiasts of the state socialist model either, and the head of the Bank of Israel (a Rhodesian-American immigrant, Stanley Fisher) did scrupulous prophylaxis of the financial system, more or less barring sub-prime mortgages and other (what we call in Yiddish) chochmes out of Israel's money blood stream.
In fact, he was the only Israeli prime minister to agree to a withdrawal from deepest Hebron, where 100,000 Palestinians live but where Jews had also lived since Abraham bought land there until a massacre in 1929. (Don't get me wrong: this is not a final settlement of the Hebron issue.) And he also agreed--until Hafaz Assad squelched the whole deal--to a large withdrawal from the Golan Heights. The extent of this proposed withdrawal is now mired in the different accounts of the various participants. Suffice it to say, the least concession attributed to Bibi, very large indeed, was one of which I would disapprove. And I suspect it was much greater than his partisans now argue.
So the demonizing of Netanyahu is simply nonsense. He knows that in a very existential sense Israel needs peace. But he will not make a peace that would fail on the morrow. And peace can no longer be mapped along the armistice frontiers of 1949, which is what the 1967 lines are precisely. Sixty years of history cannot be reduced to an empty formula. Peace will be made when the Palestinians agree among themselves that they truly want a state that will not make war on its neighbor. Only when Israel can assume that land vacated for the state of Palestine will not be used to launch rockets and missiles and terror against its population will the settlement come, and then it could be swift and final.


text:
\section{Introduction}
During last decade, an essential progress was made towards the implementation of the quantum information protocols, see \cite{1,2,3,4,5} and references therein. An essential part of these results are based on different types of the superconducting flux qubits. Whereas the dynamic properties of the noiseless qubits are effectively analyzed with the use of the lumped-element approach, \cite{6,7,8} both the mechanisms of the qubit-environment interaction and the dissipative dynamics of qubits are not investigated completely. Heretofore, a partial characterization of qubits is performed with the use of the spectroscopy in GHz region, for different regimes of the high frequency response and of the readout \cite{9,10,11,12}. Beside of this, the incoherent resonant tunneling, both between the anticrossing levels (the Landau-Zener transitions \cite{13}) and between the steady-state levels \cite{14}, or the low-frequency (sub-kHz) measurements  \cite{14a} are employed for the study. The experimental data suggest that the qubit-environment interaction is caused by the low  frequency classical noise (described by the 1/f spectral function)  and the high-frequency bosons (described by the quasi-ohmic spectral function), see analysis in \cite{10,15}. Recent studies of these processes were directed on an improvement of the fidelity of the quantum hardware. But any consideration based on a simplified model of the spin-noise interaction (e.g., see \cite{16,17} and references therein) is not enough for applications to multi-qubit hardware because such results cannot be associated to a set of parameters describing a real  device.
\begin{figure}[ht]
\begin{center}
\includegraphics[scale=0.22]{f1DD-LC}
\end{center}
\addvspace{-0.5 cm}
\caption{ (a) Sketch of qubit formed by the Josephson junction loop shunted by the transmission line. Tilt and control fluxes, $\varphi$ and $\psi$, with random contributions, $\Delta\varphi_t$ and $\Delta\psi_t$, are shown by the blue and red arrows, respectively. Regimes of relaxation are different for parallel or anti-parallel directions of fluxes $\varphi$ and $\psi$. (b) Model circuit involving the effective Josephson junction shunted by the  effective LC-contour under external fluxes $\varphi +\Delta\varphi_t$ and $\psi +\Delta\psi_t$ (blue and red). (c) Modulation of the symmetric potential energy (thick curve) via tilt ($tl$-) and control ($j$-) channels (red and green, respectively) resulting in variations of level splitting and barrier height, respectively. (d) The same as in panel (c) for the tilted potential, $\varphi\neq 0$. }
\end{figure}

Thus, it is timely to study quantum hardware based on the lumped element approach involving an effective circuit with a detailed description of the qubit-environment interaction. Under such a consideration, the twofold aim should be achieved: (i) to introduce and to justify {\it a realistic model} of the qubit-noise interaction, which is beyond of the simplified models, and (ii) to examine the dissipative dynamics of qubit in order to perform {\it a complete characterization} of this interaction through the analysis of transient processes.  Such an analysis opens a way to optimize relaxation parameters and to enhance a fidelity of the quantum hardware.

In this paper, we perform a complete analysis of the dissipative dynamics for the qubit formed by the SQUID loop shunted by the transmission line (so called fluxmon \cite{15}), see sketch in Fig. 1(a). Characteristics of such a qubit are governed by the tilt and control fluxes, $\varphi$ and $\psi$, applied through the transmission line and the SQUID loop, respectively. We restrict ourselves by the low-frequency region when interactions with 1/f noises are described by the classical random fluxes, $\Delta\varphi_t$ and $\Delta\psi_t$, which are added to the tilt and control fluxes. The calculations of transient evolution are performed for the model of the qubit used the effective Josephson junction shunted by the effective LC-oscillator, see circuit in Fig. 1(b). We employ the two-level approach taking into account {\it a softness of the double-well potential}, in contrast to the solid-state models \cite{18} based on a fixed tunnel-coupling (due to the rigid barrier), and a variable level-splitting. The shape of potential is controlled by an interplay of the inductive and Josephson energies as it is shown in Figs. 1(c) and 1(d) for the symmetric ($\varphi =0$) and tilt ($\varphi\neq 0$) cases; the thin color curves draw a noise-induced modulation of potential via a shift of minima and a modulation of  barrier height. Averaged dynamics of the qubit is determined by the correlation functions $\langle\Delta\varphi_t\Delta\varphi_t\rangle$, $\langle\Delta\psi_t\Delta\psi_t\rangle$, and $\langle\Delta\varphi_t\Delta\psi_t\rangle$, which describe noises excited in the transmission line and in the SQUID loop ($tl$- and $j$-channels) as well as {\it correlations between these noises} ($c$-channel) \cite{19}. These correlations may caused by a common external sources or an inductive coupling between $tl$- and $j$-channels. We use the 1/f spectral functions $\alpha_k /\omega$ with $k=(tl,j,c)$, so that the dissipative dynamics is determined by the parameters of qubit, the dimensionless noise strengths $\alpha_k$, and the control fluxes, $\varphi$ and $\psi$.

The two lowest electromagnetic modes of the flux qubit are described by the isospin variable and the exact dynamics of qubit is governed by the Bloch equations with a time-dependent rotation frequency. We analyze the transient evolution of the density matrix at $t>0$ for the regimes: (a) resonant tunneling between the left and right wells, when the noise-induced broadening exceeds the interlevel energy, (b) relaxation of the interlevel population, and (c) decoherence of the off-diagonal part of a density matrix. The cases (b) and (c) correspond to the weakly-coupled levels, when the gap frequency exceeds the noise-induced broadening of levels \cite{20}. The Bloch equations for the case (a) is solved with the use of the symmetric qubit frame when the eigenstate problem is solved numerically at $\varphi =0$. For the cases (b) and (c) we use the tilt ($\varphi$-dependent) frame, when the basis functions correspond the lower and upper levels. For all cases, it is convenient to transform the Bloch system into the single integro-differential equations with the different kernels. Within  the weak-fluctuation approach, the averaged responses are written through the Laplace transforms of the averaged kernels and the parameters of relaxation are obtained in the explicit forms. Straightforward calculations of the fluctuating corrections for the cases (a)-(c) give {\it the limitations at tails of relaxation} for the averaged approach outlined above.

Based on this model, we have performed a complete analysis of the incoherent tunneling rate, the population relaxation rate, and the decoherence rate, $\nu_{T}$, $\nu_{1}$, and $\nu_{2}$ (i.e. of the inverse times of the different relaxation processes), as well as the noise-induced renormalization of the gap frequency. The main new results are summarized as follows:
\begin{itemize}
\item[(1)]\vspace{-0.25 cm} The averaged dissipative dynamics is governed by the non-local in time equations [Eqs. (11), (21), and (27) below] during the initial stage of relaxation $\nu_{T,1,2}t\leq 1$, while the exponential decay takes place if $\nu_{T,1,2}t\geq 1$. Peaks of the relaxation rates between wells or between levels, $\nu_T$ or $\nu_1$ versus tilt $\varphi$, are due to the noise in $tl$-channel while the dip of decoherence rate $\nu_2$ near $\varphi =0$ is determined by an interplay of the noises in $tl$- and $j$-channels. Weak asymmetry of $\nu_{T,1,2}$ around $\varphi =0$ is determined by the $c$-channel, i.e. by correlations between the $tl$- and $j$-noises.
\item[(2)]\vspace{-0.25 cm} The half-width of the Gaussian peak of incoherent tunneling is $\propto \sqrt {\alpha_{tl}}$ while the amplitude is $\propto 1/\sqrt{\alpha_{tl}}$. Weak asymmetry of this peak is $\propto\alpha_c /\alpha_{tl}$ and the direction of shift (along $\varphi >0$ or $<0$) is determined by the orientation of fluxes $\varphi$ and $\psi$ [parallel or anti-parallel, see Fig. 1(a)]. In addition to the mechanism considered in Refs. 14 and 22, the classical 1/f noise considered here provides an essential contribution to the experimental data reported in Ref. 16.
\item[(3)]\vspace{-0.25 cm}  The population relaxation rate is $\propto\alpha_{tl}$ with tails of peak suppressed as $\varphi^3$ and the parameters of peak are comparable to the recent experimental data \cite{15}. Due to softness of the barrier, there is no the dependency $\nu_1\propto\omega_{10}^{-1}$ for the 1/f noise under consideration. This disagreement with \cite{15} may be compensated by the frequency dispersion of noise caused by the size effect in transmission line \cite{22}.
\item[(4)]\vspace{-0.25 cm} There is {\it a dip of decoherence} : the rate $\nu_2$ and the renormalization of the gap frequency are increased sharply around $\varphi =0$ and are saturated with increasing of $\varphi$. There is the two-mode oscillating decoherence regime where the depth and asymmetry of the dip are determined by the ratios $\alpha_j /\alpha_{tl}$ and $\alpha_c /\alpha_{tl}$, respectively.
\item[(5)]\vspace{-0.3 cm} The averaged descriptions fail at tails of transient relaxation because of {\it the rare fluctuations effect}. The mean-square-fluctuation of the interwell tunneling increases $\propto t^2$ and, for typical parameters, the average description of incoherent tunneling is valid at $\nu_T t<3$. There are time-independent levels of fluctuations for the interlevel population and the decoherence [cases (b) and (c)] with the logarithmically enhanced contribution of rare fluctuations. Under tilt, $\varphi\neq 0$, the fluctuation effects are suppressed for all regimes.
\end{itemize}\vspace{-0.25 cm}

The paper is organized as follows. The model of the LC-shunted qubit, which interacts with partially correlated noises in the tilt and control channels, is presented in Sec. II. The resonant incoherent tunneling between wells is considered in Sect. III. The population relaxation rate and the  decoherence process are analyzed in Sect. IV for the weak-coupling regime. For all cases, the levels of fluctuations are considered in Sect. V. The concluding remarks, the list of assumptions, and the discussion of current experimental context are given in the last section. The averaged kernels are calculated in Appendix taking into account $tl$-, $j$-, and $c$-channels.

