Here is part 10 of our 12-section bonanza – startup funding and crazy valuations.
Clearly, 2015 was a huge year for M&A and financing in the travel sector. Cash-rich acquirers moved to consolidate growth categories, and the tight IPO market drove record late-stage private growth rounds. There was talk of unicorns.
Early indications, however, are that 2016 may be less rosy.
The early-stage venture capital market at large will pull back in 2016. Well-funded breakout companies will continue to attract late stage financing as private equity firms continue to move into traditional mid- and late-stage VC deals; but it will be tough sledding for seed funded startups.
The bar to Series A has moved substantially higher in the past six months, and with a glut of angel-backed travel plays, VCs can afford to be choosy.
What does this mean for good teams with product-market fit who have yet to hit escape velocity?
The sense I get is that there are two paths.
One approach I recommend for startups that have some traction and a unique product, but no magic growth hack emergent, is to stay lean, focus on one or two sub-markets or enterprise deals as proof points, raise angel money as needed in 12-month tranches, and grind until one of your bets pays off.
In this scenario, the prudent CEO will be working the phones with Wall Street analysts, reading the filings of likely acquirers, and honing their positioning to fit gaps in existing solutions to put a floor on their deals as potential plug-ins should they not break out.
The alternative, as always, is to shoot the moon on a truly transformative idea.
In this case, though, a CEO should think like an investor – find out (spend money) as quickly as possible if your idea has market-shifting power, and kill it and move on if not.
If you have a "tweener" deal, see option one, or dump it.
Running a travel startup is challenging enough without what I believe is an inexplicable and, more often than not, inapplicable fixation on being a unicorn.
It seems as if every venture-capital-seeking travel startup believes it will be a unicorn based on its "conservative" estimates for growth.
As a skeptical investor, I would rather that you, as a startup founder, let your proprietary business model, traction, revenue and "look-what-we-achieved-in-no-time-with-limited-resources" execution overwhelmingly make the case for you.
Your travel startup may very well be a unicorn in a future year. But for an early-stage startup, you need to focus on the one ahead.
There are too many travel startups, business models, customer types, and markets around the world to give universal one-size-fits-all advice.
But here is my advice, after vetting a lot of travel startups recently.
Start by successfully identifying a large enough travel niche and a corresponding customer segment for your offering, or keep exploring until you do.
I would encourage you to look at other underserved (yet lucrative) travel products like cruises or tours. Or address a specific traveler segment, like business travelers or millennials — perhaps for a particular region.
Ask yourself whether your travel startup is a feature or a business and what do you have to justify the latter?
I can't give you a formula for choosing a large enough travel niche. But you neither want it to be too broad ("all consumers" is too broad, by the way). Nor should it be too focused or too small in size. Ask entrepreneurs with prior exits, seasoned executives (especially those from the travel industry), angel investors or mentors for advice.
I've seen countless startups race through the early stage and spend a year or two (sometimes with multi-million dollar funding) on a niche and traveler segment that I (to be blunt) knew was wrong to begin with. A cogent one- or two-paragraph email, or a 10-minute conversation, could have spared a misguided effort.
So get advice. Also: In most cases, you don't need (nor should you need) outside capital at this stage.
Secondly, having identified the right niche and customer segment, you should build a working SaaS site or app solving two or three pain points.
Ask yourself how you'll reach your target audience and why that audience should try your product or service.
Are you a feature or a business? Even worse, are you a few feature looking for a business model?
Naturally, you'll have other markets you could expand into, but for the time choosing the right initial market is critical.
Avoid being a copycat, geographic knockoff or a petty variation of an existing startup – at best those are lifestyle companies and it's rare they will get venture funding.
I suggest you provide a minimum 10X or greater total overall value across two or three qualified (researched and vetted) customer pain points versus the legacy market offerings.
At this stage you don't have all the features your clients want but startups that secure venture funding can demonstrate considerably higher than normal metrics (conversion rates, usage, loyalty, stickiness, average spend…) even at this stage.
A horrible conversion rate means you haven't found something customers want and every entrepreneur has been there. Be prepared to research, speak with customers, try entirely new features, test, fix, and iterate (or dare I say, even pivot) until you get traction.
You may need to raise friends and family money, or get help from an incubator, bootstrap entirely, raise a small seed round ($50k or $100k) or a combination thereof. Ideally you'll find traction before you need outside capital so you can raise money to build out the remaining features (and less so to spend substantively proving your business model).
This isn't where you're spending money on high-profile, high-traffic marketing campaigns unless the idea of highlighting why people should NOT be your customer appeals to you. Identify, deploy, fix, optimize, and then scale.
An important reminder comes to mind: Every startup founder knows the nuances of why their travel inspiration guide is different that what's offered by "the other guys" — no surprise there — but don't expect your customers to know.
Your B2C prospective customers are being bombarded with advertising, e-mails, and promotions day in, day out — not to mention that they already have travel vendor relationships that imply minimum feature requirements and 'switching costs' that you or the traveler may not even be aware of.
If you're B2B-facing, the totality of the offering versus switching to you needs to be considered, including enterprise sales cycles, service level agreements, compliance, customization needs, and how you integrate with a client's existing sales/marketing/payment systems.
Ultimately you want product-market fit within a big enough lucrative travel niche for a big enough market and once you do, that's when you raise big money.
Clearly there's traction in that example or, to put it simply, people want and are paying for what you offer.
Use a given city or region as an accurate proxy for a larger one. That specificity will let you spend X and consistently earn a multiple of X in return (or, more precisely, justify a path towards a return in the near future). At this stage, raising capital to spend 1000X is a natural next step.
Lastly, some things to avoid.
Don't expect to connect to a few APIs (you know, the same ones every other travel startup may be using), throw in some social media, guess what customers want, build in 'sharing' features, and expect to build a viable business from it.
Do the work and don't be lazy. Bear in mind that investors don't have to invest in any deal and chances are you have competitors who are seeking funding who you may not know about (I remind our team that we're in the secret-keeping business).
You're "competing" against the other deals the VC firm is considering that week and it's important to get the right Partner at the VC firm to champion your deal.
Unfortunately for better or worse, early-stage travel startups rarely get skyrocketing valuations unless you're in an ultra-hot VC market where all startups are getting crazy valuations.
Thankfully there are strong exit possibilities for travel startups who aren't unicorns and ultimately you want to be in a position where somebody with deep pockets resorts to buying you (because you have long-term contracts, are the market leader, fundamentally have a better approach, market share, etc..) than risk competing against you.
Again, the world is too complicated to offer a formula for startup success.
But I do hope I've pointed you in the right direction and ultimateily it's your hard work, execution, team, timing and luck that matter the most in our collective desire to make a positive impact on travel.
To this day, in my fifth year as an investor, I am pleasantly surprised by what travel founders accomplish. So I know it can be done, and I wish you the best in your pursuit.


text:
Home / Alabama News / Surveillance video reportedly shows Utah man faking fall during first day at work
Surveillance video reportedly shows Utah man faking fall during first day at work
Jess Grotjahn
Add to favorites	3 mins
MIDVALE, Utah — A restaurant owner believes surveillance video from inside his kitchen shows the challenge employers face when looking for quality, entry-level workers.
In the video shared by The Trolley Wing Company, a dishwasher on his first day on the job appears to stage two separate falls.
"There he goes," said Jeff Krie, a co-owner of the restaurant as he watched the recording. "It looked like that could have hurt, but it was all set up. This is a fraud."
The incident happened during the lunch rush Sunday.
"I am not an actor myself, but definitely not the best. I think I could do a better job [of acting]," said Jessie Pham, the general manager of the restaurant.
Krie said he and other business owners are challenged by a shrinking pool of job applicants.
"We are trying to get someone in here, trying to get them started and give them a shot at a job, and then this is what happens," Krie said.
"Having someone come in and try to pull that kind of skeeze here, just kind of sucked," Pham said.
According to the Utah Department of Workforce Services, with unemployment at 3%, the current job market favors workers.
"It is a tight labor market," said Nate McDonald with the DWS.
With the economy booming, employers are now facing challenges they haven't seen in years.
"Employers do need to be more competitive. They need to be more creative," McDonald said.
Krie said he pays entry-level workers $13-per-hour and has raised the wage considerably in recent years.
"Over the past couple of years, I've taken it up 30 percent," Krie said.
Despite the increase in entry-level wages, some of his new hires, don't show up for their first day on the job.
He understands this may be the only negative of these prosperous times.
"It's great, but it's hard. You got to work for it," Krie said.
Dealing with an apparent fake fall is a lot easier than fighting through a recession.
"It's a different challenge. It's a good challenge," McDonald said.
The worker in the video is scheduled to return to work on Saturday. Krie isn't banking on him showing up.
Shooting investigation underway in Hartselle
California teen has frightening encounter with naked intruder who undressed in his room
Deputy fatally shot as he waited at a fast-food restaurant in California
Dunbar / Jun 13
Oklahoma teen blames laced marijuana for bizarre behavior after throwing baby across parking lot, attacking cars
Get out of Jail Free by playing Petnopoly at Huntsville Animal Services
Williams / Jun 16
Alabama men notice woman eating alone, invite her to join them in touching act of kindness
Grotjahn / Apr 23

