Can I change the race distance if I have already registered?
Sure–as long as that distance hasn't filled up. If you are moving to a longer distance, you will need to pay the difference in registration. If you move to a shorter distance, you will not get that difference back.


1. Base type: GU10. 2. Input voltage: 85 ~ 240VAC. 3. Full range of colors: cool white, warm white, red, blue, green, yellow. 4. Best thermal management with aluminum housing & copper fittings. 5. Light source: USA cree 3W XR-E power led emitter. 6. Luminous flux: 120 lumens. 7. Beam angle: 50/ 70/ 100 degrees (glass lens optical grade). 8. Body temperature: less than 53centigrade. 9. Led working temperature: less than 62centigrade. 10. Temperature: -40 ~ 70 celsius degree. 11. Brightness degradation: 3% - 5%1kh. 12. Life span: 50, 000 hours. 13. No UV or IR radiation. 14. Certifications: CE & ROHS.


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redpajama_set_name: RedPajamaGithub


TIP! Do not let yourself get trapped in a negative circle. Continually replaying negative thoughts in your head can make depression even worse.
Clinical depression can affect people of any age and is usually related to a chemical imbalance in the brain. Know that there is help available. Use these helpful tips to help you fight depression and live a happier life.
TIP! If you are depressed, you should discuss your feelings with someone. It doesn't matter who you talk to, you will feel better about it.
If you work on the personal problems that you are up against, this will help with your depression. Proceed with small incremental steps so you don't become overwhelmed, and tackle issues on an individual basis. Creating smaller tasks and more concrete goals can make it much easier to address problems. Little by little, the issues evaporate and are no longer such a concern.
Meditation can temporarily calm depression symptoms. There are many benefits to meditation and they have been well documented to improve moods.
TIP! In order to help you manage your depression symptoms, you should aim to meditate regularly. You can lower blood pressure and actually lift your mood through meditations and studies have proven this.
Even if someone is clinically depressed, it can be classified differently from someone who is just sad, but similar techniques can be used that will yield positive results. It is very important to your well-being that you avoid putting yourself in a situation that might trigger your depression. If you can avoid a person or activity that repeatedly leads to depression, you should.
Get support from as many areas as you can. People who have pulled through depression themselves may be excellent sources of support and advice, because they can share their experiences and coping strategies.
TIP! Do not use the words "depression" or "depressed" in your vocabulary. The words "depressed" and "depression" have much baggage in connection with feelings of hopelessness.
Keep many positive friends around you. This will help you to overcome the tough times; make sure you talk to a variety of people, rather than just depending on one.


Change on the Go is a movement. It was a phrase created to describe the notion that even in the constant rush of life, we can all take small, simple steps towards positive change and help others join in the process.
People find inspiration in the most uncommon of places and is different for each individual. However, it is important to know that one thing remains the same: no good deed is ever too small. Whether it is educating yourself and others, donating your time and/or money or doing something completely new and spontaneous, we all have the time to step out of our comfort zone and make a significant impact.
In connection with this site, Change On The Go will plan to host networking events in New York City and raise money for various local and international organizations.


Alys Design. Interior Design. Pittsboro NC. – Stylish. Functional. Sustainable. Interior Design.
Stylish. Functional. Sustainable. Interior Design.
Alys Design is a full-service firm. We create beautiful and functional living spaces according to your personal tastes, style, and vision.
Browse our project gallery for inspiration and to see what we've been creating for our clients.
Please feel free to contact me using the contact form. You can also email me, or give us a call 919.265.9090.


It amazes me the way the world goes on. The cars whiz by. I don't want to see the bridge. Mom insisted. Just as she insisted on seeing Casey's body. Her body. Her tangible body. I didn't want to. I waited in the lobby of the funeral home, it's black wood bench, high carved ceilings. Then, too, I heard the world going on. I cracked the door, shut it quickly. I didn't want the sunlight, the pedestrians, the barking dog. Our world is here, I thought, where downstairs my mother and brother look at my sister. And it occurred to me that I am like she was: I create my own reality. I choose not to see her that way: her missing eye, the claw marks, all done by her. I want to remember her the way she was when she handed me a green basket with plastic grass and chocolate eggs on Easter in 1977.
Dana is quiet as he drives. He doesn't want to climb this bridge either, I think.
"How did she get up here?" Mom says. There's no sidewalk, no room for pedestrians.
"Stop the car," Mom says, at the top of the bridge. We're in traffic, but Dana puts on the hazards, shifts into park. It's so bright out. My hand is against the door handle. I could do it too. I could pull the handle, climb the fence, and jump.
Cars honk behind us. I don't understand Mom's insatiable need to see: the bridge, the body, Casey's one room apartment. Such probing, and years from now she won't be able to say my sister's name. And if somebody asks her how many children she has, a lump will rise from her womb and take away her voice.
"Why didn't you buy her new curtains? She had sheets on her windows, for Christ's sake. Why didn't you help your sister?" I'm still in the back and I want to stop them. We're in the shade now. The seat is cool against my let, though still damp from my sweat.
"I tried to help her. I tried so many times. Curtains, Christ." He shakes his head: disbelief. They are both quiet now. Dana is frowning; if he talks more he will cry. I wish we could go inside. We sit in the car; it's silenced our world. When one of us opens a door we'll hear the neighborhood kids, or a distant car horn, or the buzz of a lawnmower. It will remind us that the world goes on. It should stop, I think, just for a minute. As we sit I think, I believe him. I believe he tried to help her. And yet, I want to know about the curtains too. I'll never ask.


text:
One of Ireland's most respected music writers, Jackie Hayden spent 29 years with Hot Press where he interviewed artists of the stature of Mick Taylor of The Rolling Stones, Christy Moore, Sinead O'Connor, Glen Campbell, Kenny Rogers, Ronnie Drew, Glen Hansard and Bob Geldof.
He topped the Irish book charts with two editions of My Boy, his book about Philip Lynott. Jackie has also written Love and Theft? Bob Dylan's Celtic Odyssey, The Winner In Me (his biography of Don Baker), and the CD/book A Map Of Love – Around Wales With Dylan Thomas.
Prior to his writing career, he was marketing manager with Sony Music (then known as CBS), where he signed U2 to their first record contract.
He has delivered witty and informative addresses to various seminars around Europe. In his lecture Dylan, Dylan and Me, Jackie talks about discovering Dylan Thomas via Bob Dylan and The Beatles.
He has written for many overseas publications, including Sunday Times, R2, The Lampeter University Review, and Ninnau in the USA.
In 2015 he was "writer-in-residence" at Tranas Literary Centre in Sweden. Jackie spoke about Dylan Thomas as part of World Poetry Day at the State Theatre in Uppsala.
Catriona Crowe
Derek Coyle
Derek Hand
Eileen Casey
Ferdia Mac Anna
Fiona Ennis
Irene Kelleher
Melatu-Uche Okorie
Mike Hanrahan
Niall Ó Muirí
Paula Lowney
Robert Gogan

redpajama_set_name: RedPajamaCommonCrawl


Money costs more than PostPlanner, and for people who are managing webpages PostPlanner is better for your budget.
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PostPlanner status notions is an answer to this problem. This feature was created with the idea of beating the Facebook EdgeRank algorithm in mind. You are able to choose from the pool of status ideas for your pages or bands.
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PostPlanner addresses the Frequent problem Using Facebook's status update, and that's the difference. For example: If I want to publish a"Good Morning" message on my Facebook page, then I'll be posting it at 8 A.M. IST, but for nations other than India, then it might be evening or day.
This destroys the degree of personalization, Along with your page becomes more than being a page. With PostPlanner's automobile time-zone conversion, when you schedule an update for 8 A.M., then it will be submitted at 8 A.M. local time for India, and 8 A.M. local time to get the U.S., etc.. You will see detailed info regarding this feature that is excellent here.
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No. Post Planner doesn't offer free trials because of their own plans. Users will be immediately billed upon signing up.
PostPlanner is something & useful you can put Your money on. Recently, there are complaints from the users regarding support & conclusion of this program (See comment below). Anyways, at times 1-2 bad experiences are part of a program that is favorite & it is worth trying since cost begins at $19/month. For this price you can manage all your pages and groups. For advanced features such as viral trending topics, queue articles, etc., you can avail yourself of the GURU program which conveys a $29/month price tag. Social media marketing providers can opt for the agency plan which has a multi-branding option. You can check out all features and the plans here.