\section{Qubit-noise interaction }
We start with the description of the flux qubit, formed by SQUID shunted by LC-contour which are interacted with 1/f noises. Quantum mechanics of such a qubit in the $\phi$-representation is described by the Hamiltonian:
\begin{equation}
\hat H =4E_C{\hat q^2} +E_L (\phi -\varphi )^2 /2+{E_J}\cos (\psi /2)\cos\phi ~.
\end{equation}
Here $\phi$ and $\hat q=-id/d\phi$ are the dimensionless flux and the charge operator, while $\varphi$ and $\psi$ are the external tilt and control fluxes penetrated through the LC-contour and the SQUID loop, respectively. We use the dimensionless variable $\phi$ as well as the control fluxes $\varphi$ and $\psi$ in units $\Phi_0 /2\pi$ where $\Phi_0 =\pi\hbar /|e|$ is the flux quantum. Eq. (1) involves the capacitance energy $\propto E_C =e^2 /2C$, the inductive energy $\propto E_L =(\Phi_0 /2\pi )^2 /L$, and the effective Josephson energy $\propto E_J =I_c\Phi_0 /2\pi$ which describes the SQUID loop with the critical current $I_c$ and can be varied via the factor $\cos (\psi /2)$. \cite{23} If energy scale is fixed in units $E_L$, the Hamiltonian (1) is dependent on the external fluxes $\varphi$ and $\psi$, as well as on the parameters $4E_C /E_L\ll 1$, and $\beta_\psi =E_J\cos (\psi /2) /E_L\sim 1$. Noise contributions are introduced under the replacements of external factors  in Eq. (1) by $\varphi\to \varphi +\Delta\varphi_t$ and $\psi\to\psi +\Delta\psi_t$. The Hamiltonian of qubit-noise interaction,
\begin{equation}
\hat H_{\rm int}=-\Delta\varphi_t E_L (\phi -\varphi )-\Delta\psi_t E_J\sin (\psi /2)(\cos\phi )/2~,
\end{equation}
is written within the linear approach with respect to dimensionless random contributions, $\Delta \varphi_t$ and $\Delta\psi_t$. Notice, that energy spectrum determined by the noiseless Hamiltonian (1) is not changed under the separate replacements $\varphi\to -\varphi$ (with $\phi\to -\phi$) or $\psi\to -\psi$. In contrast,  $\hat H_{\rm int}$ is is not changed if  only $\varphi\to -\varphi$ and $\psi\to -\psi$, i.e. the relaxation processes are different for the parallel or antiparallel directions of the external fluxes.

Under averaging over random contributions $\Delta\varphi_t$ and $\Delta\psi_t$, we consider the Gaussian random processes taking into account a partial correlation between noises in the $tl$- and $j$-channels. Introducing the 1/f spectral function of the $k$th channel as $\alpha_k /\omega$, one obtains
\begin{eqnarray}
\left| \!{\begin{array}{*{20}c}
{\left\langle {\Delta \varphi _t \Delta \varphi _{t'} } \right\rangle }  \\
   {\left\langle {\Delta \psi_t \Delta \psi_{t'} } \right\rangle }  \\
   {\left\langle {\Delta \psi_t \Delta \varphi _{t'} } \right\rangle }  \end{array}}\! \right| = \left| {\begin{array}{*{20}c} {\alpha _{tl} }  \\ {\alpha _{j} }  \\ {\alpha _{c} } \end{array}} \right| \int\limits_{\omega_m}^{\omega_M}\!\frac{d\omega}{\pi\omega}\cos\omega\Delta t \! \equiv\! \alpha_k w_{\omega _m \Delta t}  \nonumber	\\
\approx\frac{\alpha_k}{\pi} \left\{\ln\frac{1}{\omega_m \Delta t}-\gamma + o\left[ {(\omega _m \Delta t)^2 } \right] \right\} ~, ~~~~~
\end{eqnarray}
where $\alpha_k$ determines a coupling strength in $k$th channel  ($k=tl, ~j, ~c$), $\Delta t=t-t'$, and we use the cut-off frequencies $\omega_{M,m}$ which are supposed to be the same in all channels if $\omega_M^{-1}\ll\Delta t\ll\omega_m^{-1}$. The explicit expression of the correlator $w_{\omega_m|\Delta t|}$ is approximately written through the integral cosine which has the logarithmic asymptotic at $\omega_m\Delta t\ll 1$ with the Euler's constant, $\gamma\approx 0.577$ \cite{24}. Thus, qubit-environment interaction is characterized by three constants, $\alpha_k$, and the lower cut-off frequency $\omega_m$.

Below we use the basis determined by the symmetric ($\varphi =0$) eigenstate problem $\hat H_{\varphi =0,\beta}\left| n\right\rangle =\varepsilon_{n}\left| n\right\rangle$, where $\hat H_{\varphi ,\beta}=\hat H -\hat H_{\rm int}$. In {\it the symmetric qubit frame}, the solutions $\left| n\right\rangle$ and $\varepsilon_{n}$ are parametrically dependent on the control flux through $\beta_\psi$ and $\varphi =0$. The density matrix takes form $\hat\rho_t =\sum \nolimits_{n_1 n_2}{\rho_{n_1 n_2}}{\left| {n_1 } \right\rangle }\left\langle {n_2} \right|$, where $\rho_{n_1 n_2}$ is governed by the standard equation $i\hbar\partial\rho_{n_1 n_2} /\partial t =[\hat H_t ,\hat\rho_t ]_{n_1 n_2}$ with the effective Hamiltonian,
\begin{equation}
H_{nn'}=\varepsilon_n\delta _{nn'}-E_L\varphi (\phi )_{nn'}+\left(\hat H_{\rm int}\right)_{nn'}  ~,
\end{equation}
which is written through matrix elements $(\cdots )_{nn'}\equiv\left\langle n \right|\cdots\left| {n'} \right\rangle$. Note, that $\varepsilon_n$ is determined for the symmetric barrier, while the tilt effect is described here by the off-diagonal matrix element $\propto (\phi )_{nn'}$. We employ below the two-level approach and consider only the states $\left| 0\right\rangle$ and $\left| 1\right\rangle$. Introducing the time-independent gap frequency $\omega_{10}=(\varepsilon_1 -\varepsilon_0 )/\hbar$ and the Pauli matrices $\hat\bsigma$, which are written here with respect to the basis formed by the $|0\rangle$ and $|1\rangle$ states, we arrive to the $2\times 2$ matrix Hamiltonian
\begin{eqnarray}
\frac{\hat H_t}{\hbar}\! =\!\frac{(\bomega_t\cdot\hat{\bsigma})}{2} , ~~  \bomega_t\! =\! \left[ -2\widetilde\omega (\varphi +\Delta \varphi_t ), 0, \omega_{10} -\omega_j \Delta\psi_t \right] , \nonumber   \\
\widetilde \omega \!  =\! \frac{E_L (\phi )_{10}}{\hbar} ~, ~~~~ \omega_j \! =\! \frac{E_J}{2\hbar} (\cos \phi )_{11,00}\sin\frac{\psi}{2} ~.  ~~~~
\end{eqnarray}
Here the frequencies $\widetilde\omega$ and $\omega_j$ determine the additional tunneling mixing of the $|0\rangle$ and $|1\rangle$ states due to the total tilt flux, $\varphi +\Delta \varphi_t$, and modulation of $\omega_{10}$ by the noise due to barrier fluctuations, respectively. We also omit the contributions $\propto$ const and take into account that the wave functions $\langle \phi | 0\rangle$ and $\langle\phi | 1\rangle$ are symmetric and antisymmetric with respect to $\phi \leftrightarrow  - \phi$. The matrix elements $(\phi )_{10}$ and $(\cos\phi )_{11,00}\equiv (\cos\phi )_{11}-(\cos\phi )_{00}$ are dependent on $\beta_\psi$ and $\omega_j$ is written through $\sin (\psi /2)$.

The projection operators on the left/right ($l/r$) wells in $\phi$-representation with the Hamiltonian (1) are $\hat P_{l/r}  = \theta ( -\! /\!+\phi )$, so that $\hat P_l +\hat P_r =1$ and  $\hat P_l\cdot\hat P_r =0$. Within the two-level approach describing by the Hamiltonian (5), these operators are given by
\begin{equation}
\hat P_{l/r}  = \left| \begin{array}{*{20}c}
  {\left\langle {1|1} \right\rangle } & {\left\langle {1|0} \right\rangle }   \\  {\left\langle {0|1} \right\rangle }  & {\left\langle {0|0} \right\rangle }  \end{array} \right|_{\phi <0 /\phi >0 }\approx \frac{1-\! /\! + \hat\sigma_x}{2} ~,
\end{equation}
where $\left\langle {1|1} \right\rangle_{\phi <0 /\phi >0}=\left\langle {0|0} \right\rangle_{\phi <0 /\phi >0}=1/2$ due to the symmetry reason. Numerical estimates of the off-diagonal matrix elements with the eigenstates calculated below (see Fig. 2 below) give $0.45<|\left\langle{1|0}\right\rangle_{\phi <0 /\phi >0}|<0.5$ if $\beta >1.1$ and $|\hat P_l\cdot\hat P_r |<0.05$ instead of the exact zero. This inconsistency is due to we drop the upper states, $n>1$, and below in Sect. III we use the right-hand expression of Eq. (6) which corresponds the weak-tunnel-coupling case.

If tunneling mixing increases, it is convenient to use  {\it the tilt qubit frame}. After rotation of $\hat H_t$ around 0Y-axis Eqs. (5) are transformed into
\begin{eqnarray}
\frac{\hat{\cal H}_t}{\hbar} =\frac{(\bbomega_t\cdot\hat{\bsigma})}{2}, ~~ \bbomega_t =\left[ -\frac{\Delta\varphi_t 2\widetilde\omega \omega _{10} +\Delta\psi_t\omega _j \widetilde\omega \varphi}{\Omega_\varphi} \right. , \nonumber \\
\left. 0,~ \Omega_\varphi +\frac{\Delta\varphi_t 2\widetilde \omega^2 \varphi -\Delta\psi_t\omega_j \omega_{10}}{\Omega_\varphi}\right] ~, ~~~~~~~~
\end{eqnarray}
where $\Omega_{\varphi}=\sqrt{\omega_{10}^2+(2\widetilde\omega\varphi )^2}$ is the level-splitting frequency and random contributions of $\bbomega_t$ give rise to the noise-induced inter-level transitions and the renormalization of frequency $\Omega_{\varphi}$. The projection operators on the upper ($+$) and lower ($-$) levels are determined as $\hat{\cal P}_{\pm}=(1\pm \hat\sigma_z)/2$ which is similar to Eq. (6) but $\hat{\cal P}_{\pm}$ is written in the basis formed by the eigenstates determined by the  Hamiltonian (7).
\begin{figure}
\begin{center}
\includegraphics[scale=0.22]{f2DD-LC}
\end{center}
\addvspace{-0.5 cm}
\caption{Parameters of Hamiltonians (5) and (7) versus control flux $\psi$. (a) Level splitting frequencies $\omega_{10}$ and $\omega_{21}$ in units $E_L /\hbar$ versus ratio $\beta_\psi =E_J\cos (\psi /2) /E_L$. Insets show wave functions $\langle\phi |n\rangle$ for $n=$0 (black), 1 (red), and 2 (green) at $4E_C /E_L =0.05$. (b) Matrix element $(\phi )_{10}$  versus $\beta_\psi$. (c) Matrix element $(\cos\phi )_{11,00}$ versus $\beta_\psi$. Red dashed lines in panels (a) and (c) show exponential asymptotics for the weak coupling regime. In all panels, the dotted, solid, and dashed curves correspond to $4E_C /E_L =0.01$, 0.005, and 0.0025, respectively. }
\end{figure}

Numerical solutions of the symmetric eigenstate problem $\hat H_{\varphi =0,\beta}\left| n\right\rangle =\varepsilon_{n}\left| n\right\rangle$ are obtained after discretization of the Hamiltonian (1) using  $N\sim 10^3$ points along $\phi$ axis and diagonalization of $N\times N$ matrix. In Fig. 2(a) we plot the dimensionless splitting frequencies $\omega_{10}$ and $\omega_{21}$ as well as the wave functions for $n=0$, 1, and 2 versus the ratio $\beta_\psi$ determined by the control flux. For the weak-tunneling  regime, if $\beta_\psi >1.2\div 1.3$ depending on $4E_C /E_L$, the frequency $\omega_{10}$ is suppressed exponentially. The dimensionless matrix elements $(\phi )_{10}$ and $(\cos\phi )_{11,00}$, which determine the characteristic frequencies $\widetilde\omega$ and $\omega_j$, are plotted in Figs. 2(b) and 2(c), respectively. Dependency of $(\phi )_{10}$ on $4E_C/E_L$ is negligible, see Fig. 2(b), and the matrix element $(\cos\phi )_{11,00}$ is exponentially suppressed at  $\beta_\psi >1.2\div 1.3$, see asymptotes in Figs. 2(a) and 2(c). Further we analyze relaxation rates versus $\omega_{10}$ and frequencies in Eq. (5). Under mapping between $\omega_j$- and $\psi$-variables the non-monotonic dependence of $\omega_j ={\rm sign}(\psi )(E_J /2\hbar )(\cos\phi )_{11,00}\sqrt{1-(\beta_\psi /\beta_0 )^2}$ on $\psi$ may be noticeable; below we use $\psi >0$ so that $\omega_j >0$.