redpajama_set_name: RedPajamaCommonCrawl


text:
Nedu Wazobia (born Chinedu Ani Emmanuel) is a Nigerian on-air personality, broadcast journalist, TV presenter, actor, comedian and content creator. He is known for his pidgin rendition of the daily news on popular radio station Wazobia FM 94.1 Lagos.

Early life and career
Nedu was born in Kaduna, Nigeria. He studied accounting at Madonna University, Elele Okija, Anambra state. He has his NYSC in Jigawa in a radio station as an on air personality. He moved back to Abuja to work as a site manager, a period which he tagged as unfulfilled. After 2 years working as a site manager, he moved to Lagos to fulfill his life-long dream of being a broadcaster and entertainer.

Comedy
Nedu is known for his alter ego personalities of Sister Nkechi, Alhaji Musa, EndTime Landlord and Officer Jato. He has a following of over 1.3 million people on Instagram.

Personal life
Nedu married Uzoamaka Ohiri in 2013, but their marriage crashed in 2018. The estranged couple have three children together. Nedu claimed his marriage has been dissolved but his estranged wife has said otherwise and has challenged him to produce the divorce papers.

DNA controversy
Ohiri, on Friday, September 3, 2021 called out Nedu for domestic violence. She accused Nedu of battering her a few weeks after she was delivered of their child by a Cesarean section. On September 4, 2021, Nedu responded to his wife's allegations and denied physically violating his wife. Nedu would later respond to her claims saying their marriage was plagued with a lot of issues. He wrote, ''Our marriage was plagued with a lot of issues. One of which was continuous infidelity from her side that led to me conducting a paternity test on our kids which led to the revelation that our first son is not my biological son even though he was born within the period during which we were married''. To substantiate his claims, he also posted a copy of the DNA test, which was conducted by a forensic laboratory, Viaguard Accu-metrics, located in Toronto Canada. The radio personality and Instagram skit maker, said, "The continuous infidelity from her side made me conduct a paternity test on our kids which led to the revelation that our first son is not my biological son".

Although Uzoamaka had said that she did not cheat on Nedu during their brief marriage, she noted that she did not intentionally give another man's baby to her ex-husband. Uzoamaka stated that she was already pregnant for her ex before she married Nedu, albeit, unbeknownst to her. Uzoamaka claimed that shortly after her previous relationship ended, she decided to get to know Nedu, then they were married while she was pregnant, not knowing that he wasn't responsible for the pregnancy. She was visibly pregnant during the wedding, and everyone could see it. She said that it was communications issues which were solely responsible for the disruption of their marriage. She said that their marriage was plagued with domestic violence and that it was not the DNA test report that led to their eventual divorce.

Filmography
Who Cheats More, 2017
Isoken, 2017
Meet the In-Laws, 2017
Boss of All Bosses, 2018
King of Boys, 2018
Chief Daddy, 2018
Flatmates - 2018
Chief Daddy 2: Going for Broke

Brands and endorsements
Nedu is a brand influencer. He is a brand ambassador for popular brands like MTN, Fidelity Bank, Quickteller and Sun Lottery.

External links
 OfficialNeduTV on YouTube

References

1982 births
Living people

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}

Weak scale supersymmetry (SUSY) is one of the most promising candidates for physics beyond the Standard Model (SM) \cite{Nilles:1983ge}.
The minimal SUSY extension of the Standard Model (MSSM) has several attractive features.
It, for instance, provides a solution to the gauge hierarchy problem and a dark matter
candidate as the lightest supersymmetric particle (LSP).
Moreover, supersymmetric grand unified theory (SUSY GUT) is strongly motivated by remarkable coincidence of three SM gauge coupling constants around $10^{16}$ GeV.

Grand unified theory can also explain the origin of hierarchical structures of masses and mixing angles in the SM particles by simply assuming that the $\bm{10}$'s of $SU(5)$ induce stronger hierarchical Yukawa structure than the $\bf{\bar 5}$'s.
However, the SUSY GUT scenario is generically suffering from various theoretical and phenomenological difficulties.
For instance,
\begin{enumerate}
\item SUSY flavor problem:
if generic soft SUSY breaking terms are introduced, flavor changing neutral current (FCNC) processes exceeds the experimental constraints \cite{Gabbiani:1996hi}.
\item SUSY CP problem:
if generic soft SUSY breaking terms are introduced, CP violating observables such as electric dipole moments (EDMs) exceeds the experimental constraints \cite{Gabbiani:1996hi}.
\item $\mu$ problem:
supersymmetric Higgs mass $\mu$ must be the same order of the soft SUSY breaking scale though it is a SUSY parameter.
\item The doublet-triplet splitting (DTS) problem and proton decay:
there must be huge mass separation between doublet Higgs (weak scale) and triplet Higgs (above GUT scale) in order to make proton's lifetime longer than experimental limit.
Moreover, recent proton decay constraint suggests that triplet Higgs mass should naively be larger than $10^{18}$ GeV, but it generically spoils the success of the gauge coupling
 unification.
\item Unrealistic GUT relation:
generically, unification of quark and leptons in GUT tends to result in unrealistic Yukawa relations which are inconsistent with the observed masses and mixings of quark and leptons.
\end{enumerate}

$E_6$ unification is quite attractive because it can naturally induce the feature that
the $\bm{10}$'s of $SU(5)$ induce stronger hierarchical Yukawa structure than the $\bf{\bar 5}$'s, which plays an important role in obtaining realistic Yukawa hierarchies in $SU(5)$ GUT.
Moreover, if we introduce a family symmetry, $SU(3)_F$($SU(2)_F$), all three generation quark
and leptons can be unified into a single (two) multiplet(s), and after breaking the family
symmetry and the $E_6$ symmetry, realistic quark and lepton masses and mixings can be
obtained.
Furthermore the third generation $\bm{10}$ of $SU(5)$ can have different sfermion masses from
the other sfermion masses, because it is from the third generation $\bm{27}$
of $E_6$.
It is remarkable that such effective SUSY sfermion mass spectrum \cite{Dimopoulos:1995mi} can satisfy the LHC
constraints with lighter stop, which is important to keep the naturalness in SUSY models.

Unfortunately, such effective SUSY type sfermion mass spectrum is generically suffering from
the new type of SUSY CP problem, in which Chromo electric dipole moment (CEDM) of up quark
becomes too large to satisfy the experimental constraints. The 1-3 mixings of up-type squark
masses become too large and have generically ${\cal O}(1)$ complex phase after diagonalizing
the complex Yukawa couplings if the stop mass is different from the other two up-type squarks.