DRONE produces affordable H2O2, a disinfectant and preservative, from food waste, increasing production by 20% and reducing wastage by 21%.
Kavita, a village woman from Bihar, has four children suffering from losses in their respective businesses. Ram, once a prominent poultry farmer, lost almost 70% of his chickens to flu epidemic. Shyam, a seasoned rice farmer, lost 50% of his crop to pest infestation. Karan, a vegetable wholesaler, has been earning lower margins due to limited shelf life. Sarita, a woman dairy farmer, is discouraged by poor milk yield of her cows suffering from Mastitis. Hearing from fellow villagers, they bought Ann-oxy-Ann's affordable supersolutions of H2O2 and used them as an insecticide, water disinfectant and food preservative. Family income increased 4 times with enhanced production of meat (20%), rice (15%) and milk (33%) and reduced vegetable wastage (21%).
Sufficiently supplied oxygen is a one stop solution to dozens of food production and storage problems. H2O2, an organic source of oxygen, is a natural insecticide, disinfectant and food preservative. Ann-oxy-Ann's experiments driven data shows that H2O2 in animal drinking water increases production of milk by 33%, egg by 5% and meat by 14%. H2O2 in irrigation water increases production by 15%. Dipping fruits and vegetables in diluted H2O2 increases their shelf life by 80 & 150% respectively. However, it is rarely used in farming due to its high market price. DRONE methodology of producing H2O2 using food waste, will make the expensive H2O2 affordable to poor farmers, animal keepers and local vendors. Affordability being our USP, we can feed 1.49 billion more people on global scale.
We'll collect free food waste from large fruits and veggies wholesale markets as they waste 100+ tons daily. This will be transported to our chemical plant located at nearby place, reducing transportation cost. From here, our H2O2 supersolutions will be dispatched to supermarkets(for local veggie vendors), agricultural dealers(for nurseries and uplifted farmers), government shops(for poor farmers) and animal feeding shops at half of market price. Chemical plant can fetch easy investors due to its low variability and high returns. Working capital is fully compensated by selling our byproducts, dry ice and compost; moreover fixed cost is recovered in 3 years by selling H2O2. Later, we'll sell H2O2 at pennies off the dollar ensuring long term sustainability against prospective competitors.
We are a team of 5 undergraduate students from Indian Institute of Technology, Mumbai. While working on something innovative to ensure food security by 2050, we realized food wastage is the biggest challenge in achieving this goal. Restaurants, regional markets, households, storage and transportation facilities generate tons of food wastage annually. As per the statistics, one third of the food we buy is thrown away. And, the problem being so diverse and huge, spread over developed and developing countries, it's very difficult to reduce this waste drastically in the near future. So, idea is to reuse this waste and convert into something which can revolutionize agriculture and multiply food productivity. Our mission is to build a scalable approach to effectively use food wastage around the globe and develop a product which could have varied applications in agriculture, dairy and poultry.
We are five learning beings belonging to one of the most sought after epicenter of gaining knowledge, the Indian Institute of Technology Bombay. Our team comprises of the right blend required to deliver creativity and innovation in compliance with feasibility, sustainability and scalability. Pooja, pursuing Master's Degree in the industrial design sector and having completed bachelors in design, is the backbone for designing and creativity required to tackle the problem. Arvind, Nitin and Aditya, pursuing chemical engineering, having set the benchmark with their technical expertise in the core knowledge, are the pillars for the innovative ideation and technical backdrop of the solution. Arvind, on one hand has an expertise in supply chain optimization, whereas Aditya and Nitin are specialized in process design and plant economics. Aman, pursuing civil engineering, has developed an aptitude to analyze and solve problems concerning the society as a whole. The individuals of the team have come up together as a result of a common consciousness, which is to help the world live better. Coming from India, we in our daily life, walk across countless people unable to afford 2 square meals. Children who could grow up to become the pillars of our modern society, forced to sleep daily with their stomachs empty. Every night, around 420 million people go to sleep on an empty stomach. Approximately 194.6 million people are undernourished in India. This is India, there are numerous other countries with situations even worse. The thing that even sickens us more is that we produce enough for everyone on this planet, yet these people are forced to live the life they are. Participating in this challenge is our way of giving back to the society, by building on solutions that have the potential of providing food for every human on the planet. Our team is specifically concerned regarding the immense amount of food wasted from households, restaurants and regional markets. Plate waste is not only common in developing countries but is also the major cause of food wastage in developed countries. The problem is equally prevailing throughout the globe. And, the problem being so diverse, huge and widespread, it's very difficult to zero down this waste. The idea is to use our technical expertise developed in last few years, to convert the waste into a comprehensive product which can be an asset in increasing food productivity in agriculture, dairy and poultry. We have been researching on one such product from last few months, met few pesticide dealers and farmers from Punjab, one of the most fertile state of the country. Our team have also done multiple experiments to substantiate the applications of the product in increasing shelf life and cutting down the major farming issues. "Ann" is a Hindi word meaning food and we have incorporated the same in our team name to depict our idea. We are trying to convert waste "ann" into something which can further increase availability of "ann" throughout the globe. Our exuberant team members are highly determined in carrying forward this idea and developing a scalable business model.


HMMMM I'm not sure about this idea! Hope there's no reptoids in this bunch!!
This federation is a non-monetary, non-violent, telepathic coalition of beings from numerous planets. The Federation has already greatly affected our physical and spiritual evolution throughout history and even before. Many great spiritual teachers and leaders, Boylan iterates, were actually alien in origin. They believe themselves intermediaries between the "God Force" and ourselves. They, soon after establishing open contact, will distribute their vast technology. They intend to give us the knowledge to build free energy machines, teleportation devices, food replicators and instant education machines that will be able to download a whole foreign language in a one hour session and much more. They will graciously (and speedily) give us the secrets to telepathic communication, ending disease and aging and enabling time travel. Dr. Boylan says the Mayans knew this would be taking place. By the end of the Mayan calendar, 2012, Earth and all of Humanity will be wholly integrated into this extraterrestrial federation. We will be a world consisting of real communities built on trust, mutual caring, and shared common interests. Telepathy will bring an end to violence, greed and depression. We will be a society that is ready to reach for the stars, committed to constant self-improvement and artistic expression with a greatly expanded definition of home and of all other levels of reality.


text:
\section{Introduction}

Considering a closed Hamiltonian driven system, such as a particle in a box with moving wall (the piston paradigm), the textbook assumption is that quasi-static processes are adiabatic, and therefore  {\em reversible}. This claim can be established for an {\em integrable} system by recognizing that the action-variables are adiabatic invariants~\cite{Landau}. At the opposite extreme, analysis of slowly driven completely {\em chaotic} systems \cite{Ott1,Ott2,Ott3} has led to a mesoscopic version of Kubo linear-response theory and its associated fluctuation-dissipation phenomenology \cite{Wilkinson1,Wilkinson2,crs,frc}.
However, generic systems are neither integrable nor completely chaotic.
Rather their phasespace is {\em mixed},
resulting in the failure of the adiabatic picture \cite{Kedar1,Kedar2,Kedar3,apc,lbt},
and of linear-response theory.
Namely, the phasespace structure varies with the control parameter:
tori are destroyed;
chaotic corridors are opened allowing migration between different regions in phasespace \cite{bhm,qtp};
stochastic regions merge into chaos;
sticky regions are formed \cite{stk0,stk1,stk2,stk3};
sets of tori re-appear or emerge.
Some of those issues can be regarded as a higher-dimensional version
of non-linear scenarios that are relate to bifurcations of fixed points,
notably swallow-tail loops \cite{Swallow1,Swallow2,Swallow3,Swallow4,Swallow5},
or as a higher-dimensional version of the well-studied separatrix crossing   \cite{Kruskal,Neishtadt1,Timofeev,Henrard,Tennyson,Hannay,Cary,Neishtadt2,Elskens,Anglin,Neishtadt3,lbd},
where the Kruskal-Neishtadt-Henrard theorem is followed.

\sect{Motivation}
Irreversibility is observed in hysteresis experiments with ultracold atoms \cite{exprDimerHys}.
For ring geometry see \cite{exprRingRev,exprRingNIST}.
Signatures of mixed phasespace naturally arise in the analysis
of the Bose-Hubbard Hamiltonian \cite{exprBHH1,exprBHH2,KolovskyReview}.
In this context, the effect of {\em chaos} has been taken into account while studying
the efficiency of a nonlinear stimulated Raman adiabatic passage (STIRAP) \cite{apc};
the efficiency of quasiststic transfer protocols \cite{qtp};
and the Hamiltonian hysteresis that follows the reversal of the driving \cite{lbt}.
All the latter studies concern the dynamics of systems
that feature an underlying mixed-chaotic phase-space.

\sect{Objective and choice of model system}
One would like to provide a comprehensive set of tools for the design
and the optimization of quasi-static protocols, e.g. in the context of Bose-Hubbard circuits.
The feasibility and the efficiency of such protocols is related
to phasespace spreading (`entropy-growth') as demonstrated in the above cited works \cite{apc,qtp,lbt}.
In a broader perspective, the analysis of driven systems that feature an underlying mixed-chaotic phase-space is a rather universal theme, that has relevance to many fields in physics, notably celestial mechanics. Inspired by the restricted 3~body problem, we focus below on the dynamics that is generated by a generalized Hill's Hamiltonian \cite{hill1,hill2,hill3}. This describes the mixed-chaotic motion of a test-particle in the field of force of a binary system. More interestingly, we can have in mind a binary system immersed in a cloud of dust. The dust is driven quasi-statically by the Kepler motion of the stars.

\sect{Outline}
In \Sec{sec:H} we introduce the generalized Hill's Hamiltonian.
This Hamiltonian will be used as a test case for the application of our approach.
It features a mixed chaotic phasespace
whose parametric evolution can be
visualized using a Poincaré landscape plot.
In \Sec{sec:PSM} we use a Poincaré-sequencing method
in order to characterize the time dependent dynamics.
This inspires the introduction of an effective stochastic model
in \Sec{sec:model1} and \Sec{sec:model2}.
This simplified model is used in  \Sec{sec:SnE}
to provide an explicit relation between
stickiness and the rate of entropy growth.
In \Sec{sec:cycle} we explain that the dependence on the directionality
of a cycle is linked to asymmetry that can be detected
in the Poincaré-sequencing analysis.
For completeness we present in \Sec{sec:dissipation} the theoretical
reasoning that relates the rate of dissipation to
the stochastic characterisation of the dynamics.

\section{The generalized Hill problem} \label{sec:H}

The Hamiltonian under consideration concerns the motion of a dust particle (satellite) in the vicinity of massive bodies (stars).
The stars are performing a cycle $(X(t),Y(t))$ that has frequency $\Omega$ and constant angular momentum~$\ell$.
It might be, but not have to be, the Kepler motion of \App{app:kepler}.
We define the characteristic radius~$c$ such that the scaled angular momentum is ${\ell \equiv c^2\Omega}$.
In polar coordinates the cycle is parameterized by ${ R(t) = c\mathsf{R}(\theta(t)) }$.
By definition of~$c$, one observes that the $d\theta/(2\pi)$ integral over $|\mathsf{R}(\theta)|^2$ is unity.
Regarding $\theta$ as the time variable, one obtains, after a sequence of transformations (see \App{app:hillG}),
the generalized Hill's Hamiltonian:
\begin{eqnarray} \label{eq:H}
\mathcal{H} =
\frac{1}{2}(\bm{p} - \bm{r}_{\perp} )^2 + g \mathsf{R}(\theta) u(\bm{r}) - \frac{1}{2} \mathsf{K}(\theta) \bm{r}^2
\ \ \ \ \
\eeq
where (prime indicates theta derivative):
\begin{eqnarray} \label{eq:K}
\mathsf{K}(\theta) \ = \ 1 +  \left(\frac{1}{\mathsf{R}(\theta)}\right)'' \mathsf{R}(\theta)
\eeq
and the scaled version of the attractive potential is
\begin{eqnarray}
u(\bm{r}) = -\frac{\mu_2}{\sqrt{(x-\mu_1)^2+y^2}} -\frac{\mu_1}{\sqrt{(x+\mu_2)^2+y^2}}
\ \ \ \
\eeq
with ${\mu_1+\mu_2=1}$.
The parameter~$g$ is the scaled attraction constant for the force between the satellite and the stars.
It can be due to gravitation, or (in different context) it can be of Coulomb origin.

For an arbitrary quasi-Kepler motion (as defined above) the Hamiltonian is controlled by two parameters $(\mathsf{R},\mathsf{K})$.
So in general the satellite experiences a {\em cycle}. But for a proper Kepler motion
${\mathsf{K}(\theta) =  g_{\varepsilon} \mathsf{R}(\theta) = 1/[1+\varepsilon\cos(\theta)] }$
with ${g_{\varepsilon} = (1-\varepsilon^2)^{-3/4}}$.
Consequently, see \App{app:hillK}, we get a Hamiltonian that depends on a single parameter,
\begin{eqnarray}
\mathcal{H}(\bm{r},\bm{p})
= \frac{1}{2}(\bm{p} - \bm{r}_{\perp} )^2 +  \mathsf{R}(\theta) \left( g u(\bm{r}) - \frac{1}{2}g_{\varepsilon} \bm{r}^2 \right)
\ \ \ \
\eeq
Thus, a proper Kepler motion should be regarded as a {\em modulation} and not as a {\em cycle}.
As explained at the last paragraph of \App{app:hillK},
the dimensionless constant that controls the quasi-static aspect
of the Kepler driving is ${ \varepsilon g_{\varepsilon} / g }$.
For simulations we used $g{=}25$, and $\varepsilon{=}0.2$, and $\mu_1 {=} \mu_2 {=} 1/2$.

\sect{Poincaré landscape}
\Fig{fLandscape} displays the Poincaré section for the Hill's Hamiltonian: Two (blue) regions contain quasi-regular trajectories around each of the two stars; There are additional quasi-regular regions; and there is a large (red) chaotic sea. In order to demonstrate the variation of phasespace with respect to the energy $E$, or with respect to a control parameter (here it is $\theta$ that parameterize the Kepler motion), we propose to look on the {\em Poincaré landscape} that is displayed in the additional panels of \Fig{fLandscape}. Each raw in those additional panels encodes the information regarding the phase-space structure for a different value of~$E$ or~$\theta$, respectively. In a later Section we display on top of this landscape, the evolving cloud of the time-depended Hamiltonian $\mathcal{H}(\bm{r},\bm{p}; \theta(t))$. The time-dependence of $\theta$ induces spreading in energy and migration of trajectories between different regions.

\begin{figure}
\includegraphics[width=8cm]{poancare_g25_e02_theta-0_mu05_Em22-2}
\includegraphics[width=8cm]{Poincare_kepler_Elandscape}
\includegraphics[width=8cm]{Poincare_kepler_thetalandscape}

\caption{
{\bf Poincaré landscape.}
The upper panel is a standard Poincaré section for Hill's Hamiltonian \Eq{eq:H}
with ${\mu_1{=}\mu_2{=}1/2}$,
and $\varepsilon{=}0.2$,
and $g{=}25$,
at energy~${E=-22.2}$.
The control parameter $\mathsf{R}$ is frozen at the value~${\theta=0}$.
In the middle panel each row is a ${p_x=0}$ stripe of the Poincaré section at different~$E$,
while $\mathsf{R}$ is frozen at the value~${\theta=0}$.
In the lower panel the Poincaré stripes are plotted
for frozen $\mathsf{R}$ at different values of~$\theta$.
Initially~${E=-22.2}$, and later we follow $E$ adiabatically.
The color code is such that chaotic trajectories are red,
while quasi-regular chaotic trajectories are blue.
}
\label{fLandscape}
\end{figure}

\section{Poincaré sequencing}
\label{sec:PSM}

The spreading of energy is determined by the fluctuations of the generalized force $\mathcal{F}$
that is associated with the control variable $\theta$. Note that we assume periodic driving,
and that the scaled Hamiltonian is defined such that $\theta$ is the time variable.
For typical model systems, e.g. Billiards with moving piston,
and also for the Hill's Hamiltonian, we can factorize $\mathcal{F}$ as follows:
\begin{eqnarray}
\mathcal{F} \ \ = \ \ -\frac{\partial \mathcal{H}} {\partial \theta} \ \ \equiv \ \ g(\theta) f(\bm{r})
\eeq
The variation of the energy is an integral over $-\dot{\theta} \mathcal{F}(t)$,
but for the analysis it is more convenient to consider
\begin{eqnarray} \label{eq:Q}
Q \ \ = \ \ \int_0^t f(\bm{r}(t)) dt  \ \ \equiv  \ \ \sum_j F_j
\eeq
This allows to get rid of the intra-cycle modulation that is observed
in the variation of the energy, see \Fig{fig:energy},
while the features that are essential for the analysis are preserved.
The last equality express the integral as a sum over pulses,
whose area is defined in the illustration of \Fig{fPulse}.

\begin{figure}[b]
\includegraphics[width=7cm]{energy_kepler}
\includegraphics[width=7cm]{energy_kepler_iqr}
\caption{
{\bf Variation of the energy}.
The energy for a cloud of chaotic trajectories is plotted as a function of time (upper panel).
The spreading is displayed in the lower panel (black line).
Here we define $S_E$ as the width of the central 50\% region.
The blue line is a moving average over cycle.
}
\label{fig:energy}
\end{figure}

\begin{figure}
\includegraphics[width=8cm]{fp}

\caption{
{\bf Poincaré pulses.}
Representative piece of the signal ${f(\bm{r}(t))}$.
The vertical red lines indicate the moments $t_j$ that are selected by the Poincaré section.
The signal is regarded as a sequence of rectangular pulses, displayed in green color.
Each pulse has duration $T_j$ and average height ${\bar{F}_j = F_j/T_j }$.
In the figure $\bar{F}$ is scaled vertically ($\times 10$) to improve resolution.
}
\label{fPulse}
\end{figure}

\sect{Entropy growth}
In the simulations we consider the following scenario.
Initially we launch a narrow cloud in the middle of the chaotic sea.
After a short transient this cloud fills most of the chaotic sea.
Some extra time might be required in order to penetrate
peripheral regions where the dynamics is sticky.
We shall come back to this stickiness issue later on.
For a time-dependent Hamiltonian we also have to consider:
{\bf (a)}~Spreading away from the initial energy surface;
{\bf (b)}~Migration between regions due to the time-dependence of the Hamiltonian.
The dissipation aspect (growth of the average-energy)
is directly related  to \#a and indirectly related to \#b.
In order to quantify the growth of entropy that is
associated with the spreading in the energy,
we define~$S_Q$ as the range of energy (around the median)
where $50\%$ of the probability is located.
There are traditional measures for entropy growth
in terms of phasespace volume,
but we prefer a definition that has a direct practical meaning.

\begin{figure}[b]
\includegraphics[width=8cm]{iqrintfp_1C}
\includegraphics[width=8cm]{iqrintfp_10C}
\caption{
{\bf Entropy growth.}
The dynamics is generated by \Eq{eq:H},
with the same parameters as in \Fig{fLandscape}.
The time dependence of $S_Q$ is regarded
as a measure for entropy growth,
where $Q$ is defined by \Eq{eq:Q}.
The black line is $S_Q$ for an ensemble of 1-cycle (normal panel)
and 10-cycles (log-log panel) trajectories that were launched in the chaotic sea.
In the log-scale panel, the lower and upper dashed lines indicate $\propto t$  and $\propto t^2$ dependence.
The red and blue lines are $S_Q$ if the control parameter~$\mathsf{R}$
were frozen. The selected values are at $\theta{=}0$ (red) and $\theta{=}\pi$ (blue),
for which the spreading is relatively fast/slow respectively.
According to the traditional paradigm of quasi-static processes,
the black line should be roughly between the red and the blue lines, which is clearly not the case.
The red and blue dotted lines (lower data lines in both panels)
are $S_Q$ for a signal that is composed of a randomized
sequence of the same pulses, i.e. they provide the variance that would be expected
if the actual signal did not have phase-space correlations.
We conclude that correlations are {\em enhanced} due to the time dependence of~$\theta(t)$.
}
\label{fSpreading}
\end{figure}

\begin{figure}[b]
\includegraphics[width=6cm]{image_static-pi_avgfp_1C_sort}
\includegraphics[width=6cm]{image_static-0_avgfp_1C_sort}
\includegraphics[width=6cm]{image_kepler_avgfp_1C_sort}

\caption{
{\bf Poincaré sequences of pulses.}
The rows of each image displays the color-coded sequences $\bar{F}_j$
of the trajectories for which the spreading has been calculated in the upper panel of \Fig{fSpreading}.
The 3 panels are for $\theta{=}\pi$, and for $\theta{=}0$, and for the actual $\theta(t)$ of the Kepler motion.
The trajectories in each panel are ordered by the average value of $\bar{F}_j$.
The {\em red stretches} for $\theta{=}0$ indicate stickiness in red regions
that will be identified in \Fig{fPoincare}.
The additional {\em blue stretches} in the lower panel
indicate excess dwell time in the chaotic sea.
}
\label{fPulseSeq}
\end{figure}

A very long chaotic trajectory that explores the whole chaotic sea
is regarded as a  {\em Poincaré sequence} of $F_j$ pulses.
The spreading $S_Q$ as a function of time is presented in \Fig{fSpreading}.
In order to get the spreading in,
the chaotic trajectory is divided
into sub-sequences of length~$T$ (upper panel)
or of length~$10T$ (lower panel),
where~$T$ is the period of a cycle.
Equivalently, we start the simulation with a cloud of initial points
at the middle of the chaotic sea, evolve them,
and care to exclude the initial transient.

In order to figure out whether temporal correlations are important
we randomize the original $F_j$ sequence,
and then divide it again into sub-sequences.
In \Fig{fSpreading}, the spreading of the randomized-trajectories is displayed too, for sake of comparison.
The ratio between the actual rate of spreading, and that of the randomized-trajectories,
is a robust measure for correlations.

\begin{figure}
\includegraphics[width=8cm]{chaos_poancare_static-0_fp}
\includegraphics[width=8cm]{traj2}
\caption{
{\bf Poincaré mapping of pulses.}
The upper panel displays the Poincaré section for the ${\theta=0}$ Hamiltonian.
Those are the same chaotic trajectories as in \Fig{fLandscape}
(the quasi-integrable regions are left empty),
but the points are color-coded  by the values of $\bar{F}_j$.
The black line indicates the border of the energy surface (the forbidden region is outside).
The lower panel shows a chaotic trajectory $(x(t),y(t))$.
The color encodes the time.
The black stretch indicates motion in the ``red" sticky region of the upper panel.
It is characterized by an "$\infty$" shaped loops.
}
\label{fPoincare}
\end{figure}

\begin{figure}
\includegraphics[width=8cm]{chaos_poancare_kepler_fp}
\includegraphics[width=8cm]{Poincare_kepler_thetalandscape_kepler}
\caption{
{\bf Driven system dynamics.}
In the upper panel a trajectory of the Kepler-driven Hamiltonian
is presented using the same section as that of \Fig{fPoincare}.
Gray color is used for all the points of the trajectory,
while red and blue colors are used
for the {\em correlated stretches} of \Fig{fPulseSeq}.
Parameters are the same as in \Fig{fLandscape}.
The Hamiltonian is time dependent.
Accordingly, the cloud of trajectories spreads in energy,
and can migrate between different regions.
This is demonstrated in the lower panel,
where we use the same presentation method as in \Fig{fLandscape}.
The native chaotic region, that corresponds to the red areas in \Fig{fLandscape},
is colored in black.  The evolving cloud of the Kepler-driven system is displayed
using blue, red and gray dots. Red color indicates sticking in periphery regions,
while blue indicates sticking in the native chaotic sea. The non-sticking gray points
expand into ``swamp" regions that are located outside of the native chaotic sea.
See text for further details.
}
\label{fig:cloud}
\end{figure}

\sect{Identifying correlations}
We would like to ``see" the correlation by looking on the ``signal".
For this purpose we plot images of the non-randomized sub-sequences in \Fig{fPulseSeq}.
The sub-sequences are ordered according to their average.
If the sub-sequences originate from a randomized-trajectory,
this average is close to zero, and the ordering has no significance (and no visual effect).
But sequences of the non-randomized-trajectory are correlated.
The correlations can be identified by inspection of the figure.
Namely, the  sequences of the time-independent  $\theta{=}0$ Hamiltonian
exhibit long red stretches, and the Kepler-driven sequences exhibit also blue stretches.
This should be contrasted with the sequences of the $\theta{=}\pi$ Hamiltonian,
that look rather uncorrelated.

\sect{Phasespace exploration}
Having identified correlations in the `signal',
we would like to trace out their phasespace origin.
For this purpose we point out that the value $F$ of the pulse
provides information about the location of the phasespace region that supports the pulse,
as demonstrated in \Fig{fPoincare}.
Roughly speaking, we can regard $F$ as a radial coordinate
for points in the Poincaré section. Variations in the value of~$F$
indicate migration of the trajectory between different regions.
In this specific example,
red pulses originate from peripheral regions of the chaotic sea,
while blue pulses originate from the central region of the chaotic sea.
Thus, the red and blue stretches in \Fig{fPulseSeq} indicate {\em stickiness}
in phase-space regions that have distinct typical non-zero value of~$F$.

The stickiness to peripheral regions is expected.
It has been studied in past literature.
What we find rather surprising is the extra stickiness that we find in the dynamics that
is generated by the Kepler driven system:
the additional {\em blue stretches} indicate excess dwell time in the central region of the chaotic sea.

A more careful inspection, see \Fig{fig:cloud},
reveals that the stickiness in the central region of the chaotic sea
is in the region that was chaotic also in the absence of driving.
So roughly we have the following regions:
(a)~Native chaotic sea region;
(b)~Swamp chaotic region;
(c)~Peripheral chaotic regions;
(d)~Quasi regular regions.
The swamp regions appear due to the driving.
They form in some sense a barrier
between the native chaotic sea and its periphery.
As for the quasi regular regions: they are excluded from our simulation,
and not penetrated by the chaotic trajectories.

\section{Stochastic modelling}
\label{sec:model1}

Hard-chaos dynamics can be described as a random hopping between cells in phasespace.
We have mixed-chaotic phasespace, with tendency for stickiness in e.g. peripheral regions,
and therefore an effective stochastic description becomes a challenge.
We would like to introduce a robust procedure for this purpose.
First of all we recall that:
(i)~chaotic motion is ergodic.
(ii)~the pulse strength $F$ is like a radial coordinate.
It is therefore rather natural to divide phasespace into $F$-cells.
The size of the $F$-bins is determined such that all the (binned) values have
the same rate of occurrence in the $F_j$ sequence.
In particular we distinguish in \Fig{fPoincare}
the blue and the red regions, that corresponds
to the bins that contain the smallest and the largest pulses respectively.

\sect{Stochastic Kernel}
Having done the $F$-binning of phasesapce regions, it becomes possible to define
a matrix $\bm{P}$ whose element $P_{n,m}$ provide the probability to make a transition form bin~$m$ to bin~$n$.
Note that the calculation of $\bm{P}$ is a straightforward `signal analysis' procedure
that is based solely on the inspection of the $F_j$ sequence.

An image of the $P_{n,m}$ matrix is provided in \Fig{fig:Pmatrix}.
Qualitatively, we see that the images reflects our
expectation for enhanced probability to stay in red and blue regions whenever
stickiness is observed in \Fig{fPulseSeq}. But this is misleading.
In fact $\bm{P}$ is not capable of providing an explanation for the stickiness.
We explain this point in the subsequent paragraph.

We can generate artificial $F_j$ sequences using $\bm{P}$ as the propagator (kernel)
for a memory-less Markov process. Naively one might have the hope to get sequences that
have the same statistical properties as the original Poincaré sequences.
But this is not the case: the Markov process does not reproduce red/blue stretches
that we see in \Fig{fPulseSeq}.
On the quantitative side we define the probability $\mathcal{P}(\tau)$
for survival in (say) the ``red" region after~$\tau$ steps.
It is defined as the relative number of ``red" pulses
that have at least $\tau$ consecutive ``red" pulses.
(In other words, it is the inverse-accumulative distribution
of the dwell time in the the red region).
The one-step survival probability is ${ P \equiv \mathcal{P}(\tau{=}1) }$.
Accordingly, for a Markov process with $P_{n,m}$ we get
\begin{eqnarray} \label{eNaive}
\mathcal{P}(\tau)\Big|_{\text{Naive}} \  = \ P^{\tau}
\eeq
The actual $\mathcal{P}(\tau)$ clearly does not agree with
exponential decay, as shown in \Fig{fig:Ptau}.
The naive expectation grossly underestimates the stickiness.

\begin{figure}
\includegraphics[width=8cm]{TransMatrix_0}
\includegraphics[width=8cm]{TransMatrix_kepler}
\caption{
{\bf Transition probability matrix.}
The matrix element $P_{n,m}$ is the probability to make a transition form bin~$m$ to bin~$n$.
The images of the matrix are for the frozen ${\theta=0}$ dynamics,
and for the Kepler-driven dynamics.
In both cases one observes high probability to stay in the red region (last bin).
In the Kepler-driven case there is also enhance
probability to stay in the blue region (first bin).
}
\label{fig:Pmatrix}
\end{figure}

\begin{figure}
\includegraphics[width=8cm]{PS_toymodel}
\caption{
{\bf Survival probability $\mathcal{P}(\tau)$.}
The probability to find a pulse that has at least $\tau$ consecutive pulses at the same region.
The red and blue colors refer respectively to survival in the red and in the blue regions.
The $+$ symbols are for the time-independent $\theta{=}0$ Hamiltonian,
and the $*$ symbols are for the Kepler-driven time dependent Hamiltonian.
The solid lines are the analytic results based on the minimal stochastic model
(the thicker lines are for the Kepler-driven Hamiltonian).
The dashed lines illustrate the naive exponential decay
for the time-independent $\theta{=}0$ Hamiltonian.
}
\label{fig:Ptau}
\end{figure}

\section{Minimal stochastic model}
\label{sec:model2}

The failure of $P_{n,m}$ to reproduce $\mathcal{P}(\tau)$ is easily understood by inspection
of phasespace. For presentation purpose we focus on the stickiness in the ``red" region(s)
of \Fig{fPoincare}. Regarding this region as composed of tiny phasespace cells,
we can determine what is the ``survival time" in the red region for each cell.
Then we realize that only fraction of red cells have large survivals time.
Accordingly, $P_{n,m}$ should be regarded as the coarse-graining of a finer kernel $P_{\nu,\mu}$.
Note that the type of index (Roman vs Greek) is used in order to distinguish the coarse-grained
version from the ``microscopic" version.

We would like to construct a {\em minimal} version for $P_{\nu,\mu}$,
that corresponds to $P_{n,m}$,
and that reproduces $\mathcal{P}(\tau)$ correctly.
Using this model we would like to illuminate semi-quantitatively
how the rate of entropy growth depends on the stickiness.
The calculation of $\mathcal{P}(\tau)$ given a Markov kernel $\bm{P}$ is
done as follows:
\begin{eqnarray} \label{ePt}
\mathcal{P}(\tau) \Big|_{\text{Markov}} \ \ = \ \  \left(\frac{1}{\bm{p}^{\dag}\bm{p}}\right) \bm{p}^{\dag} (\bm{Q}\bm{P})^{\tau} \bm{p}
\eeq
In this expression $\bm{p}$ is a vector that contains the initial distribution within the bins.
Specifically, we assume uniform distribution within the ``red" bins.
Note that $(\bm{p}^{\dag}\bm{p})^{-1}$ is the number of participating red bins.
The matrix $\bm{Q}$ is a projector on the red bins,
and the final projection provides the total survival probability after~$\tau$ iterations with~$\bm{Q}\bm{P}$.
We can adopt the area of $\mathcal{P}(\tau)$ as a measure for stickiness.
For a given Markov process it is calculated as follows:
\begin{eqnarray} \label{eq:stickiness}
\mathcal{S} = \sum_{\tau} \mathcal{P}(\tau)
=  \left(\frac{1}{\bm{p}^{\dag}\bm{p}}\right) \bm{p}^{\dag} \left[\frac{1}{1-\bm{Q}\bm{P}}\right] \bm{p}
\ \ \ \ \ \ \
\eeq
This can be regarded as the duration of the sticking.
Note that the naive expression \Eq{eNaive} gives
a rather low value ${ \mathcal{S}=1/(1-P) }$.

We already saw in \Fig{fig:Ptau} that a naive 2-region model is not enough to reproduce the stickiness.
So the minimum is apparently 3-regions.
We assume that we have $n_0$ phasespace cells in the non-red region,
and $n_1+n_2$ cells in the red region.
Consider the possibility of fully-connected chaos
with ${N=n_0+n_1+n_2}$ cells
with equal transition probabilities.
Then the reduced $\bm{P}$ that describes the
transitions of probabilities between the 3 regions would be
\begin{eqnarray}
\bm{P} =
\frac{1}{N}
\begin{pmatrix}
	n_0	& n_0 & n_0 \\
	n_1	& n_1 & n_1 \\
	n_2 & n_2 & n_2
\end{pmatrix}
\eeq
The survival probability in the red region
would be ${P_0=(n_1+n_2)/N}$,
that is characterized by ${ \mathcal{S}_0=1/(1-P_0) }$.

We now turn to consider a mixed phase-space, where the
chaotic sea is connected, but not fully-connected.
Specifically, we assume that the transition probabilities
from the $n_0$ cells to the $n_1$ cells are
all equal to $p_1$, while all the transition probabilities
between the $n_1$ cells and the $n_2$ cells equal $q$.
Then the {\em reduced} $\bm{P}$ that describes the
transitions of probabilities between the 3 regions is
\begin{eqnarray} \label{eq:Pnm}
\bm{P} =
\begin{pmatrix}
	1-n_1p_1 & n_0p_1 			& 0 \\
	n_1p_1 			& 1-n_0p_1-n_2q 	& n_1 q \\
	0 			& n_2 q 				& 1-n_1 q
\end{pmatrix}
\eeq
The model is characterized by 4 parameters
\begin{eqnarray} \label{eq:P}
R \ &=& \ \frac{n_2}{n_1} \\
P_0  \ &=& \ \frac{(n_1+n_2)}{n_0+(n_1+n_2)} \ \ \equiv \ \ \frac{N_{\text{red}}}{N} \\
P \ &=&  \  1 - \left(\frac{n_1}{n_1+n_2}\right) n_0p_1 \\
Q \ &=&  \ n_1 q
\eeq
The parameters $R$ and $P_0$ reflect the relative size
of the regions. Namely, $P_0$ is the relative size of the red region
(and hence  the survival probability in the red region if we had fully connected chaos),
and $R$ is fraction of sticky red cells.
The parameters $P$ and $Q$ reflect the transitions
between the regions. We could have added also direct transitions
with probability $p_2$ between the $n_0$ and the $n_2$ cells,
but it turns out that this would be a redundancy for our purpose.
Also the total number of cells is insignificant for the analysis.

All the probabilities in the $\bm{P}$ matrix must be less than~$1$.
This impose some constraints over the valid range of the model parameters.
In particular one realizes that if ${R>1}$ then ${P>(1/2)}$.
Therefore, in order to describe a model that exhibit stickiness (small~$P$)
we have to assume ${R<1}$, and then the same constraints
imply that ${ P > [R/(R+1)] }$.

In practice the parameters $P_0$ and $P$ are determined from the statistics
of the signal, while $R$ and $Q$ are effective parameters
that are determined by fitting to $\mathcal{P}(\tau)$.
These parameters control the stretch and the area of this function.
The latter, using \Eq{eq:stickiness}, is given by the following expression
\begin{eqnarray} \label{eq:S}
\mathcal{S} \ \ = \ \ \frac{1}{1{-}P} + \left[\frac{R}{R+1}\right] \frac{1}{Q}
\eeq
For ${R=0}$ we get the naive result ${ \mathcal{S}=1/(1-P) }$.
In the limit ${Q\rightarrow 0}$ there is no decay from the $n_2$ cells,
and then the survival probability approach
$\mathcal{P}(\infty) = R/(1 {+} R)$,
and $\mathcal{S}$ diverges.
The minimal value ${\mathcal{S}=\mathcal{S}_0 = 1/(1-P_0)}$
is obtained for a fully connected chaos.

On the basis of the simulations we have determined $\mathcal{P}(\tau)$
for the blue and for the red regions,
for both the $\theta{=}0$ Hamiltonian
and for the Kepler-driven Hamiltonian.
The results are displayed in \Fig{fig:Ptau}.
The effective model parameters have been extracted
via fitting, are are listed in \App{app:S}.

\section{Stickiness and entropy growth}
\label{sec:SnE}

Using the stochastic model we can try to figure out
a relation between the stickiness and the spreading.
The latter is determined by the time dependent diffusion coefficient
\begin{eqnarray}
D(t) \ \equiv  \  \frac{1}{2} \sum_{\tau=-t}^t C(\tau)
\eeq
with the correlation function
\begin{eqnarray} \label{eC}
C(\tau) \ = \ \braket{F_{\tau} F_0}
\ = \ \frac{1}{N} \sum_{\mu,\nu} f_{\mu} [\bm{P}^{\tau}]_{\mu,\nu}  f_{\nu}
\eeq
where $N$ is the number of cells,
and $f_{\mu}$ is the $F$ value that is associated with the phasespace cell
that is indexed as~$\mu$.
Note that a finite result for $\mathcal{P}(\tau)$
is obtained provided ${\sum f_{\mu}=0}$,
reflecting that the correlation function is defined
for the signal after subtraction of the average.

Without the sticky red region the correlation function
is of the form $C(\tau)=C_0\delta_{\tau,0}$.
With the red region included we get correlations
due the sticking. To evaluate the contribution
of the latter we use the {\em reduced} matrix of \Eq{eq:Pnm},
where all the cells are grouped into 3 regions.
In such case the sum over $\mu$ in \Eq{eC} is replaced
by a sum over regions, and the number of cells in each
region should be introduced as a weight factor.
Then we obtain
\begin{eqnarray} \label{eC0}
C(0) = C_0 + P_0 \mathcal{S}_0 f_{\text{red}}^2
\eeq
where $f_{\text{red}}$ is the average $F$ value of the red region.
Note that the implied average $F$ value of the non-red region
is ${ -P_0 \mathcal{S}_0 f_{\text{red}} }$.
The summation over $\tau$ leads to \Eq{eC}
with ${\bm{P}^{\tau}}$ replaced by ${1/(1-\bm{P})}$.
The zero mode has to be excluded from the inversion.
Including $C_0$ we get
\begin{eqnarray}
\sum_{\tau=0}^{\infty} C(\tau) \ \ = \ \  C_0 \ + \ P_0 \mathcal{S} f_{\text{red}}^2
\eeq
We define the correlation factor as follows:
\begin{eqnarray}
c  \ = \ \frac{ \sum_{\tau} C(\tau) }{ C(0) }
\ = \ 2 \left(\frac{  \sum_{\tau=0}^{\infty} C(\tau) }{ C(0) } \right) - 1
\ \ \ \
\eeq
It is the correlation ``time" in terms of iteration with the Poincaré map.
For the minimal model of \Eq{eq:Pnm} we obtain
\begin{eqnarray} \label{eq:c}
c \ = \ 2 \left(\frac{\mathcal{S}}{\mathcal{S}_0}\right) - 1,
\ \ \ \ \ \text{for $C_0{=}0$}
\eeq
Note that for fully connected chaos we get $c=1$ as expected.

For the Kepler-driven system we observed an additional ``blue" sticky region.
Therefore we have to generalized the minimal model,
such as to have two sticky regions, ``red" and ``blue".
The total number of cells is ${ N=N_0+N_{\text{red}}+N_{\text{blue}} }$.
We define ${P_0^{\text{red}}=N_{\text{red}}/N}$
and  ${P_0^{\text{blue}}=N_{\text{blue}}/N}$.
Each of the regions has its own $\mathcal{P}(\tau)$,
with effective parameters that have been determined in \App{app:S}.
Note that the implied average $F$ value of the $N_0$ region is
${f_0 = -(1/N_0)[N_{\text{red}} f_{\text{red}} + N_{\text{blue}} f_{\text{blue}}] }$.
Then one obtains
\begin{eqnarray}
C(0) = C_0
+ \frac{N_0}{N} f_0^2
+ P_0^{\text{red}} f_{\text{red}}^2
+ P_0^{\text{blue}} f_{\text{blue}}^2
\ \ \ \ \
\eeq
and
\begin{eqnarray}
\sum_{\tau=0}^{\infty} C(\tau) \ = \ C_0
+ P_0^{\text{red}} \mathcal{S}^{\text{red}} f_{\text{red}}^2
+ P_0^{\text{blue}} \mathcal{S}^{\text{blue}} f_{\text{blue}}^2
\ \ \ \
\eeq
Note that for $N_{\text{blue}} = 0$ these equations reduce back to \Eq{eq:c}.

The correlation factor can be extract numerically from the $S_Q$ plots of \Fig{fSpreading}.
Namely, it is the ratio between the slope of $S_Q^2$ for the true pulse sequence,
and that of the randomized sequence (of the same pulses).
By inspection of \Fig{modelSpreading} we see that the true $S_Q^2$ exhibits
a super-diffusive transient that indicates long-time correlations that
are not captured by our simplified model. The agreement with the minimal model
is qualitative rather than quantitative. Some extra details about the
quantitative aspect are provided in \App{app:S}.

We see that a model that faithfully reproduces $\mathcal{P}(\tau)$
is not enough for the determination of $C(\tau)$.
In principle we could have introduced a more elaborated stochastic model,
that features a hierarchy of ``red" and ``blue" regions,
but such an approach has no practical value,
and does not allow the derivation of analytical results.

\begin{figure}
\includegraphics[width=8cm]{Stau}
\caption{
{\bf Stochastic modelling of entropy growth.}
The solid lines are $\text{Var}(Q)$ for the $F_j$ digitized sequences.
See \App{app:S} for technical details regarding the `digitization'.
Note that the ``time" ($\tau)$ is the number of Poincaré steps.
The red lines are for the  $\theta{=}0$ Hamiltonian,
and the black lines are for the Kepler-driven Hamiltonian.
The lower dashed lines are the prediction of the effective stochastic model.
The dotted lines are for a randomized $F_j$ sequence,
namely, the expected result if the pulses were uncorrelated.
The lower and upper dashed lines indicate $\propto t$  and $\propto t^2$ dependence
(the former cannot be resolved from the dotted lines).
}
\label{modelSpreading}
\end{figure}

\section{Cycle vs Modulation}
\label{sec:cycle}

It is important to distinguish between {\em Cycle} and {\em Modulation}. Consider an Hamiltonian $H_{\bm{R}}$ where $\bm{R}$ is a set of control parameters. In a time dependent scenario we can say that the Hamiltonian varies along a curve in a parametric manifold. A {\em modulation} can be parametrized by a single non-cyclic parameter, say $R(t) = A \cos(\Omega t)$, while a {\em cycle} requires an angle parameter, say ${\theta(t) = \Omega t}$, where $\theta$ is defined modulo $2\pi$. A prototype example for cyclic driving is presented in \Fig{fBilliard}.

It is sometimes difficult to determine whether the time dependence in the Hamiltonian should be regarded as {\em Constant} or as {\em Modulated} or as {\em Cyclic} driving. For example: the time dependence for particle in a rotating box can be removed by transforming into a rotating frame. Similarly, the time dependence for a particle in an expanding box can be removed via a dilation transformation. In the case of a cycle the outcome depends in general on the sense of the cycle, and furthermore for a mixed phasespace we expect difference in the rate of entropy growth.

At first glance one may naively think that a Kepler-driven system qualifies as {\em Cyclic} driving.
The two parameters might be $(X(t),Y(t))$ or equivalently $(\mathsf{R}(\theta),\mathsf{K}(\theta))$ as in \Eq{eq:H}.
But it turns our that for a proper Kepler driving the cycle degenerates into a modulation.
In order to avoid such `degeneracy' we have to assume an asymmetric $\mathsf{R}(\theta)$,
for example ${\mathsf{R}(\theta) \propto  [1 + \varepsilon \cos(\theta) + \varepsilon' \sin(2\theta)]^{-1}}$,
that is illustrated in \Fig{fig:FK}.

If we have a non-degenerate cycle, we can ask whether the rate of entropy-growth depends
on its {\em sense} (cycle vs reversed cycle).
For a system with mixed-chaotic phasespace indeed we can have such dependence,
as discussed for e.g. the mushroom billiard in \cite{Kedar3}.
A different illustration of the same idea is provided in \Fig{fBilliard}.
During the cycle the space is divided by a barrier (that serves as a ``valve") into two regions.
This is done periodically, and out-of-phase with respect to the piston movement.
Specifically, in the plotted illustration, the splitting ratio of the cloud
is roughly 1:2 for forward cycle, and roughly 1:1 for reversed cycle.
Changes of energy due to changes in the volume obey
a simple ``ideal gas" multiplicative law ${E \mapsto \alpha E }$,
where $\alpha$ is given by \Eq{eQa}.
The value of $\alpha$ depends on the sense of the cycle
due to the different splitting ratio,
and we get ${\alpha=10/9}$ and ${\alpha=9/8}$ respectively.

However, the billiard examples are rather artificial.
They are based on construction that allows a sharp distinction between regions in (phase)space.
Generic systems, such as the Hill's Hamiltonian, do not feature dramatic splitting and merging
of well defined (phase)space regions.
Consequently, dependence on the sense  of the cycle
is not a prominent effect, and careful numerical procedure is required to detect it.
This motivates the following discussion of {\em directionality} dependence.

\begin{figure}
\includegraphics[width=8cm]{Billiard-Cycle}

\caption{
{\bf The billiard paradigm.}
This caricature clarifies the mechanism of dissipation in the quasi-static limit.
The control parameters are ${\bm{R}=(X,W)}$,
where $X$ is the position of the piston,
and $W$ is the height of a dividing barrier.
Consider the ``blue" quasi-static cycle:
The barrier is turned on ($W=\infty$);
The piston is pushed in;
The barrier is turned off ($W=0$);
The piston is pushed out.
Such cycle, unlike the ``red" modulation,
raises the average energy of the system (${E \mapsto \alpha E}$ with ${\alpha >1}$).
Note that the blue and red $E(t)$ plots reflect the average over an ensemble of trajectories.
}
\label{fBilliard}
\end{figure}

\sect{Directionality}
The dependence on the sense of the cycle is related to the directionality dependence of a modulation.
The argument is as follows: A modulation can be encoded
by a sequence $A\bar{A}A\bar{A}\cdots A\bar{A}\cdots$.
The inverse modulation is clearly the same sequence. A cycle can be encoded
as $A\bar{B}A\bar{B}\cdots A\bar{B}\cdots$.
The reversed cycle $B\bar{A}B\bar{A}\cdots B\bar{A}\cdots$
is distinct if the cycle is not degenerated (${ A \neq B }$),
and provided $A$ and $\bar{A}$ are not characterized by the same spreading rate.
It is therefore enough to establish dependence on directionality.

Regarding the sequence $F_j$ as a `signal', we ask whether it looks statistically the same during
the `forward' half period when $R(\theta)$ changes from $R(0)$ to $R(\pi)$,
and the `backward' half period when it changes from $R(\pi)$ to $R(0)$.
In the standard paradigm of quasi-static processes the directionality has no significance.
In \Fig{fig:fdistribution} we plot the distribution of the $F$ values for the two groups of pulses.
For the full signal the distribution of the $F_j$ over the bin is uniform by definition.
But if we look only on the pulses that belong to the `backward' half-periods
we see that the small values (blue pulses) become slightly more frequent,
as opposed to the large values (red pulses) that become slightly less frequent.
The difference is very small.  Still, it indicates that the steady state
is not the same for ``forward" and ``backward" driving.

\begin{figure}
\includegraphics[width=8cm]{RK}
\caption{
{\bf Cyclic driving.}
An example for a generic driving cycle in ${(\mathsf{R},\mathsf{K})}$ is illustrated
by  the blue line, where
${\mathsf{R}(\theta) \propto  [1 + \varepsilon \cos(\theta) + \varepsilon' \sin(2\theta)]^{-1}}$,
and $\mathsf{K}$ is determined by \Eq{eq:K}, with $\varepsilon{=}0.2$ and $\varepsilon'{=}0.1$.
For Kepler driving we set $\varepsilon'{=}0$ and get the black line,
which is a single-parameter modulation.
}
\label{fig:FK}
\end{figure}

\begin{figure}
\includegraphics[width=8cm]{half_probability_2T_diff}
\caption{
{\bf Directionality dependence.}
The probability distribution of the $F_j$ over the bins is uniform by definition.
It can be regarded as the sum of `forward' pulses distribution, and `backward' pulses distribution.
Here we plot the deviation of the cumulative probability distribution
of the backward pulses, from a uniform distribution.
The horizontal axis is the indexed $F$ value (smallest value is indexed as 1, largest value is indexed as 38516).
We see that the small values (blue pulses) become slightly more frequent,
as opposed to the large values (red pulses) that become slightly less frequent.
}
\label{fig:fdistribution}
\end{figure}

\section{Dissipation}
\label{sec:dissipation}

Dissipation is associated with energy spreading.
The standard theory \cite{Ott1,Ott2,Ott3}
assumes a globally chaotic energy surface that instantly ergodizes at any moment.
It follows that the phase-space volume $\mathcal{N}(E;\theta)$ is an adiabatic invariant,
where $\theta(t)$ is a slowly varying control parameter.
For a closed cycle, the conservative work is zero. Still, beyond the zero-order adiabatic result,
there is diffusion in energy with coefficient ${D_E = \nu \dot{\theta}^2}$,
where $\nu$ is the intensity of the fluctuations, i.e. the algebraic area of $C(t)$.
From the Fokker-Plank description of the spreading process,
one deduces rate of absorption ${\dot{E} = \mu \dot{\theta}^2}$,
aka the Kubo formula, with dissipation coefficient $\mu$ that is related to $\nu$
via a fluctuation-dissipation relation \cite{Wilkinson1,Wilkinson2,crs,frc},
namely ${\mu = (1/2)\beta \nu}$, where $\beta(E)$ is some version of
microcanonical inverse temperature, as defined in \App{app:qes}.
Consequently, for periodic driving with frequency ${\Omega \equiv \dot{\theta}}$
one expects an amount ${ Q = 2\pi \mu \Omega }$ of dissipated energy per cycle,
which vanishes in the quasistatic limit (${\Omega \rightarrow 0}$).

For a driven mixed chaotic system, we expect parametric dissipation,
meaning that the dissipated energy per cycle (${ Q }$)
approaches a finite non-zero constant in the limit $(\Omega \rightarrow 0)$,
and depends on the directionality of the driving as discussed in the previous paragraph.
Billiard example that have been discussed in the past,
as well as that of \Fig{fBilliard} are illuminating,
but do not fully reflect some complications that are
encountered once we deal with a generic system, such as Hill's.
In what follows we highlight those zero-order subtitles,
and also generalize the first-order formulation.

\sect{Zero order Dissipation}
In systems with mixed-chaotic dynamics we can get irreversibility (entropy growth),
as well as dissipation (growth of the average energy) even in the quasi-static limit.
The derivation of this claim requires phase-space generalization of \cite{Kedar3}.
This generalization is presented in \App{app:qes}.
We write the phasespace area as ${\mathcal{A} = \sum_{\mu}  \mathcal{A}_{\mu}}$,
where ${\mu}$ distinguishes different regions.
Each region might have a different ``inverse temperature" ${\beta_{\mu} }$.
Then we obtain the following result:
\begin{eqnarray} \label{eQ}
\braket{Q}_{0} \ \ &\approx& \ \
- \sum_{steps} \sum_{\mu}   \frac{\delta \mathcal{A}_{\mu}}{\beta_{\mu} \mathcal{A}}
+  \mathcal{O}(\delta \mathcal{A}^2)
\eeq
This expression is obtained from \Eq{eQb} after expansion
with respect to ${\delta \mathcal{A} = \mathcal{A}_{\mu}-\mathcal{A}_{\mu}^{(0)}}$.
Based on \Eq{eQ} our observation is that we can get an $\mathcal{O}(\delta \mathcal{A})$ non-zero result provided the $\beta_{\mu}$ are non-identical.
In such case $\braket{Q}_{0}$ can switch sign for a reversed cycle.
This should be contrasted with a Billiard system for which the ${\beta_{\mu}=1/E}$ are identical,
and $\braket{Q}_{0}$ is always positive.

\sect{First order Dissipation}
We define ${ \mathcal{F} = -\partial \mathcal{H}/\partial \theta }$.
For a periodically driven Hamiltonian with ${\dot{\theta} = \Omega }$
we have ${ \dot{E} = -\Omega  \mathcal{F}(t) }$.
Integrating over a cycle, squaring, and averaging over an ensemble,
we get ${\text{Var}(Q)  =  2 \pi \nu \Omega }$,
where $\nu$ is the intensity of the fluctuations
(the area of the $\mathcal{F}$ autocorrelation function).
This assumes a globally chaotic energy surface.
If we have a fragmented phase-space (as in the previous Billiard example)
we get ${\text{Var}(Q)  =  \text{Var}_0(Q) + 2 \pi \nu \Omega }$,
where $\text{Var}_0(Q)$ is the variance
that is associated with $\braket{Q}_{0}$.
Using the above explained fluctuation-dissipation reasoning
we deduce that the energy increase per cycle is
\begin{eqnarray} \label{eQcycle}
\braket{Q} \ \ = \ \ \braket{Q}_{0}
\ + \  \frac{1}{2} \beta_{\text{eff}} \left[ \text{Var}_0(Q) + 2\pi \nu \Omega \right]
\eeq
This expression goes beyond Kubo, because the zero order spreading is taken into account.
Note that if correlations persist over a time duration that is longer than a cycle,
the result is a long super-diffusive transient as in \Fig{fSpreading}.
In any case the appropriate correlation factor $c$ has to be incorporated
in the calculation of~${\nu}$, as discussed in \Sec{sec:SnE}.

\section{Summary and outlook}

We have introduced an effective stochastic theory for quasi-static entropy growth in systems with mixed chaotic phasespace.
The main objective was to provide tools for the analysis energy spreading,
which is useful for the calculation of the average energy growth (dissipation),
and possibly for estimating the rate of evaporation (dust that escapes the binary system).

The agenda was, on the one hand, to characterize  the multi-dimensional phasespace dynamics
using signal-analysis of a single chaotic trajectory. On the other hand we wanted to
reproduce the essential statistical features of the `signal' using a minimal Markovian model.

For the characterization of the chaotic motion we represent the chaotic trajectory
as a Poincaré sequence of pulses~($F_j$). The value of $F$ is regarded
as a radial phasespace coordinate that is used in order to divide phasespace into {\em regions} (indexed by $n$).
We realize that this coarse-graining is too rough: we cannot build on it a Markov process
that reproduces the observed stickiness. We therefore have to define a refined version
of the Markov process that reflects the hierarchic structure of phasespace.
Consequently we constructed a minimal model that allows to reproduce the observed stickiness.
This model suggests a relation between the stickiness and the enhancement
that is observed is the rate of entropy growth. Unfortunately, in the present model,
the quantitative agreement is poor due to long range correlations that were neglected.

Specifically, for the frozen dynamics we have identified stickiness in peripheral regions of the chaotic sea,
and the minimal stochastic model required 3 regions (central chaotic region;  non-sticky peripheral chaotic
region; sticky peripheral chaotic region).  Surprisingly in the Kepler-driven system extra stickiness
manifests in the native chaotic sea. This extra stickiness is related to the appearance
of an additional ``swamp chaotic region" where chaos penetrates due to the time-dependence of the Hamiltonian.

We also looked for directionality dependence, implying that the rate of entropy growth
is not the same if a cycle is reversed. We have clarified that also this effect
can be identified from the `signal analysis" of the Poincaré sequence.
Specifically for Kepler-driving this is a very weak effect (a few percent difference).

Finally, for sake of generality, we have explained how the Kubo theory of dissipation
can be generalized in order to incorporate both the zero-order and first-order irreversibility.
This picture implies exponential energy growth if $\braket{Q}$ of \Eq{eQcycle} is proportion to~$E$.
This is indeed the case for Billiard systems if ${\braket{Q}_0 \ne 0}$
as discussed originally by \cite{Kedar1,Kedar2,Kedar3}.
More generally we can get from \Eq{eQcycle} different energy dependence, say ${ \dot{E} = \lambda E^{\alpha} }$.
Note that for ${ \alpha >1 }$ one obtains hyperbolic-like growth that leads
to escape ${E \sim 1/(t-t_e)^{1/(\alpha-1)}}$ within a finite time~$t_e$.
The exploration of such scenario requires further study of possibly different model systems.

redpajama_set_name: RedPajamaArXiv


text:
Q: win10 pyaudio gives 'Unanticipated host error' when recoding system audio data win10 anaconda environment, remote desk access to this workstation
conda, anaconda and anaconda-navigate all updated
I used conda to install the pyaudio (have tried pip install the 'whl' file, same result)
I would like to record the system audio e.g. mp3 audio or stream audio data, not the microphone input. But I still have tried both enabled/disable 'setting' --> 'privacy' --> 'microphone', none of them works.
Here is my code:
import pyaudio
p = pyaudio.PyAudio()
stream_in = p.open(
    rate = 44100,
    channels = 2,
    format = pyaudio.paInt16,
    input = True,                   # input stream flag
    input_device_index = 3,         # select the Stereo Mix
    frames_per_buffer = 1024
)

It returns the error message: OSError: [Errno -9999] Unanticipated host error
I checked the audio device in the system:
for i in range(p.get_device_count()):
    devInfo = p.get_device_info_by_index(i)
    print(devInfo)

And it gives 6 result:
{'index': 0, 'structVersion': 2, 'name': 'Microsoft Sound Mapper - Output', 'hostApi': 0, 'maxInputChannels': 0, 'maxOutputChannels': 2, 'defaultLowInputLatency': 0.09, 'defaultLowOutputLatency': 0.09, 'defaultHighInputLatency': 0.18, 'defaultHighOutputLatency': 0.18, 'defaultSampleRate': 44100.0}
{'index': 1, 'structVersion': 2, 'name': 'Remote Audio', 'hostApi': 0, 'maxInputChannels': 0, 'maxOutputChannels': 2, 'defaultLowInputLatency': 0.09, 'defaultLowOutputLatency': 0.09, 'defaultHighInputLatency': 0.18, 'defaultHighOutputLatency': 0.18, 'defaultSampleRate': 44100.0}
{'index': 2, 'structVersion': 2, 'name': 'Line In (Realtek HD Audio Line input)', 'hostApi': 1, 'maxInputChannels': 2, 'maxOutputChannels': 0, 'defaultLowInputLatency': 0.01, 'defaultLowOutputLatency': 0.01, 'defaultHighInputLatency': 0.04, 'defaultHighOutputLatency': 0.04, 'defaultSampleRate': 44100.0}
{'index': 3, 'structVersion': 2, 'name': 'Stereo Mix (Realtek HD Audio Stereo input)', 'hostApi': 1, 'maxInputChannels': 2, 'maxOutputChannels': 0, 'defaultLowInputLatency': 0.01, 'defaultLowOutputLatency': 0.01, 'defaultHighInputLatency': 0.04, 'defaultHighOutputLatency': 0.04, 'defaultSampleRate': 44100.0}
{'index': 4, 'structVersion': 2, 'name': 'Speakers (Realtek HD Audio rear output)', 'hostApi': 1, 'maxInputChannels': 0, 'maxOutputChannels': 6, 'defaultLowInputLatency': 0.01, 'defaultLowOutputLatency': 0.01, 'defaultHighInputLatency': 0.04, 'defaultHighOutputLatency': 0.04, 'defaultSampleRate': 44100.0}
{'index': 5, 'structVersion': 2, 'name': 'Microphone (Realtek HD Audio Mic input)', 'hostApi': 1, 'maxInputChannels': 2, 'maxOutputChannels': 0, 'defaultLowInputLatency': 0.01, 'defaultLowOutputLatency': 0.01, 'defaultHighInputLatency': 0.04, 'defaultHighOutputLatency': 0.04, 'defaultSampleRate': 44100.0}

Since I want the system audio, not recording the sound from the microphone, I selected index 3 which is the 'Stereo Mix'.
The sound icon in the taskbar shows two 'Remote Audio', no other choise. I also checked the default device:
defaultCapability = p.get_default_host_api_info()
print(defaultCapability)

output:
{'index': 0, 'structVersion': 1, 'type': 2, 'name': 'MME', 'deviceCount': 2, 'defaultInputDevice': -1, 'defaultOutputDevice': 1}

Then I omit the 'input_device_index' to use the default one, and got OSError: [Errno -9996] Invalid input device (no default output device)
Anyone can help me figure out which device I should select? Thanks a lot.

redpajama_set_name: RedPajamaStackExchange


Now these days local business is the best way to promote your business. If you have local products, promoting your business locally brings you more leads then promoting to different cities. As an initial your business should be locally introduced, and a local customer trust you more than a customer from different city. It gives you a tons of business this will help you make your back in local. We promote businesses in google my business and in this campaign google review and citation helps your business grow and give you a unique clients from your city and builds a brand for your products/services.
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It's possible to enable detailed debug logging for almost all functional aspects of the tv's firmware. This can be useful when analyzing some internal RELEASE behaviour especially in conjuntion with a disassembly of it (see Reverse Engineering Hints for details).
in Saturn7 TV - press "F10" to enter "debugMain"
You have to now how to enter CFE (for Broadcom) or U-boot (for Mstar) shell (see Bootloader connection article).
You should be able to enter Debug mode connection.
This page was last modified on 24 November 2011, at 12:16.


The oxford ragwort is so-called because it originated as an escape from the Botanic garden at Oxford where it was in cultivation from at least as early as 1690. Its spread in Northern Ireland dates from after about 1964 (the date of the earliest Northern Ireland record) and it rapidly became very abundant after about 1980 on motorway verges in north Belfast.
At present it is a very common member of the weed flora of waste ground and road verges in the Belfast district. It is also spreading into other parts of Northern Ireland. The plant was introduced into Oxford Botanic Garden (and from there into the rest of the British Isles) from Mount Etna in Sicily. Recent investigations have proved that Oxford ragwort is not a true species but is actually a hybrid which occurs naturally on the Etna slopes and which is derived from two other Senecio species which grow there.
This account quotes the recent work of R.J. Abbott and collaborators published in the BSBI's journal Watsonia. Abbott, R.J. , James, J.K. , Irwin, J.A. & Comes, H.P. Hybrid origin of the Oxford Ragwort, Senecio squalidus L. Watsonia 23 123 - 138 (2000).
All names: Senecio squalidus L.


Los Banos, CA. was to be my home for the next three years (1959-1962). Santa Cruz was a coastal city, a favorite vacation spot, ninety miles to the west. At the time, it never entered my mind that Santa Cruz would become my home from 1962 to now.
The principal of Los Banos High, Sam Beneditino, did not fit the stereotype for the position. He was not too busy being important to do important things. In 1959 all of the school's new teachers were from out of state. Like me, they had never visited Los Banos, California before. We were all young and needed an open supportive hand. Sam saw his position as one created to help, not to judge.
My job was to teach junior and senior English. In that era the students were tracked into 'college prep' or 'the others'. Often they were a mischievous bunch. On one occasion they stole a copy of a test, which was to be given on Monday. On Sunday they gathered together to plan how to use the test. They decided who among them would miss which questions to be less suspicious. Word leaked out about the plot. When they got the test on Monday, it was a different much harder test. When I attend class reunions, the actual original stolen test is always presented. To this day they still do not know how I got "wind" of the plot.
Perhaps the most important thing I learned in Los Banos was that rules occasionally need to be bent, even ignored. We operated with a strict tardy policy. Tardy students had to be issued permits to enter class. One of my students, Frank Enos, worked a night shift to help support his family. He could not get to my early class on time. I told him simply come directly to class. At the last reunion in 2017, he still remembered and with tears in his eyes, he thanked me.
Yes, I did move on. I applied for and received a teacher fellowship to the University of Oklahoma. After three years, I would be leaving Los Banos. During my time there I developed some skills. During the summer, I worked as the bookkeeper for a produce company. I did get the debits and credits in the correct column. I also sold World Book encyclopedias. Through my experience with World Book I learned to ask, "Mrs. Riley, did you know that a pig is smarter than a horse?" I also learned to convince women that they, not their husbands, were in charge and should make the decision to buy.


text:
Oliva incrassata, the angled olive or giant olive, is a species of sea snail, a marine gastropod mollusk in the family Olividae, the olives.

Distribution
This species is widespread from California to Peru.

Habitat
These sea snails live at the low-tide level, at the outer side of sandspits.

Description
Shells of Oliva incrassata can reach a length of . These relatively large shells are almost cylindrical, very thick, ovate, angularly swollen in the middle, with a rather short spire, a narrow and long aperture and usually with uniformly colored body whorls, except in the colummellar area. The basic color background may vary from ash-white or greyish to light yellow and brown, mottled with gray and olive, with angled transverse dark chestnut streaks and a fleshy rosy pink columellar area.

Biology
The Giant Olives are active predators. At night they search for food, while during the day they bury themselves beneath the sand and mud.

References

External links
 Conchology Inc

Bibliography
 Sowerby G. B. [first of the name] (1825). A catalogue of the shells contained in the collection of the late Earl of Tankerville. London, privately published : VII + 92 + XXXIV pp.
 Tursch B., Duchamps R. & Greifeneder D. - Studies on Olividae, XX. The pre-Lamarckian names for Oliva species. APEX 9 (2/3) 51–78, July, 1994
 Zeigler R.F. & Porreca H.C. - Olive Shells of the World. Rochester Polychrome Press, N.Y. 1969.

incrassata
Gastropods described in 1786

redpajama_set_name: RedPajamaWikipedia


Luke 16:13-15. The world tells us, "Just one more dollar." "Cash is king." "You are nothing unless you have everything." Ever day dream of winning the lottery? At some point in our lives we have to evaluate this tug on our hearts and see if indeed they are God's thoughts.
Romans 13:7-8. If you're a slave to debt we are not completely free to do what we have been tasked to do as the church. Find out how to follow Jesus financially and get out and stay out of debt.
Luke 16:1-12. If we want to be followers of Jesus we need to be followers of Jesus financially. So, how should we use wealth? What can we do to not misuse wealth? When it is all said and done, no one wants to regret the use of resources that have been entrusted to us during our lifetime. So what does Jesus teach? Listen and find out.
Mark 12:41-44. How much should you give toward efforts to make more and better followers of Jesus? The answer is not what you think. It's not 10%. Find out what Jesus thinks to consider how much you should give to support ministry and fix the broke thinking common to all of us.
We constatly hear, "Money changes everything." But what does God have to say about money?


Vanessa Dina, Kristina Fuller, and Gemma DePalma founded The Meat Club for women who want to have their meat and eat it too. This recipe, from The Meat Club Cookbook, came to them from their French friend France, who incidentally comes from France. This cold-weather meal gets better the longer it sits. This recipe calls for two types of stewing meat for richer flavor-the classic stewing meat from the chuck and the famously tender top sirloin. Let your butcher know so he can cube your pieces in advance.
Posted by Chronicle Books • Published 29th January 2012 • See Chronicle Books's 41 projects » © 2019 Leslie Jonath / Chronicle Books · Reproduced with permission.
Melt the butter in a large cast-iron casserole over medium heat. Add the bacon and brown until softened but not crispy, about 5 minutes. Remove the bacon and save for another use.
In the same pan, cook the meat in batches until browned evenly, 4 to 5 minutes per side. Once browned, return all the meat to the pan and sprinkle the flour over it. Mix well. Add the wine to cover the meat. Stir in the carrots, onions, garlic, thyme, and bay leaves.
Cover and cook over low to medium heat until the meat is tender enough to cut with a fork, about 2 hours. Add salt and pepper to taste.
I don't eat meat but this looks delicious. I might try making it with tofu. Yum!


No Shopping Malls but most of these places will meet your requirements!
Lamu is famous for its wood carving and the fine finish of the swahili furniture.You can also use your own design and create your own bespoke furniture. Lamu Holiday Solutions can arrange packaging and shipment.
Open everyday as from 7:30 AM. It is located along the seafront next to Civil Servants. Variety of products to buy and the price is negotiable.


We are currently hiring for the Work-Trade (karma-yogi) positions.
2 hours per week of work-trade grants unlimited yoga sessions.
Must be able to commit to the position for at least 6 months. Must have attended at least 10 prior class sessions in past.