\section{Incoherent resonant tunneling }
We evaluate here the rate of the incoherent resonant tunneling  between $l$- and $r$-wells based on the Bloch equation with the random frequency $\bomega_t$ given by Eq. (5). This system is transformed into the integro-differential equation for the redistribution of population between wells. The $2\times 2$ density matrix takes form $\hat\rho_t =(1+{\bf S}_t\cdot{\hat\bsigma})/2$ with $k=l,r$ and the population in $k$th well $n_k ={\rm tr}\hat P_k\hat\rho_t$ is determined through the projection operators, $\hat P_k$, given by Eq. (6). At $t>0$ the Bloch vector ${\bf S}_t$ is governed by the standard equation
\begin{equation}
\frac{d{\bf S}_t}{dt} =\left[{\bomega}_t\times {\bf S}_t\right] ~, ~~~~ {\bf S}_{t=0}=(\mp 1,0,0)
\end{equation}
with the normalization condition $|{\bf S}_t |=1$ and the initial vector ${\bf S}_{t=0}$, where $S_{t=0x}\equiv S_0 =-1$ or $+1$  corresponds to the state localized in the $l$- or $r$-wells, respectively. In order to reduce the system (8) into equation for $S_{tx}$ we  write $S_{ty,z}$ through the integrals $\int_0^t {dt'}\cdots S_{t'x}$ as
\begin{equation}
\left|\begin{array}{*{20}c}  S_{ty} \\ S_{tz}\end{array}\right| =\int\limits_0^t{dt'} \left| \begin{array}{*{20}c} \cos\theta_{tt'}  \\ \sin\theta_{tt'}\end{array} \right|\Omega_{t'z}S_{t'x} ~.
\end{equation}
After substitution of $S_{ty,z}$ into the X-component of Eq. (8) one obtains the exact integro-differential equation
\begin{equation}
\frac{dS_{tx}}{dt}+\omega_{tz}\int\limits_0^t{dt'}\omega_{t'z}\cos\theta_{tt'}S_{t'x} =0
\end{equation}
with the phase factor $\theta_{tt'}=\int_{t'}^t{d\tau}\omega_{\tau ,x}$.

Below we separate the averaged part of the Bloch vector, $\left\langle{S_{tx}}\right\rangle$, in Eq. (10) and consider equation
\begin{eqnarray}
\frac{d\left\langle {S_{tx} } \right\rangle}{dt}\!\! +\!\! \int\limits_0^t\!\!  {dt'}K_{tt'}
\left\langle{S_{t'x}}\right\rangle\!\!  = 0 ,  ~ K_{tt'}\!\!  =\left\langle {\omega_{tz} \omega _{t'z} \cos\theta_{tt'} } \right\rangle , ~~
\end{eqnarray}
where the averaged kernel $K_{tt'}$ should be written through the correlators (3). We restrict ourselves by the weak-fluctuation approximation when $\delta S_t =S_{tx}-\langle{S_{tx} }\rangle$ can be omitted, see Sect. V A. Straightforward averaging of the kernel $\langle K_{tt'}\rangle \equiv K_{\Delta t}$ gives
\begin{eqnarray}
K_{\Delta t}=\! e^{-\Gamma_{\Delta t}}\! \left(\cos\theta_{\Delta t} {\cal A}_{\Delta t} -\sin\theta_{\Delta t}{\cal B}_{\Delta t} \right) , ~~~~ \\
{\cal A}_{\Delta t}\!\! =\!\omega_{10}^2\!\! +\! \omega_j^2\!\! \left( \alpha _{tl} w_{\omega_m\Delta t}\! - \! W_{\Delta t}^2 \right) ,~ {\cal B}_{\Delta t}\!\! =\! 2\omega_j \omega_{10} W_{\Delta t}  \nonumber
\end{eqnarray}
with the noiseless phase $\theta_{\Delta t}=2\varphi\widetilde \omega \Delta t$ caused by tilt flux, see Appendix for details. This kernel is dependent on the energies $E_{L,C,J}$ through the frequencies introduced by Eq. (5), on the noise strengths $\alpha_{tl,j,c}$ and on $\omega_{m}$ from Eq. (3), as well as on the external fluxes, $\varphi$ and $\psi$. The decrement of exponential damping, $\Gamma_{\Delta t}$, and the factor $W_{\Delta t}$ in ${\cal A}_{\Delta t}$ and ${\cal B}_{\Delta t}$ of Eq. (12) are determined by the integrals
\begin{subequations}
\begin{eqnarray}
\frac{\Gamma_{\Delta t}}{2\alpha_{tl}}\!\! =\!\! \widetilde\omega^2 \!\!\! \int\limits_0^{\Delta t}\!\! {d\tau}\!\!\! \int\limits_0^{\Delta t}\!\! {d\tau '}\! w_{|\omega_m\Delta\tau |}\!\! =\!\! (\widetilde \omega \Delta t)^2\!\! \left(\!\! {w_{|\omega _m \Delta t|}\!\! +\!\!\frac{3}{{2\pi }}} \!\!\right) , \\
\frac{W_{\Delta t}}{2\alpha_c}\! =\widetilde\omega\int_0^{\Delta t}\!\! {d\tau}w_{|\omega_m\tau |}\! =\! \widetilde\omega \Delta t \left(\! {w_{|\omega_m \Delta t|}\! +\!\frac{1}{\pi}}\!\right) . ~~
\end{eqnarray}
\end{subequations}
In order to write the explicit expressions here, we used the definition of $w_{|\omega_m\Delta\tau |}$ given by Eq. (3) and performed the integrations by parts over $\tau$ and $\tau'$. Under these integrations we replaced the upper limit $\omega_M \Delta t$ by $\infty$.

According to Eq. (6), transient evolution of the population in left [or right] well is governed by $(1-\left\langle S_{tx}\right\rangle )/2$ [or $(1+\left\langle S_{tx}\right\rangle )/2$]. The Laplace transform of the averaged Bloch vector, $S_\zeta$, is obtained from the integro-differential equation (10) with the use of the convolution theorem as follows $S_\zeta =S_0 /(\zeta +K_\zeta )$, so that $\left\langle S_{tx}\right\rangle$ takes form:
\begin{equation}
\left\langle S_{tx}\right\rangle =S_0\int_C \frac{d\zeta}{2\pi i}\frac{e^{\zeta t}}{\zeta +K_\zeta} \propto e^{-\nu_T t} ,~~ {\rm if} ~ \nu_T t\gg 1 .
\end{equation}
The relaxation rate at tail of tunneling decay, $\nu_T$, is obtained as a pole of the complex integral (14), where the contour $C$ is around complex half-plane ${\rm Im}\zeta <+0$. Such a pole is determined by the equation $\zeta +K_\zeta =0$ at $\zeta\to 0$. As a result, the rate $\nu_T \approx K_{\zeta\to 0}$ is given by the integral
\begin{equation}
\nu_T \approx \!\int_0^\infty d\Delta t e^{-\Gamma_{\Delta t}}\! \left(\cos\theta_{\Delta t} {\cal A}_{\Delta t} -\sin\theta_{\Delta t}{\cal B}_{\Delta t} \right) , ~
\end{equation}
where the time scales $\widetilde \omega\Delta t\leq{\rm const}/\sqrt{\alpha_{tl}}$ are essential only. Under integration of Eq. (15) we use the logarithmic approximation, when the factors determined by Eq. (13) are replaced by the linear and quadratic dependencies, $W_{\Delta t}\approx 2\alpha_c\Lambda_T\widetilde \omega\Delta t$ and $\Gamma_{\Delta t}\approx 2\alpha_{tl}\Lambda_T (\widetilde \omega\Delta t)^2$. Based on Eq. (3),  the logarithmic factor $\Lambda _T$ is introduced here according to
\begin{equation}
w_{|\omega_m \Delta t|}\approx\ln (\sqrt {2\alpha_{tl}\Lambda_T}~\widetilde \omega /\omega_m ) +c_T = \Lambda _T ~,
\end{equation}
so that $\Lambda_T \approx \ln (\sqrt {\alpha_{tl}}\widetilde\omega /\omega_m )+c_T\gg 1$ with $c_T\sim 1$. Straightforward integration of Eq. (15) is performed for ${\cal A}_{\Delta t}\approx \omega_{10}^2$ because $\alpha_{j,c}<\alpha_{tl}\ll 1$, see estimates below. The explicit formula for the tunneling rate versus tilt flux is given by the Gaussian peak modulated by the pre-factor which is linear-dependent on $\varphi$:
\begin{eqnarray}
\nu_T  \approx\widetilde \nu _T e^{-(\varphi /\varphi _T )^2}(1-\varphi /\varphi_c ), ~~~~~~~~~   \\
\widetilde \nu _T =\frac{\sqrt\pi\omega _{10}^2}{2\varphi _T \widetilde \omega} ,  ~~ \varphi_T =\sqrt {2\alpha_{tl}\Lambda_T} , ~~ \varphi_c =\frac{\alpha_{tl}\omega _{10}}{2\alpha_c\omega _j}\Lambda_T  .   \nonumber
\end{eqnarray}
Here we introduce the amplitude of peak at symmetric point, $\widetilde \nu _T$, the half-width of peak, $\varphi_T\ll 1$, and the asymmetry parameter, $\varphi_c$. An asymmetry of peak, with respect to the replacement $\varphi\to -\varphi$ at fixed direction of $\psi$, appears due to correlations between $tl$- and $j$-channels, $\varphi_c^{-1}\propto\alpha _c$. This effect is weak enough because $\varphi_T\ll\varphi_c$ and the shift of peak, determined by the requirement $(d\nu_T /d\varphi )_{\varphi =\varphi_0}=0$, is equal $\varphi_0 \approx \varphi_T^2 /2\varphi_c \ll \varphi_T$.
\begin{figure}
\begin{center}
\includegraphics[scale=0.22]{f3DD-LC}
\end{center}
\addvspace{-0.75 cm}
\caption{ The ratio $\omega_j /\omega_{10}=\varphi_0 /2\alpha_c$ determining the shift of peak $\varphi_0$,  versus gap frequency $\omega_{10}$, which  corresponds the interval $1.2\leq\beta_\psi \leq 1.45$. Different $4E_C /E_L$ are marked. }
\end{figure}

For the estimates below we use a typical 1/f noise level  $\leq 4\times 10^{-11}\Phi_0^2/$Hz determined by the flux-flux spectral function at 1 Hz, \cite{14,15} so that $\alpha_{tl,j,c}\leq 10^{-8}$. The half-width of peak, $\varphi_T$, is only determined by the level of noise in the $tl$-channel and by the ratio $\widetilde\omega /\omega_m$, through $\Lambda_T$. Allowing for $\Lambda_T\sim 10\div 15$, one obtains $\varphi_T\sim (4.5\div 5.5)\times 10^{-4}$, or in the  dimensional units the maximal half-width of peak is $\sim 70\div 85~\mu\Phi_0$. According to Fig. 3 the maximal shift of peak is determined by the ratio $\omega_j /\omega_{10}\sim 15\div 30$, so that $\varphi_0\approx 2\alpha_c \omega _j /\omega _{10}\leq (3\div 6)\times 10^{-7}$ or $\leq 0.1 ~\mu\Phi_0$. Since $\widetilde\omega\sim 1.2 E_L /\hbar$ is weakly ($<$ 20\% ) dependent on the barrier-control variable $\beta_\psi$ or $\omega_{10}$ [Fig. 2(b)], the amplitude $\widetilde \nu _T$ is approximately proportional to $\omega_{10}^2$, i.e. the rate increases, when overlap of the left and right wave functions increases. If $\omega_{10}/2\pi \simeq$0.5 MHz for the device with $E_L /h\approx 250$ GHz, one obtains $\widetilde \nu _T\approx 8.4\div 10.3$ ms$^{-1}$ at $\alpha_{tl}\simeq 10^{-8}$ and the maximal tunneling rate decreases with a noise level as $\widetilde \nu_T\propto\alpha_{tl}^{-1/2}$. The numerical estimates performed show that the mechanism suggested gives an essential contribution to the resonant tunneling reported in \cite{15} but a shape of peak differs from the experimental data, see discussion in Sect. VI.

\section{Weak qubit-noise coupling }
We consider the weak qubit-noise coupling, when the gap frequency $\Omega_{\varphi}$ exceeds the noise-induced modulation of levels and it is convenient to use the tilt qubit frame described by the Hamiltonian (7). The $2\times 2$ density matrix $\hat\rho_t =(1+{\bf R}_t\cdot{\hat\bsigma})/2$ is written below through the Bloch vector ${\bf R}_t$ which is governed by the equation $d{\bf R}_t /dt =\left[{\bbomega}_t\times {\bf R}_t\right]$ with the normalization condition $|{\bf R}_{t=0}|=1$. Introducing the circular components $R_{t\pm}=(R_{tx}\pm iR_{ty} )/2$ we arrive to the system
\begin{equation}
\left\{ {\begin{array}{*{20}c}
   {\left( {d/dt \mp i\Omega _{tz} } \right)R_{t \pm }  \pm i\Omega_{tx}R_{tz}/2  = 0}  \\
{dR_{tz}/dt + i\Omega_{tx}(R_{t+}\! -\! R_{t-} )= 0} \end{array}} \right.  ,
\end{equation}
where $R_{t-}=R_{t+}^*$ because $\hat\rho_t =\hat\rho_t^+$. We consider the dissipative dynamics of Z- and $\pm$-components of ${\bf R}_t$ separately. Using the initial condition $R_{t=0\pm}=0$ and expressing $R_{t\pm}$ through $R_{tz}$ one obtains the exact integro-differential equation for the Z-component of the Bloch vector
\begin{equation}
\frac{dR_{tz}}{dt}+\Omega_{tx} \int_0^t{dt'}\Omega_{t'x}\cos\Theta_{tt'} R_{t'z} =0
\end{equation}
with the phase factor $\Theta_{tt'}=\int_{t'}^t{d\tau}\Omega_{\tau ,z}$. For $t\to 0$ we use the initial condition $R_{t=0z}=1$ which corresponds to the initial population localized at the upper level because the population numbers are $n_{\pm t}={\rm tr}\hat{\cal P}_\pm \hat\rho_t$ (the conservation requirement is $n_{+,t}+n_{-,t}=1$). Similarly, using the initial condition $R_{t=0z}=0$ and eliminating the Z-component  from the upper Eq. (18), we obtain the exact integro-differential equation for the $\pm$ circular components
\begin{equation}
{\left( {\frac{d}{{dt}}\! \mp\! i\Omega _{tz} } \right)\! R_{t \pm }  \pm \frac{{\Omega _{tx} }}{2}\!\!\int\limits_0^t\! {dt'} \Omega _{t'x} (R_{t' + }\! -\! R_{t' - } )\! =\! 0} ~.
\end{equation}
As an initial condition for Eq. (20) we use the normalization condition at $t=0$ written in the form $R_{t=0+}R_{t=0-}=1/4$. Below we restrict ourselves by the weak-fluctuation regime and consider the averaged dynamics determined by Eqs. (19) and (20).

\subsection{Relaxation of population }
We consider the interlevel redistribution of population, $\Delta n_t\equiv n_{+t}-n_{-t}={\rm tr}\hat \sigma_z \hat\rho_t =R_{tz}$, and separate $R_{tz}$ into the averaged and random parts, $R_{tz}=\langle{\Delta n}_t\rangle +\delta n_t$, which are governed by the equations
\begin{eqnarray}
\frac{d}{dt}\left| {\begin{array}{*{20}c} \langle{\Delta n}_t\rangle  \\  {\delta n_t }  \end{array}} \right| + \int_0^t {dt'} N_{t - t'} \left| {\begin{array}{*{20}c}
   \langle{\Delta n}_{t'}\rangle  \\  {\delta n_{t'} }  \end{array}} \right| = \left| {\begin{array}{*{20}c} 0  \\   {-\delta f_t }  \end{array}} \right| , ~~ \\
N_{\Delta t} =\! \left\langle \Omega _{tx} \Omega _{t'x} \cos\Theta_{tt'} \right\rangle \! \approx\!\cos (\Omega_\varphi \Delta t){\cal X}_\varphi w_{\omega_m\Delta t}/\Omega _\varphi^2  .  \nonumber
\end{eqnarray}
Here we approximate the averaged kernel $N_{\Delta t}$ neglecting random contributions to the phase $\Theta_{tt'}\to\Omega_\varphi \Delta t$, see Eq. (A5). Based on Eqs. (3) and (7) we used the correlator $\left\langle \Omega _{tx} \Omega _{t'x} \right\rangle ={\cal X}_\varphi w_{\omega_m\Delta t}/\Omega _\varphi^2$, where
\begin{equation}
{\cal X}_\varphi\! =\! \alpha _{tl} (2\omega _{10} \widetilde \omega )^2\!  +\! \alpha _j (\omega _j \widetilde \omega \varphi )^2\! +\!\alpha_c \omega _{10} \omega _j (2\widetilde \omega )^2\varphi  ~~~
\end{equation}
is dependent on the control parameters $\varphi$ and $\psi$ (through $\beta_\psi$). Fluctuations of population ${\delta n}_t$ are governed by the non-uniform equation with the source $\delta f_t =\int_0^t {dt'}\cos (\Omega_\varphi \Delta t)\delta N_{tt'} \left\langle \Delta n_{t'}\right\rangle$ determined by a random part of kernel $\delta N_{tt'}=\Omega _{tx}\Omega _{t'x}-\left\langle \Omega _{tx}\Omega _{t'x}\right\rangle$ and we consider this contribution in Sect. V B.

After the Laplace transform of the upper line of Eq. (21) with the initial condition $\langle{\Delta n}_{t=0}\rangle =1$, we obtain the transient solution
\begin{equation}
\Delta n_\zeta\! =\left[\zeta  + {\cal X}_\varphi (w_{\zeta -i\Omega _\varphi} +w_{\zeta +i\Omega_\varphi})/2\Omega_\varphi^2\right]^{-1}  ,
\end{equation}
which is written through $w_\zeta =\ln [(\zeta /\omega_m )^2 +1]/2\pi\zeta$. Similarly to Sect. III, we use the logarithmic approximation  $w_{\zeta\pm i\Omega_\varphi}\approx\mp i\left(\Lambda_1 \pm i\pi /2\right)/\pi \Omega_\varphi$ with $\Lambda_1\approx\ln (\Omega_\varphi /\omega_m )+c_1\gg 1$ and $c_1\sim 1$. The $\propto\Lambda_1$ contributions cancel each other  in Eq. (23) and $\Delta n_\zeta\approx (\zeta +\nu _1 )^{-1}$ or $\langle{\Delta n}_t\rangle =\exp (-\nu_1 t)$ describes the nonoscillating  exponential decay with the population relaxation rate $\nu _1\approx {\cal X}_\varphi /2\Omega_\varphi^3$. At the symmetric point $\varphi =0$, this rate is given by $\nu _1 |_{\varphi =0}={\cal X}_{\varphi =0} /\omega_{10}\approx 2\alpha_{tl} \widetilde \omega ^2 /\omega _{10}$, when only $tl$-channel remains essential. Under non-zero  tilt $\varphi\neq 0$, the relaxation rate is suppressed for the most part due to the factor $\Omega_\varphi^{-3}$. Using a typical half-width of peak $\sim\omega_{10}/2\widetilde\omega$, we find that the $\varphi$-dependent contributions to ${\cal X}_\varphi$ are weak because $\alpha_{j,c}\leq \alpha_{tl}$ and $\omega_j /4\widetilde\omega\ll 1$ [see Figs. 2 (b) and (c)]. As a result, the rate $\nu_1$ takes form
\begin{equation}
\nu _1 \approx\frac{\widetilde \nu_1}{\left[ {1 + (\varphi /\varphi_1 )^2 } \right]^{3/2}} , ~~ \widetilde \nu_1 =\frac{2\alpha_{tl}\widetilde\omega ^2}{\omega_{10}} ,  ~~
\varphi_1 =\frac{\omega_{10}}{2\widetilde \omega}
\end{equation}
and, in analogy to the incoherent tunneling regime, the relaxation of population is only governed by the noise in the $tl$-channel, $\nu_1\propto\alpha_{tl}$.
\begin{figure}
\begin{center}
\includegraphics[scale=0.22]{f4DD-LC}
\end{center}
\addvspace{-0.5 cm}
\caption{Parameters determining relaxation of population in Eq. (24). (a) Maximal rate at symmetric point $\widetilde\nu_1 =\nu_1 |_{\varphi =0}$ versus gap frequency $\omega_{10}$ corresponding the spectral region 0.1$\div$2.5 GHz at $E_L /h=$250 GHz. Color dots  approximate $\widetilde\nu_1$ by $\propto\omega^{-q}$ dependencies with $q=1.35\div 1.55$. (b) Half-width of the rate $\varphi_1$ for the same spectral region. Color dots show near-linear approximations. In both panels, the dotted, solid, and dashed curves correspond to $4E_C /E_L =0.01$, 0.005, and 0.0025, respectively. }
\end{figure}

Apart from the tails of the rate $\nu _1 /\widetilde\nu_1\leq 10^{-2}$ versus $\varphi$, where the $\propto\varphi ,~\varphi^2$ contributions to ${\cal X}_\varphi$ are not negligible, the shape of the peak is determined by the amplitude and the half-width, $\widetilde \nu_1$ and $\varphi_1$ (we neglect a weak asymmetry of $\nu_1$ aroused from $\propto\alpha_c\varphi$ contributions). According to Eq. 2 (b), $\widetilde \omega$ varies from $\sim$0.4 to $\sim$1 over the weak-coupling region due to  the softness of barrier, so that the dependency of $\widetilde \nu_1$ on the gap frequency $\omega_{10}$ {\it differs from} $\propto\omega_{10}^{-1}$ as it is shown in Fig. 4(a) for the different ratios $4E_C /E_L$. The weak-coupling regime takes place under the requirement $\nu_1 /\Omega _\varphi\ll 1$ which is transformed into the condition $2\alpha_{tl}(\widetilde\omega /\omega_{10})^2\ll 1$ at the symmetric point $\varphi =0$. If $\alpha_{tl}\leq 10^{-8}$ this condition is satisfied and for $E_L /h\approx$250 GHz the maximal rate is $\widetilde \nu_1 \approx (0.07\div 0.16 )~\mu$s$^{-1}$ at $\omega_{10}/2\pi =$0.5 GHz. The half-width of the peak at the same $E_L /h$ and $\omega_{10}/2\pi$ is about $\varphi_1\approx 22\div 33$  m$\Phi_0$ and  $\varphi_1$ shows near-linear dependencies on $\omega_{10}$, as it is plotted in Fig. 4(b).

\subsection{Decoherence rate}
The decoherence process of the off-diagonal part of density matrix is described by the circular components of the Bloch vector governed by Eq. (20). Separating rotation with the frequency $\Omega_\varphi$ according to $R_{t \pm}=\exp (\pm i\Omega_\varphi t)r_{t\pm}$ and neglecting the high-frequency contributions [$\propto\exp (\pm i\Omega_\varphi (t+t'))$], we arrive to the closed equations for the slow amplitudes $r_{t\pm}$:
\begin{equation}
\left(\! {\frac{d}{dt} \mp i\Delta \Omega _{tz} }\!\! \right)r_{t \pm }\! +\!\frac{{\Omega _{tx} }}{2}\!\!\int_0^t\!\! {dt'} \Omega _{t'x} e^{ \mp i\Omega _\varphi  (t - t')} r_{t' \pm }\!\!  =\!\! 0 ~.
\end{equation}
Because $r_{t-}=r_{t+}^*$, we consider only the $+$ component $r_{t+}\equiv r_t$ . Within the weak-fluctuation regime, we separate the equations for the averaged and random parts of the amplitude, $r_t=\left\langle r_t\right\rangle +\delta r_t$, as follows
\begin{eqnarray}
\frac{d}{dt}\left| {\begin{array}{*{20}c}
   {\left\langle {r_t} \right\rangle }  \\
   {\delta r_t }  \\
\end{array}} \right| -i\left| {\begin{array}{*{20}c}
   {\left\langle {\Delta \Omega _{tz} \delta r_t } \right\rangle }  \\
   {\Delta \Omega _{tz} \left\langle {r_t} \right\rangle }  \\
\end{array}} \right|   ~~~~~~~   \\
+ \frac{1}{2}\int_0^t {dt'} e^{-i\Omega _\varphi  (t - t')} \left| {\begin{array}{*{20}c}
   {\left\langle {\Omega_{tx} \Omega_{t'x} } \right\rangle } \\
   {\delta N_{tt'} }  \\
\end{array}} \right|\left\langle r_{t'} \right\rangle  = 0 ~.  \nonumber
\end{eqnarray}
Here the random part of kernel $\delta N_{tt'}$ gives vanishing contribution to $\left\langle {\Delta \Omega _{tz} \delta r_{t \pm } } \right\rangle$, because it contains an average of one or three random factors. As a result, $\left\langle {r_{t \pm } } \right\rangle $ is governed by the equation
\begin{eqnarray}
\frac{{d\left\langle {r_t} \right\rangle }}{{dt}} + \int_0^t {dt'} \left\langle {\Delta \Omega _{tz} \Delta \Omega _{t'z} } \right\rangle \left\langle {r_{t'}} \right\rangle ~~~~ \\
+ \frac{1}{2}\int_0^t {dt'} e^{-i\Omega _\varphi  (t - t')} \left\langle\Omega _{tx} \Omega _{t'x} \right\rangle \left\langle {r_{t'}}\right\rangle\simeq 0  \nonumber
\end{eqnarray}
with the initial condition $\left\langle r_{t=0}\right\rangle =r_0$ where $r_0$ is normalized by the requirement $r_0r_0^* =1/4$. The first and second integral terms here describe the long- and short-scale contributions to the temporal evolution.

After the Laplace transform of Eq. (27), we obtain the transient solution
\begin{equation}
r_{\zeta}=r_0 \left[ {\zeta +{\cal Z}_\varphi w_\zeta /\Omega _\varphi^2 +{\cal X}_\varphi w_{\zeta  +i\Omega _\varphi  } /2\Omega _\varphi^2} \right]^{-1} .
\end{equation}
Here the correlator $\left\langle\Delta\Omega _{tz} \Delta \Omega_{t'z}\right\rangle ={\cal Z}_\varphi w_{\omega_m\Delta t}/\Omega _\varphi^2$ is written through
\begin{equation}
{\cal Z}_\varphi\! =\! \alpha _{tl} (2\widetilde\omega^2 \varphi )^2\!  +\! \alpha _j (\omega_j\omega_{10})^2\! -\!\alpha_c\omega_{10} \omega _j (2\widetilde \omega )^2\varphi ~,
\end{equation}
which is similarly $\left\langle\Omega _{tx}\Omega_{t'x}\right\rangle$ in Eq. (22). We consider below a slow-varied part of $\left\langle r_t\right\rangle$, when $|\zeta |\sim\nu_2 \ll\Omega_\varphi$ with the decoherence rate $\nu_2$, and apply the logarithmic approximation, when $w_\zeta$ is replaced by $[\Lambda_2 +i{\rm arg}(\zeta )]/\pi\zeta$ with $\Lambda_2\approx\ln (\nu_2 /\omega_m )+c_2$ with $c_2\sim 1$. In analogy to Sect. IV A, $w_{\zeta +i\Omega_\varphi}$  should be replaced by $(1/2 -i\Lambda_1 /\pi )/\Omega_\varphi$ with $\Lambda_1 >\Lambda_2$ because of $\Omega_\varphi\gg\nu_2$. Using these replacements, one can search the poles of the solution $r_{\zeta}$ from the quadratic equation:
\begin{equation}
\zeta ^2  + \zeta \nu_1 \left( 1/2-i\Lambda_1 /\pi\right) +\nu_\varphi^2 [ \Lambda_2  + i\arg (\zeta )]/\pi \approx 0 ~,
\end{equation}
where we introduce the characteristic rate $\nu_\varphi\equiv\sqrt{{\cal Z}_\varphi}/\Omega_\varphi$ and use $\nu _1\approx {\cal X}_\varphi/2\Omega_\varphi^3$ from Sect. IV A. This equation is transformed into $(\zeta -\zeta_+ )(\zeta -\zeta_- )\approx 0$ with a two poles $\zeta_\pm$ determined by the relation:
\begin{eqnarray}
\zeta_\pm   =  - \nu _1 (1/2 - i\Lambda _1 /\pi )/2 ~~~~~~~~~~~~  \\
 \pm \sqrt {\nu _1^2 (1/2 - i\Lambda _1 /\pi )^2 /4 - \nu _\varphi ^2 [\Lambda _2  + i\arg (\zeta )] /\pi }  \nonumber
\end{eqnarray}
and it is not an explicit solution because of the factor $\arg{(\zeta )}$. Within the logarithmic accuracy, $\Lambda_{1,2}\gg\pi /2$, the poles are near the imaginary axis and $\arg (\zeta_\pm )\approx\pm\pi /2$.

Thus the poles (31)  describe {\it a two mode behavior} of the decoherence process. This is because of a different character of the integral contributions in Eq. (27): while the XX-term is cutting off at $t\sim\Omega_\varphi^{-1}$, the ZZ-term shows a long-time memory. We obtain the poles as $\zeta_\pm \equiv i\Delta\Omega_\pm -\nu_\pm$  with the renormalizations of the gap frequency $\Delta \Omega_\pm$ and the decoherence rates $\nu_\pm$ given by:
\begin{eqnarray}
\Delta \Omega _ \pm   \approx \nu _1 \Lambda _1 /2\pi  \pm \sqrt {(\nu _1 \Lambda _1 /2\pi )^2  + \nu _\varphi ^2 \Lambda _2 /\pi } ~, \nonumber  \\
\nu_ \pm \approx \frac{{\nu _\varphi ^2  + \nu _1 |\Delta \Omega _ \pm  |}}{{4\sqrt {(\nu _1 \Lambda _1 /2\pi )^2  + \nu _\varphi ^2 \Lambda _2 /\pi } }}  ~. ~~~~~~~~
\end{eqnarray}
After the inverse Laplace transform one obtains
\begin{equation}
\frac{\langle {r_t }\rangle}{r_0}\!\! \approx\!\! \frac{{(i\Delta \Omega_+\!\! -\! \nu _ +  )e^{(i\Delta \Omega_+\! -\! \nu _ +\! )t}\!\!  -\! (i\Delta \Omega_-\!\! -\! \nu _- )e^{(i\Delta \Omega_-\!\! -\!\nu_- \! )t} }}{i(\Delta \Omega_+ -\Delta \Omega_- ) - (\nu_+ -\nu_- )} ,
\end{equation}
i.e. an oscillating temporal evolution of $\langle {r_t }\rangle$ is described through $\Delta \Omega_\pm$ and $\nu_\pm$ determined by Eq. (32).
\begin{figure}
\begin{center}
\includegraphics[scale=0.21]{f5DD-LC}
\end{center}
\addvspace{-0.8 cm}
\caption{ Characteristic frequency $\omega_j$ (a) and ratio  $\widetilde \omega /\omega_j$ (b), which determine the decoherence process, versus gap frequency $\omega_{10}$ for the same conditions as in Fig. 4 (a). Asymptotics are shown by red dots. }
\end{figure}
Shape of the damping oscillations in (33) is determined by the rates $\nu_1$ given by Eq. (24) and the characteristic rate $\nu _\varphi$ given by
\begin{equation}
\frac{\nu _\varphi }{\sqrt{\alpha_j}~\omega_j}= \sqrt {\frac{{1 + \frac{{\alpha _{tl} }}{{\alpha _j }}\left( {\frac{{\widetilde\omega \varphi }}{{\omega _j \varphi _1 }}} \right)^2  - \frac{{2\alpha _c }}{{\alpha _j }}\frac{\widetilde\omega \varphi}{{\omega _j \varphi _1 }}}}{1 + (\varphi /\varphi _1 )^2 }} ~.
\end{equation}
\begin{figure}
\begin{center}
\includegraphics[scale=0.22]{f6DD-LC}
\end{center}
\addvspace{-0.8 cm}
\caption{ Normalized rates $\nu_\varphi /\widetilde\nu_1$ (color dips) and $\nu_1 /\widetilde\nu_1$ (black) versus tilt $\varphi /\varphi_1$ plotted for $\omega_j >0$ (the case $\omega_j <0$ corresponds $\varphi\to -\varphi$). $\nu_\varphi$ is plotted for $\widetilde \omega /\omega_j =$7.5 (blue), 15 (red), and 30 (green) with different relative contributions of $tl$- and $c$-channels in panels (a)-(d): $[\alpha_{tl}/\alpha_j ,\alpha_c /\alpha_j ]=$[1,1] (a), [3,1] (b), [1,0.1] (c), and [3,0.1] (d). Black curves show $\nu_1 /\widetilde\nu_1$ for $\widetilde\nu_1 /\nu_{\varphi =0}=$1 (dashed) and 3 (solid). }
\end{figure}

This rate at symmetric point, $\nu_{\varphi =0}=\sqrt{\alpha_j}\omega_j$, and the tilt dependency of $\nu_\varphi$ are written through $\omega_j$ and $\widetilde\omega /\omega_j$ shown versus $\omega_{10}$ in Figs. 5(a) and 5(b), respectively. In contrast to $\nu_1\propto\alpha_{tl}$, we obtain $\nu_\varphi \propto \sqrt{\alpha_j}$ and the both contributions may be essential even if $\alpha_j\ll\alpha_{tl}$. There are two limiting cases, with ZZ- or XX-correlators dominate in Eq. (27), when the renormalization frequencies and the decoherence rates take forms:
\begin{subequations}
\begin{eqnarray}
\Delta \Omega _ \pm\!\approx\!\pm \nu _\varphi  \sqrt {\frac{{\Lambda _2 }}{\pi }} , ~~~~\nu _ \pm\!\approx\! \frac{\nu _\varphi}{4}\sqrt {\frac{\pi}{\Lambda_2}} , ~{\rm if} ~ \nu _\varphi\!\gg\! \nu _1 , ~~    \\
\Delta\Omega_+\!\!\approx\! \nu_1\frac{\Lambda_1}{\pi} , ~ \nu_+\!\!\approx\!\frac{\nu_1}{2}, ~ \Delta\Omega_-\!\!\approx\!\nu_-\!\!\approx\! 0, ~ {\rm if} ~ \nu _\varphi\!\ll\!\nu _1 . ~~
\end{eqnarray}
\end{subequations}
Here the imaginary and real parts of poles are connected as $|\Delta\Omega_\pm |= (4\Lambda_2 /\pi )\nu_\pm$ if $\nu_\varphi\!\gg\! \nu _1$, or as $\Delta\Omega_+ = (2\Lambda_1 /\pi )\nu_+$ if $\nu_\varphi\!\ll\! \nu _1$, i.e. they differ by the scale factors $\propto\Lambda_{1,2}/\pi\gg 1$. Note, that $\nu_\varphi$ saturates at $\nu_{max}=\sqrt{\alpha_{tl}}\widetilde\omega$ and increases $\propto\varphi$ before saturation, if $1>|\varphi |/\varphi_1 |>\omega_j /\widetilde\omega$. An interplay between these regimes is significant in the region where $\widetilde\nu_1 /\nu_{\varphi =0}=\alpha_{tr}\widetilde\omega /\sqrt{\alpha_j}\omega_j\varphi_1\sim 1$. Fig. 6 compare shapes of the sharp dips of $\nu_\varphi$ and the slow peaks of $\nu_1$ for different levels of noise and different ratios $\widetilde\nu_1 /\nu_{\varphi =0}$. For the weakly-correlated noises with $\alpha_c\ll\alpha_{tl,j}$, see Figs. 6 (c) and (d), there are near-symmetric dips but for $\alpha_c\sim\alpha_j$ the dips around $\varphi\sim 0$ are asymmetric enough and are shifted to the right if $\omega_j >0$, see Figs. 6(a) and(b). Moreover, for the fully-correlated identical noises with $\alpha_{tl}=\alpha_j =\alpha_c$, one obtains $\nu_\varphi =0$ at $\varphi =(\widetilde\omega /\omega_j )\varphi_1$, see Fig. 6(a). This peculiarity is caused by {\it the destructive interference} of noises in $tl$- and $j$-channels and it becomes essential if $\alpha_{j,c}/\alpha_{tl}> 0.5$, see Fig. 8 below.
\begin{figure}
\begin{center}
\includegraphics[scale=0.21]{f7DD-LC}
\end{center}
\addvspace{-0.8 cm}
\caption{ Normalized frequencies $|\Delta\Omega_\pm |/\widetilde\nu_1$ (a) and decoherence rates $\nu_\pm /\widetilde\nu_1$  (b) at the symmetric point $\varphi =0$ versus gap frequency $\omega_{10}$ for the same $4E_C /E_L$ as in Figs. 4 and 5. Coupling strengths are $\alpha_{tl}=10^{-8}$ and $\alpha_j /\alpha_{tl}=$0.25 (black and gray curves) or 0.05 (red and green curves). $\pm$ modes are marked and logarithms are chosen as $\Lambda_1\simeq 15$ and $\Lambda_2\simeq 10$. }
\end{figure}

At $\varphi =0$ the interplay of the long- and short-scale ($\propto\nu_{\varphi =0}$ and $\propto\nu_1$)  contributions in Eq. (32)  gives rise to the dependencies of $\Delta\Omega_\pm$ and $\nu_\pm$ which increase with $\omega_{10}$ as it is shown in Fig. 7. Similarly to Figs. 4 and 5, the growth of $\Delta\Omega_\pm$ and $\nu_\pm$ is dependent on $4E_C /E_L$ and on the noise levels, $\alpha_{tl}$ and $\alpha_j$. Finally, in Fig. 8 we plot $\Delta\Omega_\pm$ and $\nu_\pm$ versus tilt flux, $\varphi /\varphi_1$, for different gap frequencies at $4E_C /E_L =0.005$; there is the same behavior of dips with numerical variations up to 2 times if $4E_C /E_L$ varies over 0.01$\div$0.0025. Thus, the ratio $\Delta\Omega_\pm /\nu_\pm$ is about ten and contribution of the "$-$" mode in Eq. (33) is negligible around $\varphi =0$. If $\varphi /\varphi_1 >0.2$, the decoherence rate and  $\Delta\Omega_\pm$ increase fast (up to ten times at $\varphi /\varphi_1\sim 1$, if the gap frequency $\leq$1 GHz for the parameters used above).
\begin{figure}
\begin{center}
\includegraphics[scale=0.21]{f8DD-LC}
\end{center}
\addvspace{-0.8 cm}
\caption{ Normalized frequencies $|\Delta\Omega_\pm |/\widetilde\nu_1$ (a, b) and decoherence rates $\nu_\pm /\widetilde\nu_1$  (c, d) at $4E_C /E_L =0.005$ versus tilt $\varphi /\varphi_1$ for the gap frequencies $\omega_{10}\approx 1.2\times 10^{-3}$ (green), $2.3\times 10^{-3}$ (black), and $6.5\times 10^{-3}$ (or 0.3, 0.57, and 1.6 GHz at $E_L /h=$250 GHz). Solid and dashed curves show $+$ and $-$ modes, respectively. Left (a, c) and right (b, d) panels correspond $[\alpha_j /\alpha_{tl},\alpha_c /\alpha_{tl}]=$[1,1] and [0.1,0.1], respectively. }
\end{figure}

\section{Effect of fluctuations  }
Finally, we examine the random addendums to the averaged Bloch vectors considered in Sects. III and IV. We analyze the two-point correlations of fluctuations and determine the conditions for applicability of the averaged dynamics in the cases under consideration. These conditions are collected in the last paragraph of each subsection.

\subsection{Random contributions to incoherent tunneling }
Here we consider random part of the Bloch vector $\delta S_t =S_{tz}-\left\langle{S_t }\right\rangle$ governed by the linearized equation
\begin{equation}
\frac{d\delta S_t}{dt}+\int\limits_0^t {dt'}K_{\Delta t} \delta S_{t'}  =-\int\limits_0^t {dt'} \delta K_{tt'} \left\langle {S_{t'x} }\right\rangle  \equiv\delta F_t ~,
\end{equation}
which is obtained after subtraction of the averaged Eq. (11) from the exact Eq. (10). Here a random source $\delta F_t$ is introduced trough the kernel $\delta K_{tt'}=\omega_{tz}\omega_{t'z}\cos\theta_{tt'} - K_{t - t'}$ and a second-order correction ($\propto\delta K_{tt'}\delta S_{t'}$) is omitted. Similar to Sect. III, Laplace transform of Eq. (36) gives the solution $\delta S_\zeta =\delta F_\zeta /(\zeta +K_\zeta )$ and the correlation function $\left\langle {\delta S_{t_1}\delta S_{t_2} }\right\rangle$ takes form:
\begin{eqnarray}
\left\langle {\delta S_{t}\delta S_{t'} }\right\rangle  = \int_C{\frac{d\zeta}{2\pi i}} \int_C {\frac{{d\zeta '}}{2\pi i}} \frac{e^{\zeta t +\zeta 't'}\left\langle \delta F_{\zeta}\delta F_{\zeta '}\right\rangle}{\left( {\zeta +K_{\zeta} } \right)\left( {\zeta '+ K_{\zeta '} } \right)}  \\
\approx\int_0^t {dt_1 } \int_0^{t'} {dt'_1 } e^{ - \nu _T (t + t' - t_1  - t'_1 )} \left\langle {\delta F_{t_1 } \delta F_{t'_1 } } \right\rangle . \nonumber
\end{eqnarray}
Here the correlator of random sources is written through $\left\langle{S_{t,x} }\right \rangle$:
\begin{eqnarray}
\left\langle {\delta F_{t_1 }\delta F_{t'_1 } } \right\rangle\! =\!\! \int\limits_0^{t_1 }\! {dt_2 } \!\!\int\limits_0^{t'_1}\! {dt'_2 }\! \left\langle {\delta K_{t_1 t_2 } \delta K_{t'_1 t'_2 } } \right\rangle\! \left\langle {S_{t_2 x} } \right\rangle \!\langle {S_{t'_2 x} } \rangle ~, ~~~ \\
\left\langle\delta K_{t_1 t_2 } \delta K_{t'_1 t'_2 } \right\rangle\!\!\approx\! \omega_{10}^4\! \left\langle {\cos \theta_{t_1 t_2}\! \cos\theta_{t'_1t'_2 } } \right\rangle \!\!
-\!\! K_{_{t_1 -t_2} }\!\! K_{_{t'_1  - t'_2 } } ,  \nonumber
\end{eqnarray}
where $\omega_{t_1 z}\omega_{t_2 z}\omega_{t'_1 z}\omega_{t'_2 z}$ is replaced by $\omega_{10}^4$ omitting the contributions $\propto\alpha_{\ldots}$.

For the weak fluctuation regime, we approximate $\left\langle\cos\theta_{t_1 t_2} \cos\theta_{t'_1 t'_2} \right\rangle -\left\langle \cos\theta_{t_1 t_2}\right\rangle \left\langle\cos\theta_{t'_1 t'_2}\right\rangle$ by the first order contribution. Using (A.6) we obtain the four-point correlator in (38) as:
\begin{eqnarray}
\left\langle {\delta K_{t_1 t_2 } \delta K_{t'_1 t'_2 } } \right\rangle  \approx \alpha_{tl} (2\widetilde \omega )^2 \omega _{10}^2 \cos \theta _{\Delta t_{12} } \cos \theta _{\Delta t'_{12} }  \nonumber  \\
\times \int_{t_2 }^{t_1}d\tau\int_{t'_2}^{t'_1}{d\tau}'w_{\omega_m |\tau -\tau '|}  ~~~~~~~
\end{eqnarray}
with $w_{\omega_m |\Delta \tau|}$ given by Eq. (3). At $\nu_T t_{1,2}\gg 1$ one can replace $\left\langle{S_{t,z} }\right\rangle$ by the exponent $\exp (-\nu_T t)$ and the correlator (37) is transformed into
\begin{eqnarray}
\left\langle {\delta S_t^2 }\right\rangle\! \approx\! e^{-2\nu _T t} \alpha _{tl} (2\widetilde \omega )^2 \omega _{10}^4\!\! \int\limits_{\omega _m }^{\omega _M }\!\!\!\! {\frac{d\omega }{\pi\omega ^3}}\!\!\int\limits_0^t\!\! {dt_1}\!\! \int\limits_0^t\!\!{dt_1'}\!\!\int\limits_0^{t_1}\!\!{dt_2}\!\! \int\limits_0^{t_1'}\!\!{dt_2'} ~~~~  \nonumber \\
\times e^{-\nu _T (t_2 +t_2' -t_1 -t_1')} \cos \theta _{\Delta t_{12} } \cos \theta _{\Delta t'_{12} }[ \cos \omega (t_1 -t_t ') ~~~~   \\
 +\! \cos \omega (t_2 -t_2')\! -\! \cos \omega (t_2 -t_1') \!-\! \cos \omega (t_1 -t_2') ] ~. ~~~  \nonumber
\end{eqnarray}
Here we include only the contribution which is logarithmically divergent at $\omega_m\to 0$. After the straightforward integrations by parts in Eq. (40) we estimate the rare fluctuations contributions to tunneling as
\begin{eqnarray}
\left\langle {\delta S_t^2 }\right\rangle\!  \approx \frac{{(\omega _{10} /\nu _T )^8 }}{{2(1 + \eta_\varphi ^2 )^4 }}F_{\nu _T t}^2 = \left( {\frac{{\omega _{10} }}{{\nu _T }}} \right)^8 \frac{{(\nu _T t)^2 }}{2}  ~~~~   \nonumber   \\
\times\left\{ {\begin{array}{*{20}c}  {(1 + e^{ - \nu _T t} )^2 ,} & {\eta _\varphi\ll 1}  \\ {[\cos (\eta _\varphi  \nu _T t) + e^{ - \nu _T t} ]^2 }, ~ & {\eta _\varphi\gg 1}  \\
\end{array}} \right. , ~~~~~~~~   \\
F_x\equiv x \left\{ {(1-\eta_\varphi^2 )\left[ {e^{ - x}  + \cos (\eta_\varphi  x)} \right] + 2\eta_\varphi  \sin (\eta_\varphi  x)} \right\} ,  \nonumber
\end{eqnarray}
where the tilt effect is described by the ratio $\eta_\varphi =2\widetilde\omega \varphi /\nu _T$.

Because of $\sqrt{\left\langle \delta S_t^2 \right\rangle}\propto\Lambda_T^3$ the rare fluctuation contributions lead to the linear growth $\sqrt{\left\langle \delta S_t^2 \right\rangle}\propto\nu_T t$ and restrict the averaged description of tunneling by the condition $\sqrt{\left\langle \delta S_t^2 \right\rangle}<e^{-\nu_T t}$. If $\omega _{10}/\nu_T <1$ and $\eta_\varphi\to 0$, this requirement is satisfied during the time interval $\nu_T t<\lambda\ln (\nu_T /\omega _{10})$ with $\lambda\sim 1$, i.e. the average description fails down starting at $\nu_T t\sim 3\div 5$, for typical parameters. A further evolution, when a fluctuations level should be saturating, is not described in the framework of the approach used. At $\varphi \sim \varphi_T$ when  $\eta_\varphi\gg 1$, the rare fluctuations are quenched as $1/\eta_\varphi^2$ so that the average description is valid outside of the peak.

\subsection{Fluctuations of population redistribution }
Similarly to the averaged solution for population in Sect. IV A, the solution for it's fluctuation part $\delta n_t$ with the zero initial condition is given by $\delta n_t\approx -\int_0^t {dt_1} e^{-\nu _1 (t-t_1 )}\delta f_{t_1}$. The correlation function $\left\langle{\delta n_t\delta n_{t'}}\right\rangle$ is written through the correlator of sources $\delta f_t$ as follows
\begin{equation}
\left\langle \delta n_t \delta n_{t'}\! \right\rangle\! \approx\!\! \int\limits_0^t\!\! {dt_1} e^{-\nu _1 (t-t_1 )}\!\!\!\int\limits_0^{t'}\!\!{dt_1'}e^{-\nu _1 (t'-t_1 ')}\!\! \left\langle \delta f_{t_1}\delta f_{t_1'}\! \right\rangle  .
\end{equation}
Here the correlator of sources is given by
\begin{eqnarray}
\left\langle \delta f_t \delta f_{t'}\! \right\rangle\!\!  \approx \!\!
\int_0^{t_1}\!\! {dt_2}\!\! \int_0^{t_1}\!\! {dt_2 '} \cos (\Omega_\varphi\Delta t_{12}) \cos (\Omega _\varphi\Delta t_{12}') \nonumber ~~~~~~ \\
\times \left\langle\delta N_{t_1 t_2}\delta N_{t'_1 t'_2}\right\rangle\left\langle\!\Delta n_{t_2 }\! \right\rangle \! \left\langle\! \Delta n_{t_2 '}\! \right\rangle ~~~~~~~~~~~~
\end{eqnarray}
and $\left\langle\delta N_{t_1 t_2}\delta N_{t'_1 t'_2}\right\rangle\equiv \left\langle\Omega _{t_1x} \Omega _{t_2x} \Omega _{t_1'x} \Omega _{t_2'x} \right\rangle - {\cal X}_\varphi ^2 w_{\omega _m \Delta t_{12}}$ $w_{\omega _m \Delta t_{12} '}/\Omega_\varphi^4$ describes the averaged fluctuations of kernel. The four-point correlator $\left\langle\Omega_{\ldots}\ldots\right\rangle$ is determined by Eq. (A7).

Within the logarithmic approximation, at $\varphi =0$ one obtains $\left\langle\delta N_{\ldots}\delta N_{\ldots}\right\rangle\approx (2\widetilde\omega )^4(\alpha _{tr}\Lambda_1 /\pi )^2$ and the mean-square-fluctuation of population takes form:
\begin{eqnarray}
\left\langle {\delta n_t^2 } \right\rangle \approx (2\widetilde \omega )^2 \left( \alpha _{tr} \Lambda _1 /\pi \right)^2 e^{ - 2\widetilde\nu _1 t} ~~~~  \nonumber \\
\times\left\{ {{\mathop{\rm Re}\nolimits} \left[ {\int_0^t {dt_1 } \int_0^{t_1 } {dt_2 } e^{(\widetilde\nu _1  + i\omega _{10} )\Delta t_{12} } } \right]^2 } \right.     \\
 + \left. {\left| {\int_0^t {dt_1 } \int_0^{t_1 } {dt_2 } e^{(\widetilde\nu _1  + i\omega _{10} )t_1  - (\widetilde \nu _1  + i\omega _{10} )t_2 } } \right|^2 } \right\} . \nonumber
\end{eqnarray}
After the straightforward integrations over $t_{1,2}$ and averaging over period $2\pi /\omega_{10}$ ($\overline{\cos^2 (\omega_{10}t)}\to 1/2$), Eq. (44) gives
\begin{equation}
\overline{\left\langle {\delta n_t^2 } \right\rangle}  \approx 2k^2\left[ {1/2 + e^{ - 2\widetilde\nu_1 t} (1 - \widetilde\nu_1 t)^2 } \right] ~,
\end{equation}
where $k=(2\widetilde\omega /\omega _{10})^2\alpha_{tr}\Lambda_1 /\pi\ll 1$ and $\overline{\left\langle {\delta n_t^2 } \right\rangle}\propto\Lambda_1^2$, i.e. the rare fluctuations contribution limits the averaged description of transient evolution.

In analogy to Sect. V A, the averaged description is valid under the condition $\sqrt{\overline{\left\langle \delta n_t^2 \right\rangle}}<e^{-\nu_1 t}$ and at $\varphi =0$ this requirement is satisfied during the time interval $\widetilde\nu_1 t<\ln (1/k)\gg 1$. If $\varphi =\varphi_1$, we estimate $\Omega_{\varphi_1}\sim\sqrt{2}\omega_{10}$ and $\Omega_{tx}|_{\varphi \sim\varphi_1}\approx - \Delta \varphi_t\sqrt{2}\widetilde\omega$, so that $\sqrt{\overline{\left\langle \delta n_t^2 \right\rangle}}$ is different from Eqs. (44) and (45) by the numerical factor $\sim$1. As a result, the above condition for the averaged description remains valid over the peak described by Eq. (24). In addition, $\overline{\left\langle {\delta n_t^2 } \right\rangle}|_{\nu_1 t\gg 1}\approx k^2$ gives the steady-state level of fluctuations after redistribution of population.

\subsection{Random contributions to decoherence }
After integration of the lower Eq. (26) with the initial condition $\delta r_{t=0}=0$, the random contribution to the amplitude $r_t$ takes form
\begin{eqnarray}
\delta r_t\!\approx\! i\!\!\int_0^t\!\! {dt_1 } \Delta \Omega _{t_1 z}\!\! \left\langle {r_{t_1 } } \right\rangle  ~~~~~~ \\
- \frac{1}{2}\!\int_0^t {dt_1 }\! \int_0^{t_1 }\! {dt_2 } e^{ - i\Omega _\varphi  (t_1  - t_2 )} \delta N_{t_1 t_2 } \left\langle {r_{t_2 } } \right\rangle . \nonumber
\end{eqnarray}
Because the averages of $\propto\Delta \Omega _{\ldots}$ and $\propto\delta N_{\ldots}$ contributions are separated, the two-point correlation function is transformed into
\begin{eqnarray}
\left\langle {\delta r_t \delta r_{t'}^* } \right\rangle  \approx \int_0^t {dt_1 } \int_0^{t'} {dt'_1 } \left\langle {\Delta \Omega _{t_1 z} \Delta \Omega _{t_1 'z} } \right\rangle \left\langle {r_{t_1 } } \right\rangle \left\langle r_{t_1 '}\right\rangle^*
\nonumber \\
 + \frac{1}{4}\!\int_0^t\! {dt_1 }\! \int_0^{t_1 }\! {dt_2 }\! \int_0^t\! {dt_1 '}\! \int_0^{t_1 '}\! {dt'_2 } e^{ - i\Omega_\varphi  (t_1 -t_2 +t'_1 -t'_2 )} ~~~~~~~~  \\
\times \left\langle\delta N_{t_1 t_2}\delta N_{t'_1 t'_2}\right\rangle\! \left\langle {r_{t_2 } } \right\rangle\! \left\langle {r_{t_2 '}^* } \right\rangle ,  ~~~~~~~~ \nonumber
\end{eqnarray}
where the correlator $\left\langle \Delta \Omega_{t_1 z}\Delta\Omega_{t_1 'z}\right\rangle$ is given by Eq. (29). According to Fig. 7, around the symmetric point $\varphi =0$ the $+$ mode is only essential in Eq. (33) and we use $\left\langle r_t \right\rangle =r_0\exp [(i\Delta\Omega_+ -\nu_+ )t]$. Within the logarithmic approach, $\left\langle\delta N_{\ldots}\delta N_{\ldots}\right\rangle$ is replaced by the constant [see Eq. (44)] and after the straightforward integrations the mean-square fluctuation of amplitude takes form:
\begin{eqnarray}
\left\langle |\delta r_t |^2 \right\rangle  \approx |r_0 |^2 \left[\left( {\frac{{\nu _{\varphi  = 0} }}{{\Delta \Omega _ +  }}} \right)^2 \frac{{\Lambda _2 }}{\pi } + 2\left( {\frac{\widetilde \nu _1}{\Delta \Omega _ +}} \right)^2  \left( {\frac{\Lambda _1}{\pi }} \right)^2\right]  \nonumber    \\
\times \left( {1 + e^{ - 2\nu_+ t} \normalsize-2e^{-2\nu_+ t} \cos \Delta\Omega_+ t} \right) .  ~~~~~~~~
\end{eqnarray}
Here the first and second term in $[\ldots ]$ are due to the long- and short-scale contributions to fluctuations [see similar terms in Eq. (27)] and this factor is estimated as logarithmically weak, $[\ldots ]\sim 1/\Lambda_{1,2}<1$, see Eqs. (24), (32), and (34).

At $\varphi =0$ the requirement for averaged description of decoherence is $\sqrt{\left\langle |\delta r_t |^2 \right\rangle}<r_0 e^{-\nu_+ t}$. In analogy to the previous section, the results of Sect. IV B are valid if $\nu_+ t<\ln (1/[\ldots])$ and, for a typical parameters, fluctuations are weak over the time interval $\nu_+ t<3$. A similar condition remains valid over the dip region $|\varphi |<0.3\varphi_1$ (see Fig.8) where both ${\cal X}_{\varphi}$ and ${\cal Z}_{\varphi}$ are changed only due to numerical factors $\sim 1$. Thus,the fluctuations contribution is suppressed only in the saturation region, $|\varphi |\geq\varphi_1$ while the averaged description over the dip is valid during a short enough interval.

\section{Concluding remarks }
We present a comprehensive investigation of the dissipative dynamics of a flux qubit, describing interwell and interlevel relaxation as well as decoherence caused by the 1/f noises pass through the SQUID and the LC-contour. We analyze the rates of these processes and the renormalization of gap frequency versus the tilt and control fluxes taking into account correlations between the noises; this permits one to characterize the qubit-noise interaction. We show how rare fluctuations limit the averaged description at tails of relaxation. Under typical level of noises, the results obtained give contributions comparable to the recent experimental data on the interlevel population relaxation and the interwell tunneling.

Our consideration is based on a several assumptions which are shortly discussed below.
\begin{itemize}
\item[(a)]\vspace{-0.25 cm} Description of the flux qubit is based on the effective circuit formed by the effective Josephson junction shunted by the LC-contour, instead of the SQUID loop, which is shunted by the transmission line. It is a good approach for the low-frequency region, far below the characteristic frequency of the LC-contour which is $>$10 GHz for a device with typical parameters.
\item[(b)]\vspace{-0.25 cm} Consideration of 1/f noise as a classical random flux is valid for frequencies below 1$\div$2 GHz where the interaction with high-frequency bosons can be omitted \cite{15}. As a result, qubit approachs to the equi-populated distribution, $\Delta n_t |_{\nu_1 t\gg 1}\to 0$, while the equilibrium distribution can be reached due to the qubit-boson interaction, during times beyond the scales considered here.
\item[(c)]\vspace{-0.25 cm} Because of the logarithmic character of the cut-off, one can use the abrupt cut-off at $\omega \sim\omega_m$ in Eq. (3) and below. A possible deviation from 1/f spectrum, e.g. due to the size effect in the transmission line \cite{22}, may be described similarly after choosing a specific parameters of device.
\item[(d)]\vspace{-0.25 cm} The qubit-noise interaction is studied by adding random fluxes to the tilt and control fluxes and by taking into account correlations between these sources. The coupling levels in $tl$-, $j$-, and $c$-channels are given by the phenomenological parameters $\alpha_{tl,j,c}$. Both a microscopic study of a 1/f noise mechanism and a detail description of a noise effect on the SQUID loop and the LC transmission line are beyond of the scope of the paper and can be performed for specific devices.
\item[(e)]\vspace{-0.25 cm} The idealized initial conditions were used at $t=0$ without any discussion of a temporal evolution at $t<0$. A more detailed description requires an analysis of the protocol of resonant tunneling \cite{14,15} and the mechanisms of the ultrafast interlevel excitation, see \cite{9,25} and references therein. Here we neglect a possible uncertainties during the initialization and readout stages.
\item[(f)]\vspace{-0.25 cm} We restrict ourselves by the weak-fluctuation regime, when the averaged dissipative dynamics describes an evolution of qubit. Level of fluctuations gives the limitations of the averaged description at tails of relaxation. In principle, a chaotic regime contains an additional information on the qubit-environment interaction but an analysis of the two-point spectral functions requires a special consideration.
\end{itemize}\vspace{-0.25 cm}

Now we discuss the current experimental data for the LC-shunted qubits and possibilities for verification of the results obtained. In spite of these qubits were employed for demonstration of the multi-qubit clusters \cite{1,2,26}, a complete spectroscopic characterization of this type of qubits is not available \cite{23}. Recent measurements of the population relaxation rate in the region above 0.5 GHz \cite{15} give the amplitude and half-width of peak in agreement with the results of Sect. IV B but the 1/f spectral dependency is modified due to the soft barrier effect. The decoherence processes were not analyzed in \cite{15,23} but such a data are necessary in order to verify of the $j$- and $c$-channels contributions which determine the depth and asymmetry of the dip. A study of the other peculiarities discussed in Sect. IV C (the two-mode evolution and the renormalization of gap) may be complicated due to the fluctuation-induced  restrictions on the averaged response. The incoherent tunneling rate reported in \cite{14,23} was in agreement with the model \cite{21} when the levels are modulated by coupling to the boson thermostat. It lead to the temperature dependent asymmetry of the tunneling peak. Recent measurements \cite{15} show an additional temperature-independent asymmetry  which can be caused by the $c$-channel contribution, see Sect. III. In order to confirm this mechanism, one needs to demonstrate a changing of the sign of asymmetry for the parallel and antiparallel directions of $\varphi$ and $\psi$, see Fig. 1(a). Thus, the above-discussed partial experimental data does not permit to characterize the qubit-noise interaction completely. It is necessary to perform all possible measurements for the same device and, using an appropriate model of the device, find parameters which will describe all data. Similar program can be develop for other types of qubits, with  an effective circuits different from Fig. 1(b), such as the capacitively shunted flux qubit \cite{10} or another variants of transmon \cite{12,27}.

To conclude, the obtained results convincingly demonstrate that the transient dynamics of the flux qubit should be analyzed beyond of the simplified two-level model which includes only a noise-induced modulation of the interlevel gap. Our consideration, which is based on the lumped-element approach with detailed description of noise effects, opens the way to characterize the flux qubit interacting with low frequency noise and to enhance a fidelity of the device. We believe that a similar study of another types of qubits, the interqubit connections, and the multi-qubit clusters will improve parameters of the quantum hardware.

redpajama_set_name: RedPajamaArXiv


text:
Q: How to parse google calendar v3 feed in android I have an app that read a public google calendar feed and populate a listview with the events in this calendar. The problem is that I was using this url to get the feed http://www.google.com/calendar/feeds/[CalendarID]/public/full?orderby=starttime&max-results=150&singleevents=true&sortorder=ascending&futureevents=true
It seems that now that the google calendar api v2 has been discontinued, this url is not valid, and throws a "Forbidden Error 403", so that when I try to use it in my app, itcrashes.
Here are my code to parse the xml in that url:
public ArrayList<Agenda> parse() {

    ArrayList<Agenda> events = null;
    XmlPullParser parser = Xml.newPullParser();
    SimpleDateFormat formatter = new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss");

    try
    {
        parser.setInput(this.getInputStream(), null);
        int parserEvent = parser.getEventType();
        Agenda event = null;

        while (parserEvent != XmlPullParser.END_DOCUMENT)
        {
            String etiqueta = null;

            switch (parserEvent)
            {
                case XmlPullParser.START_DOCUMENT:
                    events = new ArrayList<Agenda>();
                    break;

                case XmlPullParser.START_TAG:
                    etiqueta = parser.getName();

                    if (etiqueta.equals("entry"))
                    {
                        event = new Agenda();
                    }
                    else if (event != null)
                    {
                        if (etiqueta.equals("title")){
                            String titol = parser.nextText();
                            event.setTitol(titol);
                            Log.d("Titol Event", titol);
                        }
                        else if (etiqueta.equals("where")){
                            String lloc = parser.getAttributeValue(null, "valueString");
                            event.setLloc(lloc);
                        }
                        else if (etiqueta.equals("when")){
                            Date iniciEvent = null;
                            Date finalEvent = null;
                            String dataInici = (parser.getAttributeValue(null, "startTime"));
                            Log.d("DATA INICI", dataInici);
                            String dataFinal = (parser.getAttributeValue(null, "endTime"));
                            if(dataFinal == null){
                                break;
                            }
                            Log.d("DATA FINAL", dataFinal);
                            try {
                                iniciEvent = formatter.parse(dataInici);
                                event.setData(iniciEvent);
                                formatHoraCorrecta = true;
                                event.setAllDay(false);
                            } catch (ParseException e) {
                                // TODO Auto-generated catch block
                                Log.d("ERROR FORMAT DATA", e.toString());
                                formatHoraCorrecta = false;
                                event.setAllDay(true);
                            }

                            if(!formatHoraCorrecta){
                                dataInici = dataInici + "T00:00:00";
                                iniciEvent = formatter.parse(dataInici);
                                event.setData(iniciEvent);
                                dataFinal = dataFinal + "T00:00:00";
                                finalEvent = formatter.parse(dataFinal);
                                event.setDataFinal(finalEvent);
                            }else{
                                finalEvent = formatter.parse(dataFinal);
                                event.setDataFinal(finalEvent);
                            }

                        }else  if(etiqueta.equals("content")){
                            event.setDescripcio(parser.nextText());
                        }

                    }
                    break;

                case XmlPullParser.END_TAG:
                    etiqueta = parser.getName();

                    if (etiqueta.equals("entry") && event != null)
                    {
                        events.add(event);
                    }
                    break;
            }

            parserEvent = parser.next();
        }
    }catch (Exception ex){
        Log.d("Exception ex", ex.toString());
        throw new RuntimeException(ex);
    }
    return events;
}

I find that this URL shows now the calendar feed http://www.google.com/calendar/feeds/[CalendarID]/public/basic?orderby=starttime&max-results=150&singleevents=true&sortorder=ascending&futureevents=true but actually the way the info is shown is totally different, so that that code doesn't work.
Is there a way I could parse the info from google calendar v3 feed, in a similar way I did it before or I have to use other methods?

A: In Calender v2, this code will work as the response you receive is in xml format.
But for Calender v3, the parsing method has to be changed to match the new response as specified in the Google Calendar API Version 3.0 Migration Guide.
You can also refer to this question: How to Parse the this JSON Response in JAVA
Hope that helps!

redpajama_set_name: RedPajamaStackExchange


IDST nozzles can be used in all kinds of fields. We manufacture a full line of spray nozzles including: full cone nozzles, hollow cone nozzles, flat fan nozzles, atomizing spray nozzles and fog nozzles; spray nozzles for spray drying, flue gas desulfurization, coating, humidification, misting, pollution control, distribution, mixing, tank washing, absorption and food processing.
from 10/09/2007 to today 20/04/2019 for a period of 11 years and 225 days.


There is special handling for github links. You can just paste the URL to your repo, markdown loader will auto-resolve proper githubusercontent.com to your README.md file.
I intend to use this to "synchronize" markdown and html files in my git repositories without too much fuss.
Get it from github releases.
Any element with data-md-load attribute will be filled with markdown from the specified URL.
You must include the markdown-loader.js after the target DOM element (or use async attribute).
If you want to avoid annoying jumping of HTML when markdown is loaded, you can use the synchronous variant.
In this case, I suggest you place your <script> tag right after the target element.
This will make it seem as if markdown is part of your html document.
(at least in Chrome), so pick your poison.
// You can also use it as a pure function, without DOM. String will auto-convert into "source"
Distribution files will be created inside the dist folder.


text:
Fed, state, and county offices and banks closed Jan. 2 for New Year's holiday
December 29, 2022 January 5, 2023 Editor
All county, state and federal offices will be closed on Monday, Jan. 2, 2023, for the New Year's holiday, since Jan. 1 falls on a Sunday.
Banks also will be closed Monday, Jan. 2.
All Plumas County schools and Feather River College remain on winter break. Plumas Unified and Plumas Charter students return to school Tuesday, Jan. 3. The Feather River College campus reopens Jan. 3, but the next semester does not begin until Jan. 23.
Waste Management alerted its customers that trash pickup will be on a regular schedule next week. Waste Management serves customers from Quincy to Chester.
Intermountain Disposal — serving the eastern end of the county — is also maintaining its regular schedule.

redpajama_set_name: RedPajamaCommonCrawl


Mike Leon has been a good friend to me and to the blog here since day one. He wrote a nice piece on guns, a topic he's very passionate about, and he makes some solid points on how the public is being emotionally manipulated on the topic. Check it out and check out his Postmodern Adventures of Kill Team One — urban fantasy thrillers.
I'm going to share an uncomfortable truth here. The Second Amendment wasn't written for self-defense or hunting. The Second Amendment was written so everyday people could potentially assassinate politicians.
What brought this statement on? The current political inferno over gun rights on social media. Ever since Facebook rose to the status of foremost ideological gladiatorial arena in the Rome of American hyperreality, the dispute over American gun control has raged online in increasingly frequent intervals directly corresponding to each statistically insignificant mass shooting event. Despite the infinitesimal (and shrinking) likelihood of mass shootings or school shootings in the United States, media coverage of them seems more prolific than ever before. Schools commonly have drills to practice surviving an active shooter event. Lobbyists, children, nitwits of all ages, and politicians all demand legislative action. The internet is aflame with their cries.
Here are some numbers for you: 1 in 2,273,000. Those are the annual odds of your child being killed in a school shooting according to the Cato Institute. Your child is 3 times more likely to be struck by lightning. The annual odds of there being a bona fide Columbine-style bloodthirsty mass shooting at your child's school are less than 1 in 100,000 according to these numbers from Northeastern University. The odds of anyone discharging any firearm at school, even by accident, even if no one is injured, are about 1 in 2000. You're twice as likely to hit the Pick 3 lottery. I even calculated that last probability using dodgy figures from Everyday Gun Safety, an outspoken group of gun grabbers. If I were as snaky as the mainstream media I would post a headline like "Everyday Gun Safety Shows Americans are Twice as Likely to Win Lottery than Experience School Shooting." That would be misleading, and misleading people is CNN's job, not mine.
The point of those numbers is to show that school shootings are an outlier. They don't matter. They're incredibly rare, and making public policy decisions because of them is stupid. I realize that's a cold and insensitive statement, especially to the tiny number of recently bereaved parents out there, but it's true. If you called up your accountant and he told you he knows a guy who won the Powerball so he just put all of your money into the Powerball, you would fire your accountant. It doesn't matter who he knows. I know a guy who drank himself to death twice and was resuscitated with the paddles both times. I also know a guy who survived a skydive when his parachute didn't open. I'm still not chugging two fifths of Wild Turkey and jumping naked from an airplane.
And yet the debate still rages. Why? Because too many people put their feelings in the driver's seat. CNN knows that. MSNBC knows that. Fox News knows that. If it bleeds, it leads, and they're making a mint. Conspiracy theorists often claim mass shootings are government-run false flag attacks, but they're failing to follow the money. If you told me CNN secretly hired mercenaries to shoot up a school, it wouldn't faze me. It just makes sense. More dead kids = higher ratings = more advertising dollars. It's not rocket science. They certainly have a more visible motivation than the government.
That's how we got where we are—the point at which every other post is a screed about gun control one way or the other. They all make the same talking points.
This stuff goes on endlessly because no one can articulate the reason Americans need guns in simple terms. So I'm going to lay it down right here. It is about fighting tyranny, but not in the visceral sense that most survivalist gun nuts seem to cling to. It's not about mowing down the jackboots that come to put you in a camp, or shooting down drones and helicopters. It's not a Rambo Red Dawn fantasy. The truth is much more subtle.
It's about fighting tyranny with fear. It's about making sure every politician knows that we just might kill them. It's about the Sword of Damocles. It's about them having that lingering thought in the back of their head that the next thing in the back of their head might be a 6.5x52mm Carcano fired from a book depository.
We want them to think "If I ban violent video games, somebody might fire a .308 through my aorta" and "If we pass that abortion bill somebody might get angry enough to kick in my suite door and riddle me and my $3000 escorts with 9mm rounds while we're in the Jacuzzi" and "If we vote ourselves another pay raise, somebody might nail me with an FN-Scar while I'm on the course at Martha's Vineyard." All of those things are in the realm of possibility because all of those guns are perfectly legal.
In the UK, politicians don't have to have those thoughts, and now they're throwing comedians in jail because they don't like their jokes.
In the US, officials need more restraint than in the UK because we don't need to overhaul anything. We don't need an uprising or a rebellion to keep them in line. We just need one raving lunatic with a gun—and we let every raving lunatic have guns. He doesn't need a reason. Maybe he wants to impress Jodie Foster. Maybe it's just Monday. Who cares? When it's over, we lock him up or give him the needle, and we look at all the other politicians with the same crazed-eye twitch that guy had, and we say it was just him. He acted alone. It happens sometimes. Nothing you can do about it.
That's how we do things in America, and that's why we need an AR-15.
Mike Leon is the raving lunatic responsible for The Postmodern Adventures of Kill Team One. The fourth book in the series, #Justice was just released in February.


The island of Kalymnos is getting ready to welcome "living legends and active athletes of modern rock climbing" for its annual climbing festival.
The Hilton Athens hotel has styled its pool deck with a refreshed look and invites Athenians and visitors to experience the new ambiance this summer.
Tapping into Kalymnos' vast diving legacy as well as newly emerging tourism experiences such as climbing, are among the government's top priorities.
What better way to experience the beauty of a Greek island if not from above? That's the idea behind the annual International Kalymnos Climbing Festival, which takes place on October 7-9 this year on the Dodecanese isle.
The government is considering to abolish some state-subsidized airline routes to remote Greek islands, Infrastructure and Transports Minister Christos Spirtzis said this week.
The Kalymnos Climbing Festival takes place for another year on the beautiful sun-drenched island of the Dodecanese on October 10-11.
CNN has included the Greek island groups of the Sporades and the Dodecanese among nine exclusive Mediterranean cruises for those who want to embark on a peaceful journey and avoid the crowds this summer.
Kalymnos, the fourth largest island in the Dodecanese complex in south-eastern Aegean and situated between Kos and Leros, will participate in TBEX 2014, scheduled to take place in Athens this October.
Kalymnos Island, leading Greek and European rock climbing destination, recently wrapped up its annual climbing festival in late September, organized this year by Swiss climbing equipment company North Face in cooperation with the Municipality of Kalymnos.