Recently a scenario which solves this problem as well as the old type SUSY CP problem
by introducing spontaneous CP violation has been proposed \cite{Ishiduki:2009vr}.
The essential point is that the discrete symmetry, which is introduced in order to
solve the old type SUSY CP problem, leads to real up-type Yukawa couplings which
can solve the new type SUSY CP problem and to complex down-type Yukawa couplings which
give ${\cal O}(1)$ Kobayashi-Maskawa (KM) \cite{Kobayashi:1973fv} phase.
The model has remarkable features, for example,
the doublet-triplet splitting is naturally realized by introducing the anomalous $U(1)_A$
gauge symmetry, predictive Yukawa matrices of up quarks, down quarks and charged leptons are obtained
because of the reduced number of the ${\cal O}(1)$ parameters, smaller Cabibbo-Kobayashi-Maskawa (CKM) \cite{Cabibbo:1963yz} matrix element $V_{ub}\sim\lambda^4$, where $\lambda\sim 0.22$ is the Cabibbo mixing, is obtained.

In this paper, we examine the neutrino sector in the above model with the spontaneous CP
violation, since this has not been studied in detail in the previous paper.
At a glance, the discrete symmetry, which is introduced in order to solve the SUSY CP problem,
constrains the allowed operators too strongly for the neutrino sector to be consistent with
the experimental data, i.e., the $\mu$ neutrino becomes massless as commented in the
previous paper.
We will show that this issue on the neutrino sector can be solved if some operators, which are not important in studying quark and charged lepton sectors, are taken into
account. And we clarify the reason why such operators play an important role only in the
neutrino sector. The predictions on the neutrino masses and mixings are the same as the
$E_6$ models, i.e., $\sin\theta_{12}\sim\sin\theta_{23}\sim\lambda^{0.5}$,
$\sin\theta_{13}\sim\lambda$, $\Delta m^2_{12}/\Delta m^2_{23}\sim \lambda^{2}$,
etc, which are consistent with various experiments on the neutrino oscillations.
Since the operators are restricted by the discrete symmetry, the predictions on the ${\cal O}(1)$
coefficients are expected. However, we are not able to find any simple predictions between
the ${\cal O}(1)$ coefficients because there are a lot of operators for the right-handed neutrino
masses.

As the result, we can obtain an attractive model in which
\begin{enumerate}
\item realistic quark and lepton masses
and mixings are obtained,
\item all the CP phases in the model,
the KM phase, CP phases in neutrino sector and CP phases in sfermion sectors,
are given from one phase which is obtained by the spontaneous CP violation,
\item as the result, SUSY CP problem is solved,
\item the effective SUSY type sfermion mass spectrum is predicted.
\end{enumerate}

The paper proceeds as follows: in Section 2, we briefly review the basic features of $E_6\times SU(2)_F\times U(1)_A$ SUSY GUT with spontaneous CP violation.
In Section 3, we calculate neutrino masses and Maki-Nakagawa-Sakata (MNS) \cite{Maki:1962mu} matrix explicitly, after specifying massless $\bar{\bm{5}}$ modes.
We see that a specific type of higher dimensional operators is essential for the realistic neutrino masses.
We also show that the above higher dimensional operators only affect the neutrino sector.
The last section is devoted to summary and discussion.

\section{Basic features of $E_6\times SU(2)_F\times U(1)_A$ SUSY GUT with spontaneous CP violation}

\subsection{$E_6$ unification and $SU(2)_F$ family symmetry}

First of all, $\bm{27}$ is the fundamental representation for the $E_6$ group.
In terms of $E_6\supset SO(10)\times U(1)_{V'}$ (and [$SO(10)\supset SU(5)\times U(1)_V$]) it is decomposed as
\begin{equation}
\bm{27}=\bm{16}_1[\bm{10}_{1}+\bar{\bm{5}}_{-3}+\bm{1}_{5}]+\bm{10}_{-2}[\bm{5}_{-2}+\bar{\bm{5}}'_{2}]+\bm{1}'_4[\bm{1}'_0],
\end{equation}
where acutes are used to distinguish different $\bar{\bm{5}}(\bm{1})$'s.
Note that each $\bm{27}$ contains two $\bar{\bm{5}}$'s (and $\bm{1}$'s) of $SU(5)$.
This nature is essential for realizing different Yukawa structures of up-type quarks, down-type quarks, charged leptons and neutrinos from a single hierarchical structure of an $E_6$ invariant Yukawa couplings \cite{Bando:2001bj, Bando:1999km, Maekawa:2002eh}.

In order to break $E_6$ gauge group into the SM gauge group $G_{\rm{SM}}$, we introduce three types of Higgs fields.
First one is $\bm{27}$ representation Higgs $H$.
We also introduce $\bm{\bar{27}}$ representation Higgs $\bar{H}$ in order to satisfy the
 D-flatness condition of $E_6$ gauge interaction.
$H, \bar{H}$ obtain vacuum expectation values (VEVs)
\begin{equation}
\langle H\rangle=\langle \bm{1}_H\rangle\neq 0,
\end{equation}
and they break $E_6$ into $SO(10)$.
Second one is an adjoint Higgs $A$, which belongs $\bm{78}$ representation.
It gets Dimopoulos-Wilczek (DW) \cite{Srednicki:1982aj} VEV proportional to $U(1)_{B-L}$ direction
\begin{equation}
\langle A\rangle=\langle \bm{45}_A\rangle \propto U(1)_{B-L},
\end{equation}
and it breaks $SO(10)$ into $SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}$.
Third type are $C$ and $\bar{C}$, and they are also $\bm{27}$ and $\bm{\bar{27}}$ representations.
They acquire VEVs
\begin{equation}
\langle C\rangle=\langle \bm{16}_C[\ni \bm{1}_C]\rangle\neq 0,
\end{equation}
and they break $SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ into $G_{\rm{SM}}$.
The superpotential which gives superheavy masses for ($\bm{5}, \bar{\bm{5}}$) and ($\bm{5}, \bar{\bm{5}}'$) pairs is
\begin{equation}
W=Y^H_{ij}\Psi_i\Psi_j H+Y^C_{ij}\Psi_i\Psi_j C,
\end{equation}
where $\Psi_i\ (i=1,2,3)$ are matter fields in family $i$.
After $H$ and $C$ acquire VEVs, three degrees of freedom among $\bar{\bm{5}}_i$ and $\bar{\bm{5}}'_i$ get superheavy masses, while remaining three are massless at the GUT scale.
We assume the Yukawa hierarches
\begin{equation}
Y^H_{ij}\sim Y^C_{ij}\sim \left(
\begin{array}{ccc}
\lambda^6 & \lambda^5 & \lambda^3\\
\lambda^5 & \lambda^4 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\label{eq:Yukawa_hierarchy}
\end{equation}
and ratio of two VEVs
\begin{equation}
\frac{\langle C\rangle}{\langle H\rangle}\sim \lambda^{0.5}
\label{eq:VEV_ratio}
\end{equation}
up to ${\cal O}(1)$ coefficients.
These assumption can be realized proper charge assignment of anomalous $U(1)_A$ symmetry and the breaking effect of $SU(2)_F$ family symmetry, which we explain later respectively\footnote{Strictly speaking, (\ref{eq:VEV_ratio}) is not true in $U(1)_A$ framework.
The correct relation is $\lambda^c\langle C\rangle/\lambda^h\langle H\rangle\sim \lambda^{0.5}$, where $c$ and $h$ are $U(1)_A$ charges of $C$ and $H$, respectively.}.
Under these assumption, three massless modes are mainly ($\bar{\bm{5}}_1, \bar{\bm{5}}'_1, \bar{\bm{5}}_2$).
Note that third generation does not appear at the leading order.
So we end up following different Yukawa hierarchies
\begin{equation}
Y_d\sim \left(
\begin{array}{ccc}
\lambda^6 & \lambda^5 & \lambda^3\\
\lambda^5 & \lambda^4 & \lambda^2\\
\lambda^4 & \lambda^2 & 1
\end{array}\right), \
Y_d\sim Y_e^T\sim \left(
\begin{array}{ccc}
\lambda^6 & \lambda^{5.5} & \lambda^5\\
\lambda^5 & \lambda^{4.5} & \lambda^4\\
\lambda^3 & \lambda^{2.5} & \lambda^2
\end{array}\right), \
M_\nu\sim \lambda^n\left(
\begin{array}{ccc}
\lambda^7 & \lambda^{6.5} & \lambda^6\\
\lambda^{6.5} & \lambda^6 & \lambda^{5.5}\\
\lambda^6 & \lambda^{5.5} & \lambda^5
\end{array}\right)\frac{\langle H_u\rangle^2}{\langle \bar{H}\rangle^2}\Lambda,
\end{equation}
when the MSSM Higgses $H_u$ and $H_d$ are included in $\bm{10}_H$ and $\bm{16}_C$.
Here $n$ is a number, and we used the relation $\langle\bar{C}\rangle / \langle\bar{H}\rangle\sim \lambda^{0.5}$.

In order to realize the Yukawa hierarchy between ${\cal O}(1)$ top quark and the other quarks naturally, we employ $SU(2)_F$ family gauge symmetry.
We treat first two generation fields as the doublet $\Psi_a\ (a=1,2)$ whereas the third generation fields $\Psi_3$ and all Higgs fields are treated as singlets under $SU(2)_F$.
Here the index $a$ can be raised or lowered by the anti-symmetric symbols $\epsilon^{ab}$ and $\epsilon_{ab}$.
We also introduce flavon fields $F_a$ and $\bar{F}^a$ that are singlets under $E_6$ and doublet and anti-doublet under $SU(2)_F$, respectively.
VEVs of $F_a$ and $\bar{F}^a$ break $SU(2)_F$, then this effect generate hierarchical Yukawa structure in (\ref{eq:Yukawa_hierarchy}).
Since massless $\bar{\bm{5}}$'s do not contain the third generation at the leading order in $E_6$ GUT, both left-handed and right-handed components of the top quark belongs $SU(2)_F$ singlet, while all other quarks and charged leptons are (partially or completely) $SU(2)_F$ doublets.

$SU(2)_F$ family symmetry is also useful for solving the SUSY FCNC problem.
Suppose that the soft SUSY breaking terms are mediated to the visible sector above the scale where $E_6$ and $SU(2)_F$ symmetries are respected, such as in gravity mediation.
Then the symmetry guarantees  sfermion masses which degenerate at the leading order except for $\bm{10}_3$ \cite{Maekawa:2002eh}:
\begin{equation}
\tilde m_{\bm{10}}^2=\left(\begin{array}{ccc}
m_0^2 & 0 & 0 \\
0 & m_0^2 & 0 \\
0 & 0 & m_3^2
\end{array}\right), \quad\quad
\tilde m_{\bm{\bar{5}}}^2=\left(\begin{array}{ccc}
m_0^2 & 0 & 0 \\
0 & m_0^2 & 0 \\
0 & 0 & m_0^2
\end{array}\right),
\label{eq:MUSM}
\end{equation}
where $\tilde{m}_{\bm{10}}$ and $\tilde{m}_{\bar{\bm{5}}}$ are squared sfermion mass matrices at the GUT scale in $\bm{10}$ and $\bar{\bm{5}}$ fields of $SU(5)$, respectively.
For sfermions in $\bm{10}$, FCNC observables provide stringent constraints mainly on the first two generations, while constraints for $\bar{\bm{5}}$'s are stringent for all three generations.
This is because the mixing angles of $\bm{10}$ fields are small, while those of $\bar{\bm{5}}$ fields are large.
Therefore, in this model, FCNC constraints can be evaded by raising $m_0$\footnote{There is upper limit of $m_0$ comes from charge and color breaking (CCB) effect.
For detail discussion, see \cite{ArkaniHamed:1997ab}.}.
Moreover, the weak scale is not destabilized as long as $m_3$ is around the weak scale.
So this type of sfermion masses (`` effective SUSY" or ``{\it modified} universality")
 \cite{Maekawa:2002eh, Kim:2006ab, Kim:2008yta, Ishiduki:2009gr, Kim:2009nq} solves the SUSY FCNC problem without spoiling naturalness.
We also comment that LHC constraints to this type of sfermion masses is much weaker than
to the constrained MSSM (CMSSM) type sfermion masses \cite{Sakurai:2011pt}.

Unfortunately, there is a tension between this modified universal sfermion masses and
complex Yukawa couplings which are important to obtain the non-vanishing KM phase. In the basis in which Yukawa matrices are diagonal, sfermion mass matrices become
\begin{equation}
\Delta_{\bf 10}\equiv V_{\bf 10}^\dagger \tilde m_{\bf 10}^2 V_{\bf 10}
\sim \tilde{m}^2_{\bm{10}}+(m_3^2-m_0^2)\left(\begin{array}{ccc}
\lambda^6 & \lambda^5 & \lambda^3 \\
\lambda^5 & \lambda^4 & \lambda^2 \\
\lambda^3 & \lambda^2 & 1
\end{array}\right),
\Delta_{\bf\bar 5}\equiv V_{\bf \bar 5}^\dagger \tilde m_{\bf\bar 5}^2 V_{\bf\bar 5}=
\tilde m_{\bf\bar 5}^2,
\end{equation}
where $V_{\bf 10}$ and $V_{\bf\bar 5}$ are the diagonalizing unitary matrices for
$\bm{10}$ and $\bar{\bm{5}}$ fields of $SU(5)$, respectively, and we take
the CKM like matrix as $V_{\bf 10}$. Since the mass
insertion matrices $\delta_{\bf 10}\equiv \Delta_{\bf 10}/m_0^2$ do not vanish in the
limit $m_0\rightarrow\infty$, the CEDM of up quark from this SUSY contribution are
not decoupled. The constraints for these parameters by mercury (neutron) become \cite{Ishiduki:2009gr, Griffith:2009zz, Baker:2006ts, Hisano:2004tf}
\begin{equation}
{\rm Im}[(\delta_{u_L})_{13}(\delta_{u_R})_{31}]\leq 3\times 10^{-7}(9\times 10^{-7})
\left(\frac{m_3}{500 {\rm GeV}}\right)^2,
\end{equation}
which are much smaller than the prediction $\lambda^6\sim 10^{-4}$.
This is a serious problem on the ``effective SUSY" or ``modified universality", which
we call the new type of SUSY CP problem.

\subsection{Anomalous $U(1)_A$ symmetry}

An Anomalous $U(1)_A$ symmetry \cite{Witten:1984dg, Froggatt:1978nt} is introduced in order to solve the doublet-triplet splitting problem and $\mu$ problem, and to provide the origin of the hierarchical Yukawa structures \cite{Maekawa:2001uk}.
This is a gauge symmetry whose anomalies are canceled by the Green-Schwarz mechanism \cite{Green:1984sg}.
The theory possesses the Fayet-Iliopoulos term $\xi^2$, and we assume its magnitude as $\xi=\lambda\Lambda$.
Here $\Lambda$ is the cutoff scale of the theory and we set $\Lambda=1$.
Let us denote the gauge symmetries of the theory except for $U(1)_A$ as $G_a$.
Consider a theory consisting of all the $G_a$ and $U(1)_A$ invariant terms including non-renormalizable operators.
Then it is shown in \cite{Maekawa:2001uk} that the theory has a supersymmetric vacuum where all the fields that are negatively charged under $U(1)_A$ get VEVs in the following way\footnote{From now on, each superfield is denoted by an uppercase letter, whereas the corresponding lowercase letter indicates an associated $U(1)_A$ charge.
The consistency of (\ref{eq:U(1)A_VEV}) requires the number of positively charged fields to be larger than that of negatively charged fields by one.}.
\begin{equation}
\left\{\begin{array}{cc}\langle Z_i^+\rangle = 0\ \quad & (z_i^+>0)\\
\langle Z_i^-\rangle \sim \lambda^{-z_i} & (z_i^-<0)\end{array}\right.
\label{eq:U(1)A_VEV}
\end{equation}
Here $Z_i$ is $G_a$ singlet field whose $U(1)_A$ charge is $z_i$.
This argument can be extended to the case where $Z_i$ is composite operator that is made by $G_a$ nonsinglet fields.
For example, in $Z^-=\bar{X}X$ case, $\langle \bar{X}X\rangle \sim \lambda^{-(x+\bar{x})}$ leads to $|\langle X\rangle| = |\langle\bar{X}\rangle| \sim \lambda^{-(x+\bar{x})/2}$, once the D-flatness condition of $G_a$ is taken account. Note that the above results can be
obtained under a natural assumption that all the interactions which are allowed by the
symmetry of the theory are introduced with ${\cal O}(1)$ coefficients.

It is important to mention that a term whose total $U(1)_A$ charge is negative does not appear at the $U(1)_A$ breaking vacuum.
The reason is that this type of term should originally be accompanied by at least one positively charged field but its VEV is always vanishing according to (\ref{eq:U(1)A_VEV}) (SUSY-zero mechanism) \cite{Maekawa:2001uk, Nir:1993mx}.
A $U(1)_A$ symmetry and its specific SUSY vacuum are applied in several aspects of phenomenological model building.
For example, an appropriate $U(1)_A$ charge assignment for the Higgs sector can ensure the DTS via the DW mechanism \cite{Maekawa:2001uk}, and the SUSY zero mechanism can be applied to solve the $\mu$ problem \cite{Maekawa:2001yh}.

For the following arguments, we will briefly remind the points on the solution for the $\mu$
problem. Since the MSSM Higgses, $H_u$ and $H_d$, have negative $U(1)_A$ charges, the mass
term is forbidden by the SUSY zero mechanism. With the positively charged singlet field $S$,
the term $SH_uH_d$ can be allowed, but $\langle S\rangle=0$ in the SUSY limit. However, if
SUSY is broken at the weak scale $\Lambda_W$, the VEV of $S$ becomes non-vanishing and the
order of the weak scale. This results in the SUSY Higgs mass with ${\cal O}(\Lambda_W)$.
The $b$ parameter also becomes the weak scale.

\subsection{Spontaneous CP violation and discrete symmetry}

As we have seen, one of the attractive features of $E_6\times SU(2)_F$ SUSY GUT is the modified universal sfermion mass (MUSM) (\ref{eq:MUSM}), which evades FCNC constraints with keeping naturalness.
However, such type of mass spectrum is generically suffering from the CEDM constraint of the up quark \cite{Hisano:2004tf}.
Fortunately, we can evade this constraint by introducing a spontaneous CP violation (SCPV) \cite{Lee:1973iz, Barr:1988wk}.
By using SCPV, we can realize real up-type Yukawa couplings together with the KM phase.

Let us introduce the $E_6\times SU(2)_F$ singlet field $S\ (s>0)$.
Then we obtain the following superpotential made of flavon fields $F_a, \bar{F}^a$ and $S$:
\begin{equation}
W=\lambda^sS[\sum_{n=0}^{n_f}c_n\lambda^{(f+\bar{f})n}(\bar{F}F)^n].
\end{equation}
Here $c_n$ are real ${\cal O}(1)$ coefficients and $n_f$ is the number where SUSY-zero mechanism truncates the sum.
When $n_f\geq 2$, the F-flatness condition with respect to $S$ leads to complex VEV $\langle \bar{F}F\rangle$ and then CP symmetry can be spontaneously broken.
Using $SU(2)_F$ gauge symmetry and its D-flatness condition, we can take only $\langle F\rangle$ is complex without loss of generality:
\begin{equation}
\langle F_a\rangle\sim \left(\begin{array}{c}0\\ e^{i\rho}\lambda^{-(f+\bar{f})/2}\end{array}\right), \ \langle \bar{F}^a\rangle\sim \left(\begin{array}{c}0\\ \lambda^{-(f+\bar{f})/2}\end{array}\right).
\end{equation}

Unfortunately, the SCPV affects $\mu$ generation in $U(1)_A$ framework and leads to an unwanted outcome \cite{Ishiduki:2009vr}
\begin{equation}
\mathrm{Arg}[\mu b^\ast]={\cal O}(1),
\end{equation}
if $S\bar FF$ exists.
This rephasing invariant phase induces EDMs of quarks and leptons, and give rise to the SUSY CP problem again.
In order to evade such unwanted relation, we introduce an additional discrete symmetry $Z_6$,
which forbids $S\bar FF$. Then we can avoid this old-type SUSY CP problem. Moreover,
this symmetry results in the real up-type Yukawa matrix, which solves new-type of SUSY CP
problem, i.e., the diagonalizing unitary matrices become real and therefore the mass insertion
matrices for up-type quark become real, if the MSSM Higgs $H_u$ is included in $\bm{10}_H$.
This symmetry constrains the model and reduces the number of ${\cal O}(1)$ parameters.
As a byproduct, the up-quark Yukawa coupling $y_u$ and the CKM matrix element $V_{ub}$ become closer to experimental values $y_u\sim\lambda^8$, $V_{ub}\sim\lambda^4$ than the expectation of $E_6$ GUT $y_u\sim\lambda^6$, $V_{ub}\sim\lambda^3$ \cite{Ishiduki:2009vr}.

It is also reported in \cite{Ishiduki:2009vr} that the discrete symmetry makes one of the neutrinos massless.
This result seems to be unrealistic, but we will show that this issue can be solved by introducing some operators, which have not been considered in the previous paper.

\section{Calculation of neutrino mass and MNS matrix}

\subsection{Field contents and Yukawa couplings}

First, we summarize the field content of the model and its representations under the $E_6$, $SU(2)_F$, $U(1)_A$ and $Z_6$ symmetries.

\begin{table}[tbp]
\begin{center}
\begin{tabular}{c|cccccccccc}
 & $\Psi_a$ & $\Psi_3$ & $F_a$ & $\bar{F}^a$ & $H$ & $\bar{H}$ & $C$ & $\bar{C}$ & $C'$ & $\bar{C}'$\\
\hline
$E_6$ & $\bm{27}$ & $\bm{27}$ & $\bm{1}$ & $\bm{1}$ & $\bm{27}$ & $\bm{\bar{27}}$ & $\bm{27}$ & $\bm{\bar{27}}$ & $\bm{27}$ & $\bm{\bar{27}}$\\
$SU(2)_F$ & $\bm{2}$ & $\bm{1}$ & $\bm{2}$ & $\bar{\bm{2}}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$\\
$U(1)_A$ & 4 & $\frac{3}{2}$ & $-\frac{3}{2}$ & $-\frac{5}{2}$ & -3 & 1 & -4 & -1 & 7 & 9\\
$Z_6$ & 0 & 0 & 1 & 0 & 0 & 0 & 5 & 3 & 3 & 3\\
\hline
\end{tabular}
\vspace{5mm}\\
\begin{tabular}{c|ccccccccc}
 & $A$ & $A'$ & $Z_0$ & $Z_2$ & $Z_3$ & $Z_4$ & $S$ & $S'$ & $S''$\\
\hline
$E_6$ & $\bm{78}$ & $\bm{78}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$\\
$SU(2)_F$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$ & $\bm{1}$\\
$U(1)_A$ & -1 & 5 & -1 & -3 & -2 & -5 & 9 & 8 & 5\\
$Z_6$ & 3 & 3 & 0 & 2 & 3 & 4 & 0 & 4 & 4\\
\hline
\end{tabular}
\caption{Field contents and charge assignment under $E_6$$\times SU(2)_F\times U(1)_A\times Z_6$.}
\end{center}
\end{table}

We introduce the following fields, which are listed in Table 1.
All matter fields $\Psi$ belong to $\bm{27}$ representation of $E_6$.
We make its first two generations as a doublet $\Psi_a\ (a=1,2)$ and the third generation as a singlet $\Psi_3$ of the $SU(2)_F$, respectively.
The $SU(2)_F$ and CP are simultaneously broken by the VEVs of the flavon fields $F_a$ and $\bar{F}^a$.
All the other fields are singlets under $SU(2)_F$
\footnote{
To cancel the Witten's anomaly, odd number of additional doublets of $SU(2)_F$ are required.
}.
$H$ is the field whose VEV $\langle \bm{1}_H\rangle\neq 0$ breaks $E_6$ into $SO(10)$, and $\bar{H}$ is introduced to maintain the D-flatness condition.
The VEV of $A$ breaks $SO(10)$ into $SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}$.
$C$ is the field whose VEV breaks $SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ into $G_{\rm{SM}}$, and $\bar{C}$ is also introduced to maintain the corresponding D-flatness condition.
Basically, the F-flatness conditions of the positively charged fields, $A'$, $C'$, $\bar C'$
etc., determine the VEVs of
the negatively charged fields.
For example, the F-flatness conditions with respect to $A'$ make $A$ acquire DW-type VEVs for the $SO(10)$ adjoint component to solve the DTS problem.
The alignment between the VEVs of $A$ and $C$, $\bar C$ are realized and at the same time,
the pseudo Nambu-Goldstone modes become heavy \cite{Barr:1997hq}.
In Table 1, $U(1)_A$ charges are assigned so that the DTS and appropriate Yukawa hierarchies are realized.
Also, $Z_6$ charges are determined so that the SUSY CP problem is evaded.

$S$, $S'$ and $S''$ are introduced to realize the SCPV and $\mu$ generation.
The relevant superpotential are
\begin{eqnarray}
W_S & = & \lambda^{s}S+\lambda^{s+3z_2}SZ_2^3+\lambda^{s+3h}SH^3,\\
W_{S'} & = & \lambda^{s'+z_2}S'Z_2+\lambda^{s'+\bar{c}+c}S'\bar{C}C+\lambda^{s'+2\bar{f}+2f}S'(\bar{F}F)^2,\\
W_{S''} & = & \lambda^{s''+z_2}S''Z_2+\lambda^{s''+\bar{c}+c}S''\bar{C}C.
\end{eqnarray}
First, we obtain the VEV $\langle Z_2\rangle$ from the F-flatness condition of $W_S$ with respect to $S$.
Since the one of the three solutions is real, we assume $\langle Z_2\rangle$ is real.
Second, the F-flatness condition of $W_{S''}$ determines the real VEV $\langle\bar{C}C\rangle$\footnote{We must forbid the term $S^{(')}\bar{F}F\bar{C}C$, which lead the complex VEV $\langle\bar{C}C\rangle$.
If we can choose the basis in which $\langle C\rangle$ is real and $\langle \bar{C}\rangle$ has an opposite phase to $\langle F\rangle$, the up-type Yukawa can keep real.
However, it changes the phase of the down-type Yukawa into removable, and the KM phase cannot be realized.}.
Third, the F-flatness condition of $W_{S'}$ leads the complex VEV $\langle\bar{F}F\rangle$, which breaks the $SU(2)_F$ and CP spontaneously.
Note that the operator $H^3$ gives the SM Higgs mass after developing the VEV of $H$
if the SM Higgses are included in ${\bf 10_H}$.
Then, after breaking SUSY, $W_S$ generates $\mu$ and $b$ terms.
Since $H^3$ does not couple to $S'$ and $S''$, so $\mu$ and $b$ are real.

Let us examine the mass matrices of quarks and leptons in this model.
Under the charge assignment of Table 1, the following interactions between matter and Higgs fields are allowed:
\begin{equation}
Y^H: \quad\left(
\begin{array}{ccc}
0 & d\Psi^a(A,Z_3, \bar HH)\Psi_a & 0\\
d\Psi^a(A,Z_3, \bar HH)\Psi_a & c\lambda^{2(\psi_a+\bar{f})}\bar{F}^a\Psi_a\bar{F}^b\Psi_b & b\lambda^{\psi_a+\psi_3+\bar{f}}\bar{F}^a\Psi_a\Psi_3\\
0 & b\lambda^{\psi_a+\psi_3+\bar{f}}\Psi_3\bar{F}^a\Psi_a & a\lambda^{2\psi_3}\Psi_3\Psi_3
\end{array}
\right)\lambda^hH,
\label{eq:YH}
\end{equation}
\begin{equation}
Y^C: \quad\left(
\begin{array}{ccc}
0 & f'\lambda^{2\psi_a+f+\bar{f}}F^a\Psi_a\bar{F}^b\Psi_b & g'\lambda^{\psi_a+\psi_3+f}F^a\Psi_a\Psi_3\\
f'\lambda^{2\psi_a+f+\bar{f}}\bar{F}^a\Psi_aF^b\Psi_b & 0 & 0\\
g'\lambda^{\psi_a+\psi_3+f}\Psi_3F^a\Psi_a & 0 & 0
\end{array}
\right)\lambda^cC.
\label{eq:YC}
\end{equation}
Here we explicitly write in all ${\cal O}(1)$ coefficients, $a, b, c, d, f'$ and $g'$.
Note that all the ${\cal O}(1)$ coefficients are assumed to be real because of the original CP symmetry.

In (\ref{eq:YH}), the structure of (1,2) and (2,1) elements is a little bit complicate, so we should see this point carefully.
$\Psi^a(A,Z_3, \bar HH)\Psi_a$ consist of several types of terms.
Cleally, some additional field(s) for (1,2) and (2,1) elements are needed because
$\Psi^a\Psi_a=\epsilon^{ab}\Psi_a\Psi_b=0$, where $\epsilon^{12}=-\epsilon^{21}=1, \epsilon^{11}=\epsilon^{22}=0$.
The negatively $U(1)_A$ charged fields which can have non-vanishing VEVs can be a
candidate for the additional fields.
There are two possibilities.
One is using the adjoint Higgs $A$: $\Psi^aAZ_3\Psi_a$, $\Psi^aA^2\Psi_a$, etc.
Since the VEV of $A$ breaks $SO(10)$ into
$SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}$,
the contributions of these terms are different for the different components of $\Psi_a$
under $SU(3)_C\times SU(2)_L\times SU(2)_R\times U(1)_{B-L}$.
Because the VEV of $A$ is proportional to the $B-L$ charge, there is no contribution
for the field which has vanishing $B-L$ charge.
The other possibility, which has not been considered in the previous paper, is using $\bar{H}H$: $\Psi^a\bar{H}H\Psi_a$, etc. Since the VEV of $H$ breaks $E_6$ into $SO(10)$, it is
useful to write down the contributions with the representations of $SO(10)$.
 For example,
$\epsilon^{ab}\bm{10}_{\Psi_a}\bm{1}_{\Psi_b}$ and
$\epsilon^{ab}\bm{16}_{\Psi_a}\bm{10}_{\Psi_b}$.
Note that the terms
$\epsilon^{ab}\bm{10}_{\Psi_a}\bm{10}_{\Psi_b}$ and
$\epsilon^{ab}\bm{16}_{\Psi_a}\bm{16}_{\Psi_b}$
are vanishing and give no contribution.
Here we use a conventions for the component fields of $SO(10)$ of a field $X$ as
\begin{eqnarray}
X&=&\bm{27}_X=\bm{16}_X+\bm{10}_X+\bm{1}'_X, \\
\bm{16}_X&=& Q_X+U_X+E_X+D_X+L_X+N_X, \\
\bm{10}_X&=& H^C_X+(H_u)_X+\bar{H}^C_X+(H_d)_X.
\end{eqnarray}
Then, we can write down the concrete components of the interactions
$\Psi^a(A,Z_3, \bar HH)\Psi_a$ as
\[
d\Psi^a\langle(A, Z_3,\bar HH)\rangle \Psi_aH \ni d_5\lambda^5\epsilon^{ab}H^C_{\Psi_a}\bar{H}^C_{\Psi_b}\bm{1}'_H, \ -\frac{1}{2}d_q\lambda^5\epsilon^{ab}Q_{\Psi_a}U_{\Psi_b}(H_u)_H,
\]
\begin{equation}
-\frac{1}{2}d_q\lambda^5\epsilon^{ab}Q_{\Psi_a}D_{\Psi_b}(H_d)_H, \ -\frac{3}{2}d_l\lambda^5\epsilon^{ab}L_{\Psi_a}E_{\Psi_b}(H_d)_H, \ h\lambda^5\epsilon^{ab}L_{\Psi_a}N_{\Psi_b}(H_u)_H,
\end{equation}
where $d_5$, $d_q$, $d_l$, $h$ are the ${\cal O}(1)$ coefficients that are different from each other generically.
As we will discuss later, the $h$ term is very important for neutrino masses.

\subsection{Massless modes}

Once we write down the Yukawa couplings, we can calculate the massless combinations of  $\bar{\bm{5}}_i$ and $\bar{\bm{5}}_i'$.
We mainly follow the procedure given in \cite{arXiv:1005.1049}.
First, we fix ${\cal O}(1)$ coefficient of two VEVs:
\begin{equation}
\frac{\lambda^c\langle C\rangle}{\lambda^h\langle H\rangle}\equiv x\lambda^{0.5},
\end{equation}
where $x$ is a real ${\cal O}(1)$ coefficient.
Then, after the Higgs and flavon fields acquire VEVs, (\ref{eq:YH}) and (\ref{eq:YC}) induce following mass matrix for $\bm{5}_i$ and $(\bar{\bm{5}}_i', \bar{\bm{5}}_i)$:
\begin{equation}
\left(
\begin{array}{ccc|ccc}
0 & \alpha d_5\lambda^5 & 0 & 0 & fe^{i\rho}\lambda^{5.5} & ge^{i\rho}\lambda^{3.5}\\
-\alpha d_5\lambda^5 & c\lambda^4 & b\lambda^2 & fe^{i\rho}\lambda^{5.5} & 0 & 0\\
0 & b\lambda^2 & a & ge^{i\rho}\lambda^{3.5} & 0 & 0
\end{array}
\right)
\equiv(M_1\ M_2).
\label{eq:5_mass_matrix}
\end{equation}
Here, we reparametrize ${\cal O}(1)$ coefficients as $f\equiv xf'$ and $g\equiv xg'$.
Each power of $\lambda$ is determined by the corresponding $U(1)_A$ charge.
It is important to note that $\alpha=1$ for the colored Higgs components $(H^C, \bar{H}^{\bar{C}})$ of $\bm{5}$ and $\bar{\bm{5}}'$, and $\alpha=0$ for the doublet Higgs components $(H_u, H_d)$ of those, since $(1, 2)$ and $(2, 1)$ elements of (\ref{eq:5_mass_matrix}) originate from the $B-L$ conserving VEV of $A$.

In order to find the massless combinations, let us diagonalize the $3\times 6$ matrix (\ref{eq:5_mass_matrix}) as follows:
\begin{equation}
V^\dagger(M_1\ M_2)
\left(\begin{array}{cc}
U_{10}^H & U_{10}^0\\
U_{16}^H & U_{16}^0
\end{array}\right)=(M_H^{\rm{diag}}\ 0).
\label{eq:diagonalization}
\end{equation}
Here $V$ is a $3\times 3$ unitary matrix and
\begin{equation}
U\equiv\left(\begin{array}{cc}
U_{10}^H & U_{10}^0\\
U_{16}^H & U_{16}^0
\end{array}\right)
\end{equation}
is a $6\times 6$ unitary matrix, and they rotate $\bm{5}_i$ and $(\bar{\bm{5}}'_i, \bar{\bm{5}}_i)$ $(i=1,2,3)$ into their mass eigenstates, respectively.
Our task is finding matrices $U^0_{10}$ and $U^0_{16}$ which are related by
\begin{equation}
M_1U_{10}^0+M_2U_{16}^0=0.
\label{eq:diagonal_condition}
\end{equation}
According to the calculation in Appendix A, they become
\begin{equation}
U_{10}^0=\left(\begin{array}{ccc}
-\frac{a\alpha d_5(bg-af)}{(ac-b^2)^2}\lambda^{2.5}e^{i\rho} & 1 & {\cal O}(\lambda^{5.5})\\
\frac{bg-af}{ac-b^2}\lambda^{1.5}e^{i\rho} & \frac{a\alpha d_5}{ac-b^2}\lambda &{\cal O}(\lambda^{4.5})\\
-(\frac{g}{a}+\frac{b}{a}\frac{bg-af}{ac-b^2})\lambda^{3.5}e^{i\rho} & -\frac{b\alpha d_5}{ac-b^2}\lambda^3 & {\cal O}(\lambda^{6.5})
\end{array}\right),
\label{eq:U10}
\end{equation}
\begin{equation}
U_{16}^0=\left(\begin{array}{ccc}
1 & 0 & 0\\
{\cal O}(\lambda^6) & 0 & 1\\
-\frac{bg-af}{ac-b^2}\frac{\alpha d_5}{g}\lambda^3 & -\frac{\alpha d_5^2}{ac-b^2}\frac{a}{g}\lambda^{2.5}e^{-i\rho} & -\frac{f}{g}\lambda^2
\end{array}\right).
\label{eq:U16}
\end{equation}
The calculation is taken at the leading order, but $(U^0_{10})_{13, 23, 33}$ and $(U^0_{16})_{21}$ are calculated at the next-leading order because the corresponding leading terms are cancelled.
Therefore, the massless modes of $\bar{\bm{5}}$ can be written as
\begin{equation}
\bar{\bm{5}}^0_i\equiv(U_{10}^{0\dagger})_{ij}\bar{\bm{5}}'_j+(U_{16}^{0\dagger})_{ij}\bar{\bm{5}}_j
=\left(\begin{array}{c}
\bar{\bm{5}}_1+\cdots\\ \bar{\bm{5}}'_1+\cdots\\ \bar{\bm{5}}_2+\cdots
\end{array}\right).
\label{eq:massless}
\end{equation}

In order to calculate neutrino mass, we should also specify the MSSM Higgs doublets $H_u$ and $H_d$.
They are the combinations which remain massless at the GUT scale.
According to the Appendix A in \cite{Ishiduki:2009vr}, they are
\begin{equation}
H_u\subset \bm{5}_H
\end{equation}
\begin{equation}
H_d\subset \bar{\bm{5}}'_H+\beta_He^{-i\rho}\lambda^{0.5}\bar{\bm{5}}_C.
\label{eq:HD}
\end{equation}
Here $\beta_H$ is a real ${\cal O}(1)$ coefficient and the phase $e^{-i\rho}$ comes from VEVs of the $F$ and $Z_4$\footnote{If we choose $z_2=-1$ (or $z_2=-2$), then the term $\bar{C}'Z_2^5C$ (or $\bar{C}'Z_2^2C$) changes the phase in (\ref{eq:HD}) into arbitrary.
For detailed discussion of the Higgs sector, see the Appendix A in \cite{Ishiduki:2009vr}.}.
As mentioned in \cite{Ishiduki:2009vr}, the second term in (\ref{eq:HD}) is important to ensure the KM phase and make all charged leptons massive.

\subsection{Neutrino mass}

Now we calculate neutrino masses in our model.
In this subsection we explicitly write the cutoff scale $\Lambda$.
First, we compute the Dirac neutrino mass matrix. Since we have 6 right-handed neutrino,
$\bm{1}_i$ and $\bm{1}'_i$, from the interactions ${\bf 10}_i{\bf 1}'_j{\bf 10}_H$
and ${\bf 16}_i{\bf 16}_j{\bf 10}_H$,
$3\times 6$ Dirac neutrino Yukawa matrix $Y_{\nu_D}$ is given by
\begin{equation}
Y_{\nu_D}= (Y_{\nu_D1'}\ Y_{\nu_D1})=(U_{10}^{0T}(Y^H_{1'})^T\ U_{16}^{0T}(Y^H_1)^T),
\label{eq:Dirac_mass}
\end{equation}
where
\begin{equation}
Y^H_{1'}=\left(\begin{array}{ccc}
0 & h\lambda^5 & 0\\
-h\lambda^5 & c\lambda^4 & b\lambda^2\\
0 & b\lambda^2 & a
\end{array}\right), \quad
Y^H_1=\left(\begin{array}{ccc}
0 & -\frac{3}{2}d_l\lambda^5 & 0\\
\frac{3}{2}d_l\lambda^5 & c\lambda^4 & b\lambda^2\\
0 & b\lambda^2 & a
\end{array}\right).
\end{equation}
It is also important that $\alpha=0$ in the mixing matrices (\ref{eq:U10}) (\ref{eq:U16}).
Using these facts, we can express the Dirac mass as follows:
\begin{equation}
Y_{\nu_D}=\left(\begin{array}{ccc|ccc}
h\frac{bg-af}{ac-b^2}\lambda^{6.5}e^{i\rho} & -f\lambda^{5.5}e^{i\rho} & -g\lambda^{3.5}e^{i\rho} & 0 & -\frac{3}{2}d_l\lambda^5 & 0\\
0 & -h\lambda^5 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & \frac{3}{2}d_l\lambda^5 & (c-\frac{bf}{g})\lambda^4 & \frac{bg-af}{g}\lambda^2
\end{array}\right).
\end{equation}
Note that the second generation would be massless without $h$.
The contribution from the term $\Psi^a\bar{H}H\Psi_aH$ is essential for obtaining the realistic neutrino sector.

Second, we introduce the $6\times 6$ Majorana right-handed neutrino mass matrix.
Since each $\bm{27}$ has two $\bm{1}$'s, the Majorana mass has following three types of contribution:
\begin{eqnarray}
W & = & \frac{(Y_{1'1'})_{ij}}{\Lambda}\Psi_i\Psi_j\bar{H}\bar{H}+\frac{(Y_{1'1})_{ij}}{\Lambda}\Psi_i\Psi_j\bar{H}\bar{C}+\frac{(Y_{11})_{ij}}{\Lambda}\Psi_i\Psi_j\bar{C}\bar{C}\nonumber\\
 & \to &  \frac{(Y_{1'1'})_{ij}}{\Lambda}\bm{1}'_i\bm{1}'_j\langle\bm{1}'_{\bar{H}}\rangle\langle\bm{1}'_{\bar{H}}\rangle+\frac{(Y_{1'1})_{ij}}{\Lambda}\bm{1}'_i\bm{1}_j\langle\bm{1}'_{\bar{H}}\rangle\langle\bm{1}_{\bar{C}}\rangle+\frac{(Y_{11})_{ij}}{\Lambda}\bm{1}_i\bm{1}_j\langle\bm{1}_{\bar{C}}\rangle\langle\bm{1}_{\bar{C}}\rangle.
 \end{eqnarray}
Then the Majorana mass term is $6\times 6$ matrix
\begin{equation}
(\bm{1}'_i\ \bm{1}_i)\left(Y_{N_R^c}\right)_{ij}\left(\begin{array}{c}\bm{1}'_j\\ \bm{1}_j\end{array}\right)\frac{\langle\bar{H}\rangle^2}{\Lambda},\qquad
Y_{N_R}=\left(\begin{array}{cc}
Y_{1'1'} & Y_{1'1}\\
Y_{1'1}^T & Y_{11}
\end{array}\right).
\end{equation}
Here, we parametrize $Y_{N_R}^{-1}$ with ${\cal O}(1)$ coefficients as
\begin{equation}
Y_{N_R}^{-1}=\left(\begin{array}{ccc|ccc}
N_{11}\lambda^{-13} & N_{12}\lambda^{-12} & N_{13}\lambda^{-10} & N_{14}\lambda^{-12.5} & N_{15}\lambda^{-11.5} & N_{16}\lambda^{-9.5}\\
N_{12}\lambda^{-12} & N_{22}\lambda^{-11} & N_{23}\lambda^{-9} & N_{24}\lambda^{-11.5} & N_{25}\lambda^{-10.5} & N_{26}\lambda^{-8.5}\\
N_{13}\lambda^{-10} & N_{23}\lambda^{-9} & N_{33}\lambda^{-7} & N_{34}\lambda^{-9.5} & N_{35}\lambda^{-8.5} & N_{36}\lambda^{-6.5}\\
\hline
N_{14}\lambda^{-12.5} & N_{24}\lambda^{-11.5} & N_{34}\lambda^{-9.5} & N_{44}\lambda^{-12} & N_{45}\lambda^{-11} & N_{46}\lambda^{-9}\\
N_{15}\lambda^{-11.5} & N_{25}\lambda^{-10.5} & N_{35}\lambda^{-8.5} & N_{45}\lambda^{-11} & N_{55}\lambda^{-10} & N_{56}\lambda^{-8}\\
N_{16}\lambda^{-9.5} & N_{26}\lambda^{-8.5} & N_{36}\lambda^{-6.5} & N_{46}\lambda^{-9} & N_{56}\lambda^{-8} & N_{66}\lambda^{-6}\\
\end{array}\right),
\end{equation}
where $N_{ij}$ are ${\cal O}(1)$ complex parameters.

Finally we can calculate the neutrino mass using the seesaw mechanism.
The result is
\begin{equation}
M_\nu\equiv Y_\nu\frac{\langle H_u\rangle^2}{\Lambda}, \qquad Y_\nu  =  Y_{\nu_D}Y_{N_R}^{-1}Y_{\nu_D}^T=\left(\begin{array}{ccc}
y_{11}\lambda^{-1} & y_{12}\lambda^{-1.5} & y_{13}\lambda^{-2}\\
y_{12}\lambda^{-1.5} & y_{22}\lambda^{-2} & y_{23}\lambda^{-2.5}\\
y_{13}\lambda^{-2} & y_{23}\lambda^{-2.5} & y_{33}\lambda^{-3}\\
\end{array}\right),
\end{equation}
where $y_{ij}$ are complicate combinations of ${\cal O}(1)$ coefficient:
\[
y_{11}=N_{11}(h\frac{bg-af}{ac-b^2})^2e^{2i\rho}+N_{22}f^2e^{2i\rho}+N_{33}g^2e^{2i\rho}+N_{55}(-\frac{3}{2}d_l)^2
\]
\[
\qquad\qquad -2N_{12}fh\frac{bg-af}{ac-b^2}e^{2i\rho}-2N_{13}gh\frac{bg-af}{ac-b^2}e^{2i\rho}-2N_{15}h(-\frac{3}{2}d_l)\frac{bg-af}{ac-b^2}
\]
\begin{equation}
\qquad\qquad +2N_{23}fge^{2i\rho}-2N_{25}f(-\frac{3}{2}d_l)e^{i\rho}-2N_{35}g(-\frac{3}{2}d_l)e^{i\rho},
\end{equation}
\begin{equation}
y_{12}=-h\left[N_{12}h\frac{bg-af}{ac-b^2}e^{i\rho}-N_{22}fe^{i\rho}-N_{23}ge^{i\rho}+N_{25}(-\frac{3}{2}d_l)\right],
\end{equation}
\[
y_{13}=h\frac{bg-af}{ac-b^2}e^{i\rho}\left[N_{14}(\frac{3}{2}d_l)+N_{15}(\frac{ac-b^2}{a}+\frac{bg-af}{b}\frac{b}{a})+N_{16}\frac{bg-af}{g}\right]
\]
\[
-fe^{i\rho}\left[N_{24}(\frac{3}{2}d_l)+N_{25}(\frac{ac-b^2}{a}+\frac{bg-af}{b}\frac{b}{a})+N_{26}\frac{bg-af}{g}\right]
\]
\[
-ge^{i\rho}\left[N_{34}(\frac{3}{2}d_l)+N_{35}(\frac{ac-b^2}{a}+\frac{bg-af}{b}\frac{b}{a})+N_{36}\frac{bg-af}{g}\right]
\]
\begin{equation}
-\frac{3}{2}d_l\left[N_{45}(\frac{3}{2}d_l)+N_{55}(\frac{ac-b^2}{a}+\frac{bg-af}{b}\frac{b}{a})+N_{56}\frac{bg-af}{g}\right],
\end{equation}
\begin{equation}
y_{22}=h^2N_{22},
\end{equation}
\begin{equation}
y_{23}=-h\left[N_{24}(\frac{3}{2}d_l)+N_{25}(\frac{ac-b^2}{a}+\frac{bg-af}{b}\frac{b}{a})+N_{26}\frac{bg-af}{g}\right],
\end{equation}
\[
y_{33}=N_{44}(\frac{3}{2}d_l)^2+N_{55}(\frac{ac-b^2}{a}+\frac{bg-af}{b}\frac{b}{a})^2+2N_{46}(\frac{3}{2}d_l)\frac{bg-af}{g}
\]
\begin{equation}
+2N_{56}\frac{bg-af}{g}(\frac{ac-b^2}{a}+\frac{bg-af}{b}\frac{b}{a}).
\end{equation}

These masses give $\Delta m_{12}^2/\Delta m_{23}^2\sim \lