She's the "real deal" and I'm here to testify that this is NO SCAM. It seems she is pedaling her arss off and moving ever slower to the edge. PLEASE pass this on, and let's get this hard working mother some temporary help. It just feels right. This is a plea from me to you, to help this woman stop the free fall. Some are just meant to be saved.
A reader remarked that they didn't know what Paris looks like, so I'm posting this.
You know someone like this: They are constantly living on the edge, either as a "drama queen" or "drama king," or they are competing in dangerous activities such as racing, performing stunt actions, participating in extreme sports and so-called X Games, or drinking, smoking and imbibing too much.
Maybe this person (or persons) is constantly living in a roller coaster fashion of emotional highs and lows brought on by choices, although rarely recognized as having any input or control over the emotionally charged circumstances.
Perhaps this is a victim or an abuser, feeding on the constant flow of stressors and fear factors. Even victims get a charge out the victim behavior: While the victimizer has a huge rush of adrenaline before and during an attack, so does the victim who experiences the fight or flight reaction and must always be on high alert.
Certain professions feed this addiction to adrenaline: Realtors, Lawyers, Business Professionals, Astronauts, Military Personnel, Pilots, Stunt-Performance actors, and live stage performers all live hectic, adrenaline-fused lives unless they take the time to notice, and to calmly go about the business without the chaos and stress.
We participate in these activities because it is fun, and because we get a rush of adrenaline that makes us feel alive.
Sometimes our adrenaline is brought about because conflict resolution is a rare rather than typical means of communication. Humans fight over money, and even have disputes with co-workers. There is never a good reason for lowering oneself to a level of hostility.
It is when the addiction to dramatic moments demands one live in constant chaos with toxic levels of adrenaline pumping through the body that attention and action need to intervene. Hypertension, heart failure, stroke, cancer, and a plethora of maladies are brought about by stress and drama. It also leads to adrenal burn-out, adrenal fatigue is a dangerous and debilitating condition.
Chaos often masks an aversion to stillness, a fear of hearing and/or facing one's inner voice. The fear of being alone with oneself triggers the constant level of mania and manifests constant drama, thus bringing the fix of the hormone.
The fix will kill you. The answer is in the stillness.
President Barack Obama visited Las Vegas on Thursday. The pictures today are all shots taken at the gathering. His speech was focused mainly on clean energy.
Traffic Gridlocked when the local police department closed the roads so access to the President was restricted. Not necessarily because of "energy conservation" consciousness, folks turned off their engines, and got out and milled about as they waited for the barricades to be lifted.
Even UPS drives couldn't gain access to the UPS facility where the gathering was held.
Look at the size of that tour bus!
Two of these, parked end to end, successfully blocked any inappropriate access to the President. And if the two buses weren't enough of a barrier, look at the top right of the picture to see the snipers on the rooftop.
No word needed. When the air traffic flew over, these guys were ready for anything.
Look at the size of these binoculars! I'm thinking they can see the California coast from this perch in Las Vegas.
Yep. His eyes and binoculars are trained on me. Soon afterward the Secret Service crew and bomb sniffing dogs showed up to make sure all was well.
Close up of the bus.
Not so secret service is checking out the onlookers in my circle.
Just another day in the lives of security….
Look closely and you can see the backside of the big guy.
Young Obama supporters in Las Vegas.
And with that, he was gone. Air Force One leaves Mc Carran International Airport.
Ram Dass said, "The quieter you become the more you can hear." I've been in a deep pool of noise over the past few days as I traveled to the mourning & celebration of life services for my recently departed friend; it is such a relief to come back to my friendly keyboard with my thoughts slipping out of my fingertips.
I inhale deeply as I write that last sentence. It is quiet, serene and warm in my office. I take a moment to express gratitude for my safe haven. Soon it will change, as well-meaning friends will show up at the door to continue the flow of condolences over loss. Food spreads will line the counters and beer and wine will be consumed. Noise, an infusion of tears and laughter and anger and all the emotions that can possibly spill forth will fill the environment. Expletives and kind sentiments will explode to mask the heartaches, and little by little the venting will release the dam and the feelings of love will flow out with even more velocity than the pouring wines.
We each have our own ways of dealing, of mourning, and of living. I am mostly introspective, although friends would argue that I am not introverted. It depends, partially, on the company I'm keeping, I suppose. Loud boisterous types annoy my sense of self. I prefer whispers and intimacies over large gatherings. But I also speak publicly and facilitate gestalt training groups, so I am around groups of people often. Maybe that's why the solace and solitude are so valuable when I can steal those oh-too-rare moments of quietness.
Ram Dass has it right. "The quieter you become the more you can hear." And this is a wonderful thing, only for those not afraid to hear. A lot of folks are scared out of their skin to even consider being still and listening to the self. I see it every month in the gestalt groups; so many folks are so alienated from themselves that they refuse to allow even one second of quietness. They self-filter; they run (generally screaming and crying) quickly away. It is as though the silence contains too much truth. But can the truth ever be scary? Sunlight burns if you get too much, but truth??
There is great empowerment in the truth. I have witnessed miracles in personal growth, and it is because of these miraculous experiences that I wrote Escaping the Chrysalis. I cannot possibly reach every human on Earth with my gestalt groups. I can, however, provide the Tools for Transformation into Divine Wholeness. Gestalt is inside of each of us. And the gestalt tools for changing any behavior are contained in Escaping the Chrysalis: Tools for Transformation into Divine Wholeness. The release of the book is nearing, and my heart races with excitement for you, the reader, because I know the magic contained in the pages.
Until then, in the silence of your self, take 5 minutes each day to let the thoughts settle and chaos begin to make sense. Don't fear the power of the quiet. Embrace the gift. Get in touch with you. You deserve to be gestalt/whole and balanced.
For anyone not currently living in 72 degree temperatures with a light warm ocean breeze blowing gently against your skin, my condolences. The beaches of Southern California are unseasonably warm this week, and the negative ions did much to alert me that fact.
My first book was written as I inhaled the negative ions of the Pacific, and I will, I fear, always have a deep romantic relationship with the coast. Try as I might, to live in other locales, I am drawn by the pull of the tides. I've spent years in other areas, but it is when I return that I feel I am coming home, and it is when I leave, that I feel the loss of love in my breaking heart.
This trip was different, only in that I was there for such a short visit. In that regard, it only adds to the emotion of deprivation that I sense. Such a short visit leaves me longing for more…like the thoughts of a lover fading into yesterday.
Any travel is good for helping one take stock of life, and of what is important. The sea is for me, and it is not for everyone. And the occasional earth rumblings make the California coast an area some folks shudder to consider. A few little earth quakes don't bother me. As long as I can stroll on the boardwalk, breathe in the benefits of sea level living, and relax into a less stressful experience, I am content. And still, I am happy to be home, and back to my typical life as a writer and gestalt practitioner.
~As alway, from Paris with love & light.
Today I am on my way to California to attend a funeral for the brother of a close friend. The deceased was tormented for most of his life, and never learned that he held the key to his own release by means less drastic than hanging.
Suicide is a subject of which I know far too much. It is also an action that takes place far too often for my taste. In the United States alone, over 30,000 individuals each year "successfully" kill themselves. The youngest documented case is that of a five year old child. Yes, I know this is hard to believe, but it is true. Suicide is the number three cause of death for American adolescents ages 15-25. And although more males than females take their own lives, more females make the attempt. Males generally leave via bullets and/or ropes, but recently, females choice of tools has become hanging as opposed to drug over doses.
Suicide is that all too permanent solution to a temporary feeling of helplessness. But in the case of my friend's brother, the pain had enveloped him for decades. He saw no other way out of the aching in his heart. He attempted to deaden the pain thru self-medicating and drowning in alcohol. In the end, his sense of self had become too diluted to stand stoic. His esteem was squelched and damaged and it seemed impossible that he would ever come up for air again. Down for the fourth or tenth time, he could not rise above his own life mire.
I've heard it said that, "he's at peace now." I don't think so. I think the I Am, the consciousness of our whole spirit is still in chaos. Death kills the body, but the spirit is alive infinitely. This is reason enough to finish any loose ends prior to checking out, when at all possible.
Those left behind, the survivors left with such a deep pain of loss, are left with all the "what ifs" and "coulda, shoulda, didn't," and "whys"? Trying to make sense of the loss and of the residing anger at the deceased, the survivors take the roller coaster of emotions straight up and unnervingly straight down. Survivors step onto that same train car as crahsed the deceased head first into the pits.
Suicides are on the increase, correlating with homelessness, poverty, and unemployment. Suicides in the Military are also on the increase. This isn't meant to be a buzz kill or to color your day with darkness. It's only to spread a little light on a very dark subject.
The media doesn't want to broadcast public service announcements or cover suicides as they fear the possibilities of "copy cat" suicides. I don't think the media has much to worry about. Rather, I believe that if the media paid more attention to the good that various support groups are doing, perhaps a few less deaths might take place.
There's a lot of good taking place. And there's a lot to be curious about. What waits just beyond the next curve in the road? After the rocky, may be a smooth trail. And despite the feeling of helpless foreboding, the sun rises again.
Rest in peace Todd. May you stay in the arms of the angels until your pain subsides.
One of the declarations on my bucket list is to, "Learn to knit really well." Except for that "really well" part, I'm almost ready to check knitting off my to-do list. I'm a pretty good scarf and hot pad manufacturer, but that's as far as it goes. Too bad I didn't simply make, "Learn to knit," one of my aspirations. Determining if I'm "good enough" to cross it off as being achieved has become an issue between Id and Ego.
I took a knitting class. They offered free wine and had a huge fire blazing in the fireplace. It was like sitting around in a friend's living room, sipping Merlot and comparing skill levels and talent, chatting with the kindred. It felt very accepting and nonjudgmental. We all learned that there are no "mistakes" in knitting, there are only "signatures." My first few pieces were wrought with signatures.
I can knit, but I can't purl. I don't even know what purling looks like. But it doesn't matter to me, because I don't knit to impress anyone. I knit, because my mind is not tied into the project with the yarn. My mind is allowed to just be; to watch with what I like to refer to as perceptive intelligence, (the I Am spirit nature of me) as my hands are busily wrapping and tying and pulling and knotting the strand mindlessly around and back off of the chosen needles.
I actually watch myself knitting, my conscious mind watching my unconscious rote activities. As each knot is formed, there is an energy flow that travels from me and into that yarn as slowly, but eventually an item begins to reveal itself (Nothing akin to Michelangelo's David, mind you!). My energy flows smoothly with the wooly thread as it winds around the clickity-clackity long, thin needles. Each knot is a conscious effort to add to the next, and to the last, and yet it is not a conscious effort at all. Each unforced knitting motion is made in order to achieve an outcome of creation. It requires no force.
Knitting has become something I can do while the rest of my self is busy with other activities. It's relaxing, meditative almost. For instance, I can now knit and watch television, knit and talk, and I can even knit and sip a glass of Cabernet. But I cannot knit and write this blog.
Much of the time, knitting is a very personal experience. I seek out specific yarns for the individual I will be gifting the eventual creation to. As a gift, I made a gorgeous purple scarf for a very close friend. I trimmed it with glass beads and silk threads that made it appear to be a very couture scarf. Ironically, she gave me a gorgeous purple silk scarf she had picked up in London. I'm thinking I got the better half of that deal.
It all starts with just a skein, chosen deliberately for the exact hue, softness or stiffness, fatness, fineness, and/or artistry depending on what it is that I intend that ball of yarn to eventually become. Shopping for perfect yarn and for the corresponding needle size and of course, for any accentuating trims is a large part of the process in creation of the end result. In fact, the hunting and gathering experience is almost as much a Zen process as is the actual knitting.
Once the perfectly suited materials for the envisioned final outcome have been purchased, the relaxing and rewarding art of creation begins. The entire event is a very holistic experience. It is calmly exciting to know that something pretty wonderful is about to be created.
Visualizing what will eventually come into fruition, and then creating the reality of that vision takes patience and a bit of movement in that direction each day. It's also a pretty accurate metaphor for successful fulfillment in life.
I've learned a lot through knitting. As an example, I learned that agitating certain yarns will cause them to change, to transform into solid and very different conditions than they were in originally. All the care and concern must be taken with fragile hearts, err, I mean, with fragile wool yarns. Some of the most beautiful are the most difficult to handle, and some of the least expensive turn out to be surprisingly lovely. It's a lot like interacting with people, I think. And each individual has his or her personal signatures.
Two people can take the exact ball of yarn, and the exact gauge needles, and create something extraordinarily dissimilar. One may create a tight, close-knit effect, and the other may have a loose and relaxed result. Neither is any better or worse; there is no right or wrong in knitting. In knitting, it is the process that makes the difference in the outcome.
I'm vowing to take at least as much time planning my next destination in life, as I spend choosing the perfect pieces for my latest creation in yarn. Life can be just as soft, or rigid, or rough, or flexible, or as colorful or muted as we determine to make it. It's just like those scarves and hot pads. The end result is a simple matter of intention.
~As always, with love & light.


text:
\section{Introduction}
\label{sec:intro}
The study of the internal composition of neutron stars is an active field of research which relies on astrophysical observations that allow to refine theoretical models.
In this respect, the recent observations of massive neutron stars
\cite{Demorest:2010bx,Antoniadis:2013pzd} have imposed important constraints on the stiffness of the equation of state (EoS), and therefore on the density ranges
covered by the density profiles of such high-mass compact star interiors.
On the other hand radius measurements are still far from being precise, with most of the methods relying
on either indirect measurements or model dependent assumptions like, e.g., for the neutron star atmospheres.
While there is a wide range of claimed radii starting from, e.g., $\sim 9$ km \cite{Guillot:2013wu}
to $\sim 15$ km \cite{Catuneanu:2013pz} we will proceed here on the assumption that the actual radii
are large, as reported by~\cite{Bogdanov:2012md,Hambaryan:2014}.
For a recent review of astrophysical constraints on dense matter see, e.g., Ref.~\cite{Miller:2013tca}.

In this contribution, we present a Bayesian analysis (BA) study case with a class of hybrid EoS characterized by two parameters.
The first one stands for the baryonic exluded volume that determines the stiffness of hadronic matter at
high densities.
The second one is the coupling strength for an 8-quark vector current interaction which regulates the stiffness of the high-density quark matter phase.
It turns out that within the range of variation for the excluded volume parameter there is a qualitative change in the mass-radius relation for high-mass stars: beyond a certain value for the excluded volume
the first order phase transition proceeds with a sufficiently large jump in the energy density to cause an instability which, thanks to the stiffness of the quark matter phase at high densities goes over to a stable sequence of hybrid stars, the so-called "third family" of  compact stars.
In this situation, the conditions are fulfilled for the high-mass twin phenomenon, where stars on the high-mass end of the second family of purely hadronic neutron stars are degenerate in mass with their  twin stars on the lower mass part of the third family of hybrid stars bearing a quark matter core, see
\cite{Benic:2014jia} and references therein.
For a recent classification of stable hybrid star sequences under generic conditions for the EoS, see
Ref.~\cite{Alford:2013aca}.
We note that the high-mass twin phenomenon is quite substantially based on a stiffening of both, the
hadronic and the quark matter EoS towards higher densities; it is not obtained within a systematic
parameter scan of hadronic vs. NJL quark matter EoS \cite{Klahn:2013kga} which lacks additional stiffening effects as those introduced in Ref.~\cite{Benic:2014jia}.

This possibility of high-mass twin stars is of great importance not only due to the possibility of identification of a critical endpoint in the QCD phase diagram~\cite{Blaschke:2013ana,Alvarez-Castillo:2015xfa} but also because it provides a solution to several issues discussed in~\cite{Blaschke:2015uva}:
the hyperon puzzle~\cite{Baldo:2003vx}, the masquerade problem~\cite{Alford:2004pf} and the reconfinement case~\cite{Lastowiecki:2011hh,Zdunik:2012dj}.
Moreover, the transition between twin stars bears an energy reservoir \cite{Alvarez-Castillo:2015dqa}
that qualifies it as a possible engine for most energetic explosive astrophysical phenomena like gamma-ray bursts and fast radio bursts or play a role in contributing to the complex mechanism of core collapse supernova explosions.
The present BA in the restricted two-dimensional parameter space of the new hybrid EoS
performed with the modern high mass and large radius priors will give an answer to the question whether
the high-mass twin star case is preferable over the connected hybrid star branch alternative.

\section{New class of quark-hadron EoS for hybrid stars}
\label{sec:hybrid}
In this study we consider hybrid neutron stars that are composed of hadronic matter and might undergo a phase transition to quark matter in their cores if parameter values of the models physically allow for it.
In this way both \textit{pure hadronic} and \textit{hybrid} star configurations with physical properties determined by
fixed parameter values shall be faced against observational data for model descrimination.
The EoS description is presented in the following subsections.

\subsection{Hadronic EoS with excluded volume corrections}
The description of hadronic matter in terms of pointlike hadrons with appropriately chosen interactions has to be limited to the low density region where effects of the finite size of hadrons (due to their compositeness) can be neglected.
In the high density region, however, the quark substructure of nucleons requires antisymmetrization of the many-nucleon wave function w.r.t. quark exchange among them, leading to the Pauli blocking effect in the EoS.
This effect is expected to happen as density increases beyond saturation density and can be viewed as a precursor of quark delocalization as the equivalent of the quark deconfinement transition~\cite{Ropke:1986qs}
Pauli blocking will be intensified by the simultaneous partial chiral restoration~\cite{Blaschke:2016}.
The resulting consequences for the EoS can be mimicked by adopting excluded volume corrections to any purely hadronic EoS.

The excluded volume correction is applied at suprasaturation densities and has the effect of stiffening the EoS without modifying any of the experimentally
well constrained properties below and around saturation $n_{\textmd{sat}}=0.16$ fm$^{-3}$, the density in the interior of atomic nuclei. We introduce the
the available volume fraction $\Phi_N$ for the motion of nucleons at a given density $n$ as~\cite{Typel:2016srf}
 \begin{equation}
    \Phi_N=\left\{
                \begin{array}{lll}
                  1~,& \textmd{if} &n \leq n_{\textmd{sat}}\\
                  \exp[-{v\vert v \vert}(n-n_{\textmd{sat}})^{2}/2]~, & \textmd{if} &n > n_{\textmd{sat}}~,
                \end{array}
              \right.
              \label{vex}
  \end{equation}
with $v=16\pi r_N^3/3$
as the van-der-Waals excluded volume corresponding to a nucleon hard-core radius $r_N$.
The mathematical form of (\ref{vex}) with positive (negative) values for $v$ leads to a stiffening (softening)
of the original EoS.
We shall consider only positive values of excluded volume in this work and introduce for them the dimensionless parameter $p=10\times v[{\rm fm}^3]$, taking
values between $p=0$ and $p=80$.

For the hadronic part of the neutron star EoS we will consider here the density dependent relativistic meanfield  EoS named "DD2" \cite{Typel:2009sy} (which is rather stiff) and the slightly softer EoS "DD2F" which fulfills the flow constraint from heavy-ion collision experiments
\cite{Danielewicz:2002pu}.
This flow constraint version of the DD2 EoS is obtained by multiplying the density dependent meson-nucleon couplings
$\Gamma_i(n)$ of the DD2 model \cite{Typel:2009sy}  for $n>n_{\rm sat}$ with the functions $g_i(n)$, where $i=\omega, \sigma$.
These functions are defined as
\begin{equation}
g_\omega(n) = \frac{1+\alpha_- x^s}{1+\alpha_+ x^s} = \frac{1}{g_\sigma(n)}~,
\end{equation}
where $x=n/n_{\rm sat} - 1$ and $\alpha_\pm = k(1\pm r)$, with the parameter values being adjusted to
$k=0.04$, $r=0.07$ and $s=2.25$.

For both these EoS we shall adopt a variation of the nuclear symmetry energy as introduced
in~\cite{Typel:2014tqa} in the context of the description of neutron skin thickness of heavy nuclei.
The symmetry energy $E_s(n)$ is defined as the difference in the energy per nucleon between pure neutron matter and symmetric matter in a uniform, infinite system.
In RMF models the isovector $\rho$ meson usually represents the only contribution to the isospin
dependence of the interaction. Following~\cite{Typel:2014tqa} we use here three parametrizations
for the density-dependent $\rho$ meson coupling
\begin{equation}
\Gamma_\rho(n) = \Gamma_\rho(n_{\rm sat}) \exp (-\alpha_\rho x)~,
\end{equation}
corresponding to a "soft", "medium" and "stiff" symmetry energy, see Table~\ref{tab:rho}.

\begin{table}[!h]
\label{tab:rho}
\begin{tabular}{lllll}
\hline
\hline
$E_s(n)$ & \multicolumn{2} {l} {parametrization} & $\Gamma_\rho(n_{\rm sat})$ & $a_\rho$ \\
\hline
stiff & DD2$+$ & DD2F$+$ & 3.806504 & 0.342181\\
medium & DD2 & DD2F & 3.626940 & 0.518903\\
soft & DD2$-$ & DD2F$-$ & 3.398486 & 0.742082\\
\hline
\hline
\end{tabular}
\caption{Parametrization of the symmetry energy variation by different density dependences of the
$\rho$ meson coupling, adapted from Ref.~\cite{Typel:2014tqa}.}
\end{table}

It turns out that $E_s(n)$ has a direct impact on the neutron star radius, in particular for the low-mass stars like star (B) of the double pulsar PSR J0737-3039(B) \cite{Kramer:2006nb}, thus affecting the compactness and binding energy, important observables for our analysis in this work.
We have hereby defined a family of six EoS which we label according to their symmetry
energy functionals as DD2, DD2-, DD2+, DD2F, DD2F-, and DD2F+, respectively.
For each of these EoS we will vary the excluded volume as the first free EoS parameter of this study.

\iffalse

In order to quantify the excluded volume effects, we introduce the closest packing parameter
$\nu= 100 \times \left[n_{\nu}/{\rm fm}^{-3}\right]$, where $n_\nu$ is the closest packing density.
Increasing the excluded volume leads to a lowering of the closest packing parameter and therefore to
a lowering of the critical pressure and energy density where the first order phase transition to the high density quark matter phase occurs,
implemented in the form of a Maxwell construction.
The excluded volume modification is implemented for baryon densities exceeding saturation
$n_{\textmd{sat}}=0.16$ fm$^{-3}$
(the density in the interior of atomic nuclei) by considering the available volume $\Phi_N$ for the motion of nucleons at
a given density $n$ as defined in~\cite{Typel:2016srf}
 \begin{equation}
    \Phi_N=\left\{
                \begin{array}{lll}
                  1~,& \textmd{if} &n \leq n_{\textmd{sat}}\\
                  \exp[-{v\vert v \vert}(n-n_{\textmd{sat}})^{2}/2]~, & \textmd{if} &n > n_{\textmd{sat}}~,
                \end{array}
              \right.
              \label{vex}
  \end{equation}
where $v=16\pi r_N^3/3$
is the van-der-Waals excluded volume that is related to the nucleon hard-core radius $r_N$.
Note that in the form (\ref{vex}) assigning positive (negative) values for $v$ leads to a stiffening (softening)
of the original EoS for which we adopt DD2 \cite{Typel:1999yq} with parameters from \cite{Typel:2009sy}.
Here, we will consider only positive values of excluded volume and introduce for them the dimensionless parameter $p=10\times v[{\rm fm}^3]$,
varying it in the range from $0$ to $80$.

\fi

\begin{figure*}[!bht]
\begin{center}$
\begin{array}{ccc}
\includegraphics[width=0.25\textwidth]{pvsmu_dd2fm_p80_case_A-eps-converted-to} & \includegraphics[width=0.25\textwidth]{pvsepsilon_dd2fm_p80_case_A-eps-converted-to} & \includegraphics[width=0.25\textwidth]{M-R_dd2fm_p80_case_A-eps-converted-to}\\
\includegraphics[width=0.25\textwidth]{pvsmu_dd2fm_eta4_case_B-eps-converted-to} & \includegraphics[width=0.25\textwidth]{pvsepsilon_dd2fm_eta4_case_B-eps-converted-to} & \includegraphics[width=0.25\textwidth]{M-R_dd2fm_eta4-10_Case_B-eps-converted-to}
\end{array}$
\end{center}
\caption{Variations of the hybrid EoS for the DD2F$^-$ model. \textit{Upper row}. The hadronic EoS is kept fixed while the quark EoS is allowed to vary for the parameters $\eta_4=0,1,2..30$.
\textit{Lower row}. The quark EoS is fixed whereas the hadronic EoS takes the values $p=0,5,10,...80$. For all these models the EoS is shown on the left and central plots while the resulting mass radius diagrams are shown on the right side.}
\label{Case_A_n_B}
\end{figure*}

\subsection{Quark matter EoS with multi-quark interactions}

The EoS in the high density phase is obtained from a NJL model with multiquark interactions \cite{Benic:2014jia,Benic:2014iaa}.
The Lagrangian for two quark flavors, $q=(u,d)$ is defined as
\begin{equation}
\mathcal{L}=\bar{q}(i\partial_\mu\gamma^\mu-m)q+\mu_u\bar{u}\gamma^0 u+\mu_d\bar{d}\gamma^0 d +
\mathcal{L}_4+\mathcal{L}_8~,
\label{eq:njllag}
\end{equation}
where $\mu_f$ are the chemical potentials of flavor $q_f$ and $m$ is
the current mass.
The interaction terms are
\begin{eqnarray}
\label{eq:l4}
\mathcal{L}_4 &=& \frac{g_{20}}{\Lambda^2}
[(\bar{q}q)^2 + (\bar{q}\bm{\tau} q)^2]-\frac{g_{02}}{\Lambda^2}[(\bar{q}\gamma_\mu q)^2 + (\bar{q}\gamma_\mu\bm{\tau} q)^2]\,,\\
\mathcal{L}_8 &=& \frac{g_{40}}{\Lambda^8}[(\bar{q}q)^2 +
(\bar{q}\bm{\tau} q)^2]^2-\frac{g_{04}}{\Lambda^8}[(\bar{q}\gamma_\mu q)^2+(\bar{q}\gamma_\mu\bm{\tau} q)^2]^2 \nonumber \\
&&-\frac{g_{22}}{\Lambda^8}[(\bar{q}\gamma_\mu q)^2+(\bar{q}\gamma_\mu\bm{\tau} q)^2][(\bar{q}q)^2 + (\bar{q}\bm{\tau} q)^2]\,.
\label{eq:l8}
\end{eqnarray}
While the NJL model has additional interactions to complete its chiral symmetry, in Eqs.~(\ref{eq:l4}) and (\ref{eq:l8}) only the components that condense at finite density are shown.
Within the mean-field approximation the thermodynamic potential is found
\begin{eqnarray}
\Omega &=& U+ \sum_{f=u,d}\Omega_f(M_f,T,\tilde{\mu}_f)-\Omega_0~,
\label{eq:thnjl}
\end{eqnarray}
where
\begin{eqnarray}
U &=& 2\frac{g_{20}}{\Lambda^2}(\phi_u^2+\phi_d^2) +
12 \frac{g_{40}}{\Lambda^8}(\phi_u^2+\phi_d^2)^2 \nonumber \\
&&-2\frac{\eta_2 g_{20}}{\Lambda^2}(\omega_u^2 + \omega_d^2)-12 \frac{\eta_4 g_{40}}{\Lambda^8}(\omega_u^2+\omega_d^2)^2~,\\
\Omega_f &=&-2 N_c\int \frac{d^3 p}{(2\pi)^3}
\Big\{E_f + T\log[1+e^{-\beta(E_f-\tilde{\mu}_f)}] \nonumber \\
&&+ T\log[1+e^{-\beta(E_f+\tilde{\mu}_f)}]\Big\}~,
\end{eqnarray}
where we have set the mixing term $g_{22}=0$ \cite{Benic:2014iaa}.
The parameter $\eta_4$ is the dimensionless scaled coupling strength for the 8-quark interaction in the vector meson channel which determines the stiffness of the quark matter EoS at high densities.
It is the second parameter that will be subject to free variation in this study.

The quark pressure $P_q$ is obtained by solving the gap equations
\begin{equation}
\frac{\partial\Omega}{\partial \phi_f} = 0 ~, \quad
\frac{\partial\Omega}{\partial \omega_f} = 0 ~.
\end{equation}
for the scalar ($\phi_f \equiv \langle \bar{q}_f q_f\rangle$) and vector
($\omega_f\equiv \langle q^\dag_f q_f\rangle$) mean-fields
and evaluating (\ref{eq:thnjl}) as $P_q=-\Omega$.
$\beta$-equilibrium is maintained through the processes
$d\to u+e^- +\bar{\nu}_e$ and $u+e^- \to d + \nu_e$, so that
\begin{equation}
\label{beta-eq}
\mu_u = \mu_d + \mu_e ,
\end{equation}
where $\mu_e$ is the electron chemical potential.
We take into account charge neutrality by
\begin{equation}
\label{charge}
\frac{2}{3}n_u - \frac{1}{3}n_d - n_e = 0~,
\end{equation}
where $n_f = -\partial \Omega/\partial \mu_f$.

\begin{figure*}[!thb]
\begin{center}
\begin{tabular}{l|c|c|c}
\hline
Symmetry energy $\rightarrow$&&&\\
&soft & medium & stiff\\
EoS $\downarrow$&&&\\
\hline
&&&\\
DD2F (semi-soft)&
\includegraphics[width=0.25\textwidth]{M-R_dd2fm-eps-converted-to} & \includegraphics[width=0.25\textwidth]{M-R_dd2f-eps-converted-to} & \includegraphics[width=0.25\textwidth]{M-R_dd2fp-eps-converted-to}\\
&&&\\
\hline
&&&\\
DD2 (stiff)&
\includegraphics[width=0.25\textwidth]{M-R_dd2m-eps-converted-to} & \includegraphics[width=0.25\textwidth]{M-R_dd2-eps-converted-to} & \includegraphics[width=0.25\textwidth]{M-R_dd2p-eps-converted-to}\\
&&&\\
\hline
\end{tabular}
\end{center}
\caption{Mass radius relations for the six hybrid EoS classes constructed from the hNJL quark matter EoS and the six hadronic RMF EoS by a Maxwell construction.}
\label{All_M-R}
\end{figure*}

From these two constraints (\ref{beta-eq}) and (\ref{charge}) we can find the total pressure of the
quark matter phase, $P_q + P_e$, as a function of the
baryon chemical potential $\mu_B = 2\mu_d+\mu_u$.
The total energy density of the system is
\begin{equation}
\varepsilon = - P_q - P_e + n_u \mu_u + \mu_d n_d + n_e \mu_e~.
\end{equation}

\subsection{Phase transition: Maxwell construction}

In our study we consider that
compact stars might undergo a first order phase transition to quark matter. The transition point is determined by enforcing the \textit{Gibbs conditions}: both the pressure and
chemical potential should have the same value in both hadronic and quark matter phases. Whether the resulting compact star will be a hybrid or a pure hadronic will
depend on having these conditions fulfilled at densities lower than the central density of the most massive star of each EoS sequence.

A systematic analysis is performed by varying the EoS parameters both in the hadronic and the quark phase as shown in figure~\ref{Case_A_n_B}.
This has important consequences for the compactness of the neutron star as well as for the possible existence of a disconnected branch of hybrid stars ("third family") in the mass-radius diagram.

\subsection{Mass-radius relations for hybrid EoS}

Once the equation of state of neutron star matter is defined, the structure and global properties of compact stars are
obtained by solving the Tolman-Oppenheimer-Volkoff (TOV) equations~\cite{Tolman:1939jz,Oppenheimer:1939ne}
\begin{eqnarray}
\frac{dP(r)}{dr}&=& - \frac{G M( r)\varepsilon( r)}{r^2}\frac{\left(1+\frac{P( r)}{\varepsilon( r)}\right)
\left(1+ \frac{4\pi r^3 P( r)}{M( r)}\right)}{\left(1-\frac{2GM( r)}{r}\right)},\nonumber\\
\frac{dM( r)}{dr}&=& 4\pi r^2 \varepsilon( r) ,\nonumber\\
\frac{d N_B( r)}{dr}&=& 4\pi r^2 \left(1-\frac{2GM( r)}{r}\right)^{-1/2}n( r)~.
\end{eqnarray}

The necessary boundary conditions to solve these equations are picking up
a central energy density $\varepsilon_c=\varepsilon(r=0)$ and a central pressure $P_c=P( r=0)$ at $r=0$. The integration is carried out from the center of the star up to
the distance $r=R$ where the pressure vanishes $P( r=R)=0$, defining the radius $R$,
the mass $M=M(R)$ and the baryon number $N_B=N_B(R)$ of the star.
By varying the central energy density is possible to obtain a sequence of star configurations for a given EoS,
which then uniquely corresponds to a mass-radius curve $M(R)$.

\begin{figure*}[htb!]
\begin{center}
\begin{tabular}{l|c|c|c}
\hline
Symmetry energy $\rightarrow$&&&\\
&soft & medium & stiff\\
EoS $\downarrow$&&&\\
\hline
&&&\\
DD2F (semi-soft)&
\includegraphics[width=0.25\textwidth]{MG-MB-dd2fm-eps-converted-to} & \includegraphics[width=0.25\textwidth]{MG-MB-dd2f-eps-converted-to} & \includegraphics[width=0.25\textwidth]{MG-MB-dd2fp-eps-converted-to}\\
&&&\\
\hline
&&&\\
DD2 (stiff)&
\includegraphics[width=0.25\textwidth]{MG-MB-dd2m-eps-converted-to} & \includegraphics[width=0.25\textwidth]{MG-MB-dd2-eps-converted-to} & \includegraphics[width=0.25\textwidth]{MG-MB-dd2p-eps-converted-to}\\
&&&\\
\hline
\end{tabular}
\end{center}
\caption{Gravitational mass vs. baryonic mass for the six classes of new hybrid EoS.
For the explanation of the boxes, see text.
}
\label{All_Mg-Mb}
\end{figure*}

\section{Bayesian analysis for Compact Stars}
\label{sec:bayesian}

Bayesian methods have proven to be a poweful technique for model descrimination and parameter descrimination.
In a primer Bayesian study performed by Steiner et al. \cite{Steiner:2010fz} the luminosity of expanding photospheric radius
extracted for burst sources has been used to constrain a combined mass-radius
relationship. However, this method is problematic, in particular because of the unknown stellar
atmosphere composition, uncertainties in the distance to the
source, the bias of the parabolic M-R constraint with the shape of stellar
sequences in the M-R diagram for typical EoS and last but not least due to unknown
details of the burst mechanism. In this work we do BA as well but we implement different observables which will be used as constraints:
the highest measured mass~\cite{Antoniadis:2013pzd}, a radius
measurement~\cite{Bogdanov:2012md} and a gravitational mass vs. baryonic mass determination by
Podsiadlowski et al. \cite{Podsiadlowski:2005ig}.
These constraints were already included in our earlier Bayesian analyses, e.g., of
Refs.~\cite{Alvarez-Castillo:2014xea,Blaschke:2014via,Ayriyan:2015kit}.
We will describe the Bayesian method and the chosen constraints in the following subsections.

\subsection{Bayesian analysis technique}

We start by defining a vector of free parameters $\overrightarrow{\pi}=\{p,\eta_{4}\}$,
which correspond to all the possible models with or without phase transition
from nuclear to quark matter using the EoS described above. The way
we sample these parameters is
\begin{equation}
\overrightarrow{\pi}_{i}=\left\{ p_{(k)},\eta_{4(l)}\right\} ,\label{pi_vec}
\end{equation}
where $i=0\dots N-1$ with $N=N_{1}\times N_{2}$ such that $i=N_{2}\times k+l$
and $k=0\dots N_{1}-1$, $l=0\dots N_{2}-1$, with $N_{1}$ and $N_{2}$
being the total number of parameters $p_{(k)}$ and $\eta_{4(l)}$,
respectively.
After integration of the TOV equation each EoS model will provide estimations for NS properties that we shall use for Bayesian analysis.
Thus, these results allow us to use different neutron star observations in order to determine the
probability that a given EoS fulfils the observational constraints.
Our goal is to find the set of most probable $\overrightarrow{\pi}_{i}$
matching the above constraints using the BA technique. For initializing
the BA we propose that \textit{a priori} each vector of parameters
$\overrightarrow{\pi}_{i}$ have the same probability, $P\left(\overrightarrow{\pi}_{i}\right)=1/N$,
for all $i$.

\begin{figure*}[!t]
\begin{center}
\begin{tabular}{l|c|c|c}
\hline
Symmetry energy $\rightarrow$&&&\\[-2mm]
&soft & medium & stiff\\[-2mm]
EoS $\downarrow$&&&\\
\hline
&&&\\[-2mm]
DD2F (semi-soft)&
\includegraphics[width=0.25\textwidth]{FirstTask_DD2fm-eps-converted-to} & \includegraphics[width=0.25\textwidth]{FirstTask_DD2f-eps-converted-to} & \includegraphics[width=0.25\textwidth]{FirstTask_DD2fp-eps-converted-to}\\
&&&\\[-2mm]
\hline
&&&\\[-2mm]
DD2 (stiff)&
\includegraphics[width=0.25\textwidth]{FirstTask_DD2m-eps-converted-to} & \includegraphics[width=0.25\textwidth]{FirstTask_DD2-eps-converted-to} & \includegraphics[width=0.25\textwidth]{FirstTask_DD2p-eps-converted-to}\\
&&&\\
\hline
\end{tabular}
\end{center}
\caption{Probabilities without the gravitational mass vs. baryon mass constraint.
The stiffest possible EoS are favored, corresponding to large radii and small gravitational binding.}
\label{First_Lego}
\end{figure*}

\begin{figure*}[!htb]
\begin{center}
\begin{tabular}{l|c|c|c}
\hline
Symmetry energy $\rightarrow$&&&\\[-2mm]
&soft & medium & stiff\\[-2mm]
EoS $\downarrow$&&&\\
\hline
&&&\\[-2mm]
DD2F (semi-soft)&
\includegraphics[width=0.25\textwidth]{SecondTask_DD2fm-eps-converted-to} & \includegraphics[width=0.25\textwidth]{SecondTask_DD2f-eps-converted-to} & \includegraphics[width=0.25\textwidth]{SecondTask_DD2fp-eps-converted-to}\\
&&&\\[-2mm]
\hline
&&&\\[-2mm]
DD2 (stiff)&
\includegraphics[width=0.25\textwidth]{SecondTask_DD2m-eps-converted-to} & \includegraphics[width=0.25\textwidth]{SecondTask_DD2-eps-converted-to} & \includegraphics[width=0.25\textwidth]{SecondTask_DD2p-eps-converted-to}\\
&&&\\
\hline
\end{tabular}
\end{center}
\caption{Probabilities with the gravitational mass vs. baryon mass constraint.
The picture of Fig.~\ref{First_Lego} is reversed: now the soft EoS with small excluded volume parameter $p$
are favored which correspond to stars with small radii and large gravitational binding.}
\label{Second_Lego}
\end{figure*}

\subsection{Mass constraint}

We describe the error for the event $E_{A}$ of a mass measurement
of the high-mass pulsar PSR~J0348+0432~\cite{Antoniadis:2013pzd}
with a normal distribution $\mathcal{N}(\mu_{A},\sigma_{A}^{2})$,
where the mean value of the mass is $\mu_{A}=2.01~\mathrm{M_{\odot}}$
and the variance is $\sigma_{A}=0.04~\mathrm{M_{\odot}}$. Using this
assumption we compute the conditional probability of the event $E_{A}$
(under the condition that the neutron star is described by the EoS
model with the parameters $\overrightarrow{\pi}_{i}$) with
\begin{equation}
P\left(E_{A}\left|\overrightarrow{\pi}_{i}\right.\right)=\Phi(M_{i},\mu_{A},\sigma_{A})~.\label{p_anton}
\end{equation}
Here $M_{i}$ is the maximum mass accessible with the vector $\overrightarrow{\pi}_{i}$
and $\Phi(x,\mu,\sigma)$ is the cumulative distribution function
for the Gaussian distribution
\begin{equation}
\Phi(x,\mu,\sigma)=\frac{1}{2}\left[1+{\rm erf}\left(\frac{x-\mu}{\sqrt{2\sigma^{2}}}\right)\right].\label{Laplas}
\end{equation}

\subsection{Radius constraint}

We consider here a very promising technique to measure radii of neutron
stars that is based on the pulse phase resolved X-ray spectroscopy
which properly accounts for the system geometry of a radio pulsar.
This radius measurement gives $\mu_{B}=15.5~\mathrm{km}$ and $\sigma_{B}=1.5~\mathrm{km}$
for PSR~J0437-4715~\cite{Bogdanov:2012md}.
Moreover, Hambaryan et al. \cite{Hambaryan:2014} have also reported compatible radius
measurements for RXJ 1856.5-3754.

We compute the conditional probability of the event $E_{B}$ that
the measured radius of the neutron star corresponds to the model with
$\overrightarrow{\pi}_{i}$ as
\begin{equation}
P\left(E_{B}\left|\overrightarrow{\pi}_{i}\right.\right)=\Phi(R_{i},\mu_{B},\sigma_{B})~.\label{p_bogdan}
\end{equation}
Here the value $R_{i}$ is the maximum radius for the given vector
$\overrightarrow{\pi}_{i}$.

\subsection{Gravitational mass vs. baryonic mass constraint}

For the selection of the EoS with different symmetry energies we
consider as an observational constraint the properties of the star B in the double pulsar
PSR~J0737-3039(B) \cite{Kramer:2006nb}
Following \cite{Podsiadlowski:2005ig},
the evolution of this object based on the hypothesis that the neutron
star is born in a supernova collapse after electron capture instability of an O-Ne-Mg star.
This method allows us to estimate the mass of the progenitor core, being
approximately the baryon mass of the new-born neutron star.
The measured neutron star gravitational mass is $M_{G}=1.249~M_{\odot}$, with error-bar $\Delta M=\pm 0.001~M_{\odot}$, while from the evolution model the baryon mass is expected to be $\mu_{B}=1.366~M_{\odot}$ with statistical uncertainty $\sigma_{M}=0.003~M_{\odot}$,
see the red boxes in Fig.~\ref{All_Mg-Mb}.
Meanwhile we know a second object of this kind, the low-mass neutron star companion of
PSR J1756-2251 \cite{Ferdman:2014rna}
with $M_{G}=1.249 \pm 0.007~M_{\odot}$ which, if it underwent the same evolutionary history as
PSR~J0737-3039(B) and originated from an O-Ne-Mg star by an electron capture supernova, then it
should have the same baryon mass, which would be rather troublesome as none of the known
neutron star EoS candidates would explain such a large gravitational binding energy,
see the blue boxes in Fig.~\ref{All_Mg-Mb}.
There are two ways out of this dilemma. Either the mass measurement should get corrected upwards
or there is another mechanism to create a low-mass neutron star in a binary system which would work for lower baryon masses, such as the so-called "ultra-stripped supernovae" \cite{Tauris:2015xra}.
Recently, Suwa et al.~\cite{Suwa:2015saa} demonstrated in a simulation the formation of a neutron star with $M_B=1.35~M_\odot$ from such a scenario.
Conversely, also PSR~J0737-3039(B) could be formed this way.
Therefore, we derive from the above discussion the following constraint.
From the two measured neutron star masses discussed above we take the mean value
$M_{G}=1.24~M_{\odot}$, with the error-bar $\Delta M=\pm0.01~M_{\odot}$, and from both alternative  evolution models we take the mean baryon mass to be $\mu_{B}=1.36~M_{\odot}$ with the error-bar $\Delta M=\pm0.01~M_{\odot}$ (see the grey box in Fig.~\ref{All_Mg-Mb}; the statistical uncertainty is taken to be $\sigma_{M} = \Delta M / 3 = 0.0033~M_{\odot}$.

We compute the conditional probability of the event $E_{P}$ that
the assumed baryon mass is reproducible in the model with parameters $\overrightarrow{\pi}_{i}$
given by normal distribution with mean value $\mu_{B}$. So, using the model
dependance between the masses described by $M_{B}=M_{B}(M_{G};\overrightarrow{\pi}_{i})$
the probability to fulfill the constraint can be calculated from the normal distribution function for that
$ M_{B}$ values, which are in the area corresponding to the observed gravitational mass range
$M_{G}\pm\Delta M$:
\begin{eqnarray}
P\left(E_{P}\left|\overrightarrow{\pi}_{i}\right.\right) &=& \Phi(M_{B}(M_{G}+\Delta M;\overrightarrow{\pi}_{i}),\mu_{B},\sigma_{M}) \nonumber\\
&-& \Phi(M_{B}(M_{G}-\Delta M;\overrightarrow{\pi}_{i}),\mu_{B},\sigma_{M}).
\end{eqnarray}
In the plots of results we show the $1\sigma$-range of $ M_{B}$ values as a box on the $M_{G}\otimes M_{B}$ plane.

\subsection{Fictitious radius measurement constraints}

To find out the best suggestion for future observations, which will
be powerful for the model discrimination we employ fictitious
radius measurement constraints. For our "experiment'' we choose
the two known objects with well measured high masses:
PSR~J$0348+0432$~\cite{Antoniadis:2013pzd}
and
PSR~J$1614-2230$~\cite{Demorest:2010bx}.
We assume that the possible radii of these
objects will be different and in the resolution range $\Delta R$.
The masses of the objects are measured $M_{G_{A}}=2.01~M_{\odot}$,
with error-bar $\Delta M_{G_{A}}=\pm0.04~M_{\odot}$ and $M_{G_{D}}=1.94~M_{\odot}$,
with error-bar $\Delta M_{G_{D}}=\pm0.04~M_{\odot}$ correspondingly
for the PSR~J0348+0432 and PSR~J1614-2230 pulsars.
The fictitious radii we assumed to be $R_{A}$ and $R_{D}$ with
statistical uncertainty $\sigma_{R_{A}}$ and $\sigma_{R_{D}}$ correspondingly.

We compute the conditional probability of the event $E_{F}$  for fixed model with parameters $\overrightarrow{\pi}_{i}$ under the assumption that
the "measured" radii should be producible with normal distribution with mean values
$R_{A}$ and $R_{D}$. Each
model defines dependence of the radii on masses for all
possible stable branches (families of neutron stars) given by $R_{\alpha}=R_{\alpha}(M_{G_{\alpha}};\overrightarrow{\pi}_{i})$
functions.
Here the index $\alpha$ stands for the definition of the pulsar.
The probability to fulfil the constraint will correspond to the area where the configurations
have values of radii predicted from the model when the masses are in the interval of the observational mass range $M_{G_{j}}\pm\Delta M_{j}$:
\begin{eqnarray}
P\left(E_{F_{\alpha}}\left|\overrightarrow{\pi}_{i}\right.\right) &=& \Phi\left(R_{\alpha}(M_{G_{\alpha}}+\Delta M_{\alpha};\overrightarrow{\pi}_{i}),\mu_{R_{\alpha}},\sigma_{R_{\alpha}}\right) \nonumber\\
&-& \Phi\left(R_{\alpha}(M_{G_{j}}-\Delta M_{\alpha};\overrightarrow{\pi}_{i}),\mu_{R_{\alpha}},\sigma_{R_{\alpha}}\right)
\label{p_bogdan-2-1}
\end{eqnarray}
Because in some cases (mainly for the hybrid stars) the $R_{\alpha}(M_{G_{\alpha}};\overrightarrow{\pi}_{i})$
can be not uniquely defined functions, we have excluded possible overlaps of
the boxes of the radius probability
regions on the $M_{G_{\alpha}}\otimes R_{\alpha}$ plane to avoid the double counting.

\subsection{Calculation of \textit{a posteriori} probabilities}

It is important to note that these measurements are independent of
each other. This means that we can compute the complete conditional
probability of an event $E$ given $\overrightarrow{\pi}_{i}$ that
corresponds to the product of the conditional probabilities of all
measurements, in our case resulting from the constraints on maximum mass $E_{A}$,
on maximum radii $E_{B}$, from gravitational mass - baryon mass relation  $E_{P}$ and for
fictitious radii measurements for two objects $E_{F_A}$ and $E_{F_D}$.
\begin{equation}
P\left(E\left|\overrightarrow{\pi}_{i}\right.\right)= \prod_{\alpha} P\left(E_{\alpha}\left|\overrightarrow{\pi}_{i}\right.\right).
\label{p_event}
\end{equation}
Thus, we can derive the probability of the measurement of an EoS represented
by a vector of parameters $\overrightarrow{\pi}_{i}$ using Bayes' theorem
\begin{equation}
P\left(\overrightarrow{\pi}_{i}\left|E\right.\right)=\frac{P\left(E\left|\overrightarrow{\pi}_{i}\right.\right)P\left(\overrightarrow{\pi}_{i}\right)}{\sum\limits _{j=0}^{N-1}P\left(E\left|\overrightarrow{\pi}_{j}\right.\right)P\left(\overrightarrow{\pi}_{j}\right)}.\label{pi_apost}
\end{equation}
In this article we consider BA for three different groups of constrains (cases) as follows
\begin{eqnarray*}

       {\rm Case~ 1:~}  \alpha&=&{\rm A, B;} \\
       {\rm Case~ 2:~}  \alpha&=&{\rm A, B, P; }\\
       {\rm Case~ 3:~ } \alpha&=&{\rm F_A, F_D. }
\end{eqnarray*}

For the Case~3 we have chosen different sets of fictitious radius measurements (see Fig.~\ref{Prob_Fic}),
assuming that the more massive object PSR~J0348+0432~\cite{Antoniadis:2013pzd} should have the smaller radius and, therefore, PSR~J1614-2230~\cite{Demorest:2010bx} has the larger fictitious radius.
Anyway, we also consider one case (last row of Fig.~\ref{Prob_Fic}) where the less massive pulsar has the lower radius.

\iffalse
\begin{figure}[htb]
\includegraphics[width=0.45\textwidth]{HybridEoS_p-e}
\caption{Family of hybrid EoS (black lines) with a first order phase transition
between hadronic matter described by the excluded volume corrected
DD2 relativistic meanfield EoS and quark matter described by a NJL
model with higher order (8-quark) interactions that provide the important
stiffening at high densities due to a large coupling strength $\eta_{4}$
in the vector current channel, see \cite{Benic:2014jia}. The optimal
EoS (bold red line) corresponds to an available volume parameter $\nu=33$
and $\eta_{4}=5$. The limits of the $1\sigma$ range are indicated
by bold green lines.}
\label{fig:p-e}
\end{figure}
\fi

\begin{figure*}[!htpb]
\begin{center}
\begin{tabular}{l|c|c|c}
\hline
Radius error $\sigma \to$ &&&\\[-2mm]
&1.5 km& 1.0 km& 0.5 km\\[-2mm]
$R_A , R_D$&&&\\
\hline
&&&\\[-2mm]
11 km, 13 km&
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=11_R_D=13_sigma_D=1dot5-eps-converted-to} &
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=11_R_D=13_sigma_D=1dot0-eps-converted-to} &
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=11_R_D=13_sigma_D=0dot5-eps-converted-to} \\
&&&\\[-2mm]
\hline
&&&\\ [-2mm]
11 km, 15 km&
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=11_R_D=15_sigma_D=1dot5-eps-converted-to} &
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=11_R_D=15_sigma_D=1dot0-eps-converted-to} &
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=11_R_D=15_sigma_D=0dot5-eps-converted-to} \\
&&&\\[-2mm]
\hline
&&&\\[-2mm]
13 km, 13 km&
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=13_R_D=15_sigma_D=1dot5-eps-converted-to} &
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=13_R_D=15_sigma_D=1dot0-eps-converted-to} &
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=13_R_D=15_sigma_D=0dot5-eps-converted-to}\\
&&&\\[-2mm]
\hline
&&&\\[-2mm]
15 km, 11 km&
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=15_R_D=11_sigma_D=1dot5-eps-converted-to} &
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=15_R_D=11_sigma_D=1dot0-eps-converted-to} &
\includegraphics[width=0.25\textwidth]{ThirdTask_DD2fm_R_A=15_R_D=11_sigma_D=0dot5-eps-converted-to}\\
&&&\\
\hline
\end{tabular}
\end{center}
\caption{\textit{Probabilities for an extra fictitious radius measurement}.
$R_A$ and $R_D$ denote NS with masses corresponding to the ones measured by Antoniadis et al. and by Demorest et al., resp.}
\label{Prob_Fic}
\end{figure*}

\section{Results}
\label{sec:results}

In order to cover a relevant set of possible hybrid compact star EoS in the pressure-energy density plane
we have varied the excluded parameter in the range $p= 0,5, \dots, 80$
as well as the 8-quark vector current coupling in the range $\eta_4=0,1,2,\dots, 30$.

The hybrid EoS resulting from Maxwell constructions between all combinations of hadronic and quark
matter EoS in this two-dimensional parameter space is shown in Fig.~\ref{All_M-R} together with the corresponding NS sequences.

Note that compact star sequences in the mass-radius plane which have a vertical branch correspond to hadronic stars and an almost horizontal branch corresponds to
hybrid stars with a quark matter core.
The parameters are chosen in such a range that their variation entails that the hybrid star branch
becomes disconnected from the hadronic one due to the appearance of a set of unstable configurations.
This characterizes the appearance of high-mass twin stars and happens in particular when varying the the excluded volume value in all of these models.
We have already observed in \cite{Benic:2014jia} that increasing the $\eta_4$ parameter for a fixed $p$ value corresponds to an increase of the maximum mass,
while the difference between the radius of the hybrid star and its hadronic twin decreases.
This general behaviour is preserved for any fixed $p$.

The general behavior of the symmetry energy in each class of EoS is to shift radius values while preserving the maximum mass for each sequence. Even though  the general result
is that the DD2F class presents lower average radii NS than the DD2, the symmetry energy and the excluded volume can modify the average radius values.
The DD2+ class is therefore
the stiffest EoS leading to larger radii whereas the DD2F- shows the lowest radii by being the softest EoS class.

{\it A posteriori} probabilities of identification for these twin EoS are shown in figures ~\ref{First_Lego} and \ref{Second_Lego}.
The models with higher probabilities correspond to the ones that predict
large radii and are associated to large excluded volume parameters $p$.
The optimal value of the vector coupling strength is $\eta_4=5$.
We note that the family of hybrid EoS accessible within the given two-dimensional parameter space
describes sequences of compact stars that have a hadronic branch and a hybrid star branch.
The latter appears connected to the former for not too large excluded volumina.
For sufficiently large excluded volume parameters the compact stars on the hadronic branch have radii
exceeding $14$ km and the phase transition proceeds with a sufficiently large jump in the energy density
so that the hybrid star sequence gets disconnected from the hadronic one, forming a so-called "third family".
The observation of a corresponding (almost) horizontal branch in the $M-R$ diagram would be a clear signal
for a strong first order phase transition in the high-density neutron star EoS.
Using Bayesian analysis technique we have demonstrated that the measurement of significantly different radii
for two high-mass compact stars (like the $2~M_\odot$ objects we already know)  would have sufficient discriminating power to favor a hybrid EoS over a purely hadronic one.

\section{Conclusions}
\label{sec:conclusion}

We summarize our conclusions from this study of a set of six classes of two-parameter hybrid EoS for compact star interiors:
\begin{enumerate}
\item The most probable models exhibit high-mass twin star configurations with quite distinguishable radii,
differing by about 2 km.
\item The region of the most probable models in the two-dimensional parameter space is sufficiently narrow, covering the ranges $40<p < 80$ and $3<\eta_4< 7$.
\item The most probable models have a large excluded volume parameter $p> 40$ and a
not too large vector coupling strength $\eta_4\sim 5$.
\item The existence of the horizontal branch signals a strong first order deconfinement phase transition and is a feature accessible to verification by observation.
To that end, at least for two high-mass pulsars with masses $\sim 2~M_\odot$ (like PSR J1614-2230 and PSR J0348+0432) the radii should be measured to sufficient accuracy and turn out to be significantly different.
\item Fig.~\ref{Prob_Fic} shows that there are strong peaks of probabilities in the parameter space, even if fictitious radius measurements have quite large uncertainties with
$\sigma_{\rm R_A} = \sigma_{\rm R_D} = 1.5$ km, where the ''measurements'' have overlap of $5\sigma$ regions. It means that even quite uncertain measurements of radii for massive pulsars could have a strong selective power of EoS models. Cf. cases 1) and 2) which demonstrate that knowing only either mass or radius of an object results in a constraint which is not very robust against a possible third observational constraint, like the gravitational binding energy.
\item When fictitious radius measurements yield the smaller radius for the object with the slightly smaller mass
(see the bottom line of Fig.~\ref{Prob_Fic}), then the most probable value of the excluded volume parameter is lowered from $p= 80$ to the moderate $p\sim 50$, while the optimal stiffness of the quark matter remains unchanged, $\eta_4\sim 5$.
\end{enumerate}
The next two steps in the development of the approach are devoted to an improvement of the variability of the dense matter EoS within a two-dimensional parameter space embodying, e.g., also the purely hadronic case without a phase transition and to mimicking the occurrence of structures (so-called "pasta phases") in the phase transition region \cite{Yasutake:2014oxa,Alvarez-Castillo:2014dva}.

\subsection*{Acknowledgements}
We acknowledge the partial support by the Helmholtz Association (HGF) through the Nuclear Astrophysics Virtual Institute (VH-VI-417) and by the COST Action MP 1304 "NewCompStar" for our international
networking activities in preparing this article.
This work received support from the Polish NCN under grant No. UMO-2014/13/ B/ST9/02621.
D.E.A-C. and H.G. are grateful for support from the programme for exchange between JINR Dubna and
Polish Institutes (Bogoliubov-Infeld programme).
\\
D.E.A-\-C. and S.T. received support  form the Heisenberg-Landau programme for scientist exchange between JINR Dubna and German Institutes.
S. B. acknowledges partial support by the Croatian Science Foundation under Project No. 8799.
D.B. was supported in part by the Hessian LOEWE initiative through HIC for FAIR.

redpajama_set_name: RedPajamaArXiv


Christmas Party 2012, we certainly had fun that day!
A selection of our Christmas celebrations from making the Christmas Cake to Christmas Party, Christmas Day and New Year celebrations.
We had another wonderful party - some wierd and wonderful costumes were worn.
Our Olympic Games - everyone joined in, there was a medal ceremony (everyone won something). Had a really enjoyable afternoon.


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My son often have fits of anger and rage. He already threatened to kill me or whished for me to die. He is 24 and I am very concerned that he will harm me or his girlfriend. I have seen him pushing her but he is always sorry later and promisses never to hit her. How do I look for help before it is to late. I have already suggested he sees a thearapist but he refuses.
The basic problem, usually, with someone like this who causes severe problems and concerns to other people and couldn't care about it himself, is that it's impossible to help them unless the agre and sincerely participate in proper expert help. Any psychiatrist or good clinical psychologist ought to be able to be of some help to your son, if he agrees that he has a problem and truly wants to get rid of the problem. But that sounds unlikely.
Until something or someone else convinces him that this is the only good alternative for him, you need to take steps to protect yourself and to discourage him from being violent. A lawyer can advise, that it is possible to obtain a court order forbiding him to harass or threaten you, and he would go to jail if he broke such a court order. Threatening to kill someone is a crime, so you can also make a formal complaint about it to the police, so that his threats are on record, and they can visit him and make it clear that they'll be back if he does get physically violent. Abusers usually claim to feel soprry ( but thyey're never sorry enough to stop doing it again, and again ).
Whahahahaha k00s, is ook net jy wat so sal dink!
Maybe there could be some truth in what k00s says ... maybe your son does need shock therapy (it could be that only if you give him some of his own treatment he will be shocked to sanity).


text:
Trump administration asks Supreme Court to allow federal executions to go forward
A federal appeals court rejected an emergency bid from the Trump administration to move forward next week with the first federal execution in nearly 17 years, setting up a potential showdown at the Supreme Court. By David Shortell and Ariane de Vogue, CNN
(CNN) -- The Trump administration asked the Supreme Court on Monday to reverse a lower court ruling and allow a series of federal executions to begin, starting on December 9.
The move comes after a federal appeals court rejected an emergency bid from the administration to move forward next week with the first federal execution in nearly 17 years, setting up the potential showdown at the Supreme Court.
Three judges on the US Court of Appeals for the District of Columbia Circuit came down Monday against a request by the Justice Department to bypass a lower court ruling that paused the series of executions.
Attorney General William Barr revived the use of the federal death penalty in July after a nearly two-decade hiatus in a move that underscored the stark law and order philosophy of the Trump administration.
Daniel Lewis Lee, a white supremacist convicted of killing a family in the 1990s, was days away from execution when the lower court ruled that the lethal injection protocol planned by the Justice Department may be incompatible with federal law, putting on hold the plan to put Lee and three other death row inmates to death.
In a filing last month, the Justice Department appealed the decision to block the executions, and asked the appeals court to pause or remove an injunction placed by DC District Judge Tanya Chutkan, with prosecutors warning that they planned to take their appeal to the Supreme Court if they didn't get what they wanted.
A Bureau of Prisons official wrote in a filing that preparations for the executions at the death row facility in Terre Haute, Indiana, had been exhaustive -- including the assignment of 200 security personnel and the advance preparation of meals for 2,600 inmates -- and any delay in the procedure would be costly.
But attorneys for the inmates last week accused the Justice Department of trying to "side-step judicial review" by seeking a way around the injunction. If the appeals court were to stay or vacate that injunction, it could allow for the executions to take place, even before a full appeal on the merits of the injunction could take place.
If the Supreme Court also declines to put the injunction on hold, the executions will not occur until the courts consider the underlying merits of the appeals case.
The three appeals court judges who ruled Monday were Neomi Rao, a recent Trump appointee, Judith Rogers, a Clinton appointee, and Thomas Griffith, a George W. Bush appointee.
There was no dissent noted in the short unsigned order.

redpajama_set_name: RedPajamaCommonCrawl


text:
Bharti Airtel Hopes for Balanced Approach on Adjusted Gross Income (AGR) Issue
By Morton L. Richardson on October 30, 2019 Gross revenue
Airtel said the SC's decision comes at a time when the industry faces serious financial problems.
Bharti Airtel on Wednesday expressed hope that the government will take a "balanced approach" on the AGR issue in order to protect the long-term interests of the ailing telecommunications industry.
Airtel senior management, during a call to investors on Wednesday, said the company hopes the government will fairly address the issue of Adjusted Gross Income (AGR) for the viability of the industry.
"It is indeed in the best interest of all parties to formulate a constructive mechanism to ensure that large debits, including this one, can be resolved in a fair manner," said Airtel CFO Badal Bagri , during the call to investors.
"We are also evaluating the judgment in detail and its implications," he said, adding that the case has been the subject of litigation for a long time, there is room for reflection on aspects of the penalty. and interest.
Mr Bagri said it was difficult to say who was going to take a final call on this, but the DoT (Department of Telecommunications) will calculate the amount.
It comes a day after a group of secretaries was formed to suggest ways to ease financial stress in the telecommunications industry. Airtel said the Supreme Court ruling comes at a time when the industry faces serious financial problems.
The company released its operating highlights for the quarter ended September 2019 on Tuesday, but postponed profits due to SC's AGR order.
"We are evaluating the judgment in detail and its overall implication and therefore ask that we cannot comment much on it," Bagri said.
Market share is a strong performance parameter. But the underlying drivers are more important, namely reducing churn and network upgrade where spectrum redevelopment and investment, as well as shutting down 3G networks.
Bharti Airtel Chairman Sunil Mittal and his brother Rajan Mittal met Telecom Minister Ravi Shankar Prasad on Monday in this regard. Bharti Airtel faces a liability of around Rs 42,000 crore after including license fees and spectrum usage fees, while Vodafone-Idea could have to pay around Rs 40,000 crore. But the latest official figures on which the demand will be raised are expected.
A committee of secretaries has been set up to work out a financial bailout that could include lower spectrum fees and to set a floor price for voice and data.
The panel, chaired by Cabinet Secretary Rajiv Guba, was tasked with examining "all aspects" of "financial stress" facing service providers and proposing measures to alleviate them.
adjusted gross gross income long term


text:
National and International News
UAPD Investigates Report of Rape in Founders Hall
UA Staff Member Reports Harassment by Supervisor to UAPD
Senior Erin Freier posts a score of 9.875 during her uneven bars routine at the NCAA Regionals on April 2.
Courtesy of Bill Adams
editor's pick featured top story
Gymbacks Finish Third at Regionals
Lauren Krakau
The Arkansas Razorbacks gymnastics team competed in the 2016 NCAA Regionals on April 2 at the Carver-Hawkeye Arena in Iowa City, Iowa, and placed third in the six-team regional event.
Although the Gymbacks did not advance to the NCAA Regionals Session II, junior Amanda Wellick qualified for Nationals with a score of 39.350. Among all competitors, Wellick finished fifth, and was the second-highest all-arounder who was not on an advancing team.
"Although we had some uncharacteristic mistakes early on, we fought all the way through the night," Wellick said in a press release. "After our first two rotations, we could have put our heads down and just done our routines, but we didn't. We came back out and fought for every little tenth we could get the rest of the way. We learned a lot about ourselves tonight."
Seniors Sydnie Dillard and Stephani Canizaro started off the night's first rotation with back-to-back scores of 9.800s for Arkansas. Dillard has never missed a floor and balance beam rotation, and she made her 50th career start as a Razorback at this year's Regionals.
After Dillard and Canizaro's rotation, freshman Sydney McGlone scored a 9.825 with her double layout, and Wellick tied for third among all competitors in the event with her team-high score of 9.850, which lead the Gymbacks to an opening score of 49.000.
Not only did Wellick stand out during the first rotation, she also rose to the occasion and tied for second on the vault with a score of 9.875.
Wellick was in the lead up until the sixth rotation when the Sooners' Chayse Capps, with a score of 9.900, and Haley Scaman, with the same score as Wellick (9.875), took over Arkansas' lead. Sophomore Gymback Braie Speed also vaulted a score of 9.900.
At the uneven bars lineup, Canizaro notched a career-high score of 9.875 for the sixth time of her career. Erin Freier added to Arkansas' uneven bar score of 49.100, with her matching score of Canizaro's. Braie Speed was in the spotlight again, as she scored her second 9.800 of the night, leading her into the No. 5 spot in the uneven bar lineup.
The final event for the Razorbacks at the 2016 NCAA Iowa City Regional was the balance beam. Dillard gave the Razorbacks to a good start with her score of 9.800 in her final performance. Paige Zaziski scored a 9.850, reaching her mark for the fourth time this season. Wellick also scored a 9.850, and it was her seventh time to score that or higher at this event.
The Arkansas Razorbacks finished the night with a final score of 49.025 on their last event, the beam. At the Cancun Classic, the Gymbacks scored at least a 49.000 on beam at dozen of meets since the beginning of the season.
Although the Razorbacks did not get to proceed to Session II of Regionals, they did finish ahead of host No. 19 Iowa (195.450), Central Michigan (194.675) and Kent State (194.525) in the meet overall.
Wellick qualified for Nationals her freshman year and advanced to Birmingham, Alabama, in 2014.
"It's really a bittersweet thing to make Nationals as an individual," Wellick said in the release. "I wish so badly I could go with my team and be fighting for a top spot with them by my side. However, I'm excited to be able to represent my coaches, my teammates and the University of Arkansas."
Wellick's next move is to compete alongside one of the final 12 teams at the NCAA Nationals on April 15 in Fort Worth, Texas.
uatrav.com
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Email: traveler@uark.edu
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Privacy, Technology and Cybersecurity Issues in Tech Transactions
Lyndsay A. Wasser*
Robert C. Piasentin
Kristen Pennington
Yue Fei
December 6, 2022 Business Law Bulletin 8 minute read
Lyndsay A. Wasser*, Robert C. Piasentin, Kristen Pennington, Yue Fei
With few exceptions, software and information technology systems (collectively, "IT") are now integral to most businesses. As a result, an increasing number of transactions involve technology companies ("Tech Transactions"), whether they are large IT providers, "tech start-ups" that have attracted the attention of buyers or investors, or even companies that traditionally focused on selling physical products but now use IT to generate revenue through the collection, analysis and/or monetization of data.
As technology permeates more businesses, and the collection, use, sharing and other processing of data becomes increasingly pervasive, privacy, technology and cybersecurity have become areas of significant potential liability in Canada. For example:
Organizations can face administrative monetary penalties ("AMPs") of up to $10 million under the Competition Act for false or misleading privacy representations;[1]
Effective September 2023, Quebec's Act respecting the protection of personal information in the private sector (the "Quebec Act") will provide for AMPs for non-compliant organizations up to the greater of $10 million or 2% of worldwide turnover for the preceding fiscal year, and fines for certain offences up to the greater of $25 million or 4% of worldwide turnover;
The federal government has tabled the Consumer Privacy Protection Act, which (if passed) would substantially replace the current Personal Information Protection and Electronic Documents Act ("PIPEDA"), and provide for AMPs up to the greater of $10 million or 3% of worldwide turnover for the preceding fiscal year, and fines for certain indictable offences up to the greater of $25 million or 5% of worldwide turnover; and
Data breaches routinely give rise to expensive class action litigation, and reputational harm caused by the erosion of customers' or business partners' trust and/or adverse media attention.
Accordingly, it is important for potential purchasers in Tech Transactions to fully evaluate the target company's privacy, technology and cybersecurity compliance in the diligence phase of the transaction, and for each of the parties to ensure that risks and liabilities are appropriately allocated in the purchase agreement.
Organizations seeking to purchase a technology-focused business should thoroughly canvas the target's history and current practices and procedures with respect to privacy, technology and cybersecurity. Poor personal information ("PI") handling practices, outdated or unsupported IT, or inadequate information security controls may require a significant investment to bring the target into compliance with relevant laws, and give rise to the aforementioned financial and reputational risks.
The documents and information requested in the diligence process will vary depending upon the circumstances. Often, technology diligence may be performed by the purchaser's technical personnel or external consultants while the corresponding legal review is conducted. Examples of materials that may be requested in connection with privacy, technology and cybersecurity diligence include:
A list of all IT owned or used by the target, identifying proprietary and third party IT, and copies of licenses and other agreements relating to the target's use of third party IT;
A description of the PI the target collects, holds or otherwise processes in the course of its business;
Copies of privacy, data security and IT policies and procedures, including (without limitation) breach response and disaster recovery plans, vendor and service provider selection and management procedures, and cybersecurity governance and risk procedures;
Information about privacy and cybersecurity audits, including frequency, copies of recent reports, and remedial actions taken to address any identified issues;
Information relating to, or measuring, the effectiveness, security, availability, or integrity of the target's IT;
Information about the target's process for obtaining, recording and giving effect to consents (and withdrawals of such consents), including copies of the target's privacy notices and consent forms;
Information about the security measures used by the target to protect IT and safeguard PI;
Information respecting employee training on privacy and cybersecurity compliance, and copies of any relevant agreements with personnel;
Information about any significant or recent privacy or cybersecurity breaches ("Breaches");
Information on any actual or threatened claims, complaints, litigation or regulatory action related to privacy or data security;
Copies of all contracts containing privacy and data protection terms (e.g., data sharing agreements or relevant provisions in service agreements); and
Copies of any cybersecurity insurance policies.
Overall, through the diligence process, the goal is to gain an understanding of: (1) the target's process for collecting, using, storing, protecting and disclosing personal and other sensitive information, and (2) the performance levels, adequacy, suitability and scalability of the target's IT in view of the target's business and business plans. Such understanding will allow the purchaser to evaluate legal compliance and identify risks and potential liabilities.
While it may be necessary for certain PI to be disclosed by the target to the purchaser during the due diligence process, organizations must consider the potential limits on doing so.
For example, pursuant to PIPEDA, PI can only be disclosed in the context of a prospective business transaction without the knowledge and consent of affected individuals if such information is necessary to determine whether to proceed with the transaction, and, if the determination is made to proceed, to complete it.[2] Similar restrictions exist under private sector privacy legislation in Alberta[3], British Columbia[4] and Quebec[5] (the "Provincial Legislation").
Therefore, broad and indiscriminate requests for and disclosure of PI in the diligence process are not permitted under Canadian privacy laws. Rather, the parties should exchange the minimum amount of PI that is required in the circumstances. For example, if aggregate statistics would provide sufficient information to the purchaser, information about identifiable individuals should not be disclosed.
PIPEDA and the Provincial Legislation[6] also contain specific requirements for the parties to enter into an agreement when PI will be disclosed in the due diligence process. For example, under PIPEDA[7], parties to a prospective business transaction may use and disclose PI without the knowledge or consent of individuals if they have entered into an agreement that requires the recipient: (i) to use and disclose the PI solely for purposes related to the transaction, (ii) to protect the PI by security safeguards appropriate to the sensitivity of the PI, and (iii) if the transaction does not proceed, to return or destroy the PI within a reasonable time. In practice, these terms can be incorporated into a broader non-disclosure or confidentiality agreement that the parties sign at the outset of the due diligence process.
There are a number of privacy, technology and cybersecurity issues that may need to be addressed in a purchase agreement (the "Agreement"). For example, the purchaser may want to include representations and warranties ("Reps & Warranties") addressing the following:
Compliance with applicable laws and the target's own privacy, information technology and cybersecurity policies and procedures, and confirmation that such policies, procedures, and practices meet or exceed industry standards;
Compliance with all privacy, data protection and cybersecurity requirements under contracts with third parties;
Sufficiency of IT owned or used by the target in meeting its data processing and other computing needs;
Training of employees on privacy and data security, and that employees are subject to appropriate contractual obligations;
Accuracy of the target's external-facing privacy policies, notices and representations;
Sufficiency of data security controls, including that the organizational, technological and physical security measures are reasonable in relation to the sensitivity of the PI processed by the target; and
Disclosure of all Breaches, as well as malfunctions, defects, technical concerns and failures related to IT owned or used by the target, and confirmation that all of the foregoing have been remedied.
From the target's perspective, it may be necessary to limit or qualify some Reps & Warranties, by including materiality thresholds or adding appropriate knowledge qualifiers. The target will need to carefully consider what Reps & Warranties can realistically be provided, without risking exposure to potentially significant liability if a pre-closing Breach is discovered after completion of the transaction. Also, the target will need to ensure it is familiar with relevant legal requirements and all IT that it owns or uses before making certain Reps & Warranties.
Other issues that may need to be considered in connection with the Agreement include:
Purchase price adjustments and holdbacks – A purchase price adjustment and/or holdback may be warranted if due diligence identifies significant risks or vulnerabilities that may impact the target's value, and: (a) substantial resources will be required to bring the target into compliance with applicable laws or to fix outdated or compromised IT; or (b) the target has experienced a Breach that has not yet resulted in litigation or other liability, but applicable limitation periods have not yet expired.
Indemnities – Although often covered by general indemnities, specific privacy and cybersecurity indemnities may be warranted in some cases. For example, stand-alone indemnities may be necessary if specific concerns are identified in the due diligence process, or if: (a) the duration of general indemnities is not long enough to take into account the typical delay in identifying Breaches; or (b) the cap on general indemnities is too low to adequately cover the risk of a major Breach.
To decrease the chances of future disputes regarding any holdbacks or indemnities included in the Agreement, it is prudent for the parties to include specific mechanisms for the purchaser to make a claim against them, including provisions addressing how damages will be calculated and by whom.
Closing and Beyond
After the Tech Transaction is completed, the purchaser may want to consider whether the existing IT is sufficient to accomplish its plans for the purchased business. Any deficiencies regarding IT discovered during the due diligence process should be addressed promptly to align with the purchaser's plans for the business.
With respect to the post-closing processing of PI collected by the business pre-closing, statutory requirements must be taken into account. For example, under PIPEDA, the parties can only use and disclose PI that was disclosed in connection with the transaction without obtaining consent from affected individuals, if:[8]
The PI is necessary for carrying on the business or activity that was the object of the transaction; and
One of the parties notifies individuals, within a reasonable time after the transaction is completed, that the transaction has been completed and that their PI has been disclosed.
Similar obligations exist under the Provincial Legislation.[9] Accordingly, the purchaser must not use PI obtained by the target prior to the transaction for purposes other than those permitted by applicable law and covered by existing consents (where applicable). In addition, as outlined previously, PIPEDA requires that an agreement between the parties specifically provide that they will give effect to any withdrawal of consent after individuals are notified that their PI has been disclosed in connection with the transaction.
The legal framework around privacy, data protection, technology and cybersecurity is complex, and the common law is rapidly developing. Although these are evolving areas, it is clear that poor PI handling practices and mismanaged IT can have a significant impact on a business, and also expose it to material costs and liabilities. Therefore, parties to Tech Transactions should consider and address these issues before, on and after closing of the deal.
[1] See seminal 2020 case at: https://decisions.ct-tc.gc.ca/ct-tc/cdo/en/item/471812/index.do.
[2] PIPEDA s. 7.2(1)(b). Note: Section 7.2(1) of PIPEDA does not apply to a business transaction of which the primary purpose or result is the purchase, sale or other acquisition or disposition, or lease, of PI.
[3] Personal Information Protection Act (Alberta) ("Alberta PIPA") s. 22(3)(a)(ii). Note: Section 22 of Alberta PIPA does not apply to a business transaction where the primary purpose, objective or result of the transaction is the purchase, sale, lease, transfer, disposal or disclosure of PI.
[4] Personal Information Protection Act (British Columbia) ("B.C. PIPA") s. 20(2)(a). Note: Section 20 of B.C. PIPA does not authorize an organization to disclose PI to a party or prospective party for purposes of a business transaction that does not involve substantial assets of the organization other than this PI.
[5] Effective September 2023, s. 18.4 of the Quebec Act will provided that: "Where the communication of personal information is necessary for concluding a commercial transaction to which a person carrying on an enterprise intends to be a party, the person may communicate such information, without the consent of the person concerned, to the other party to the transaction." (emphasis added).
[6] Alberta PIPA s. 22(3)(a)(i); B.C. PIPA s. 20(1)(b). Effective September 2023, s. 18.4 of the Quebec Act will require that the agreement must stipulate, among other things, that the recipient of the personal information undertakes: "(1) to use the information only for concluding the commercial transaction; (2) not to communicate the information without the consent of the person concerned, unless authorized to do so by this Act; (3) to take the measures required to protect the confidentiality of the information; and (4) to destroy the information if the commercial transaction is not concluded or if using the information is no longer necessary for concluding the commercial transaction."
[7] PIPEDA s. 7.2(1)(a). Note: Section 7.2(2) of PIPEDA does not apply to a business transaction of which the primary purpose or result is the purchase, sale or other acquisition or disposition, or lease, of PI.
[8] PIPEDA s. 7.2(2).
[9] Alberta PIPA s. 22(3)(b); B.C. PIPA s. 20(3). Effective September 2023, s. 18.4 of the Quebec Act will provide that: "[w]here the commercial transaction has been concluded and the other party wishes to continue using the information or to communicate it, that party may use or communicate it only in accordance with this Act. Within a reasonable time after the commercial transaction is concluded, that party must notify the person concerned that it now holds personal information concerning him because of the transaction."
by Lyndsay Wasser, Robert Piasentin, Kristen Pennington, and Yue Fei
A Cautionary Note
The foregoing provides only an overview and does not constitute legal advice. Readers are cautioned against making any decisions based on this material alone. Rather, specific legal advice should be obtained.
© McMillan LLP 2022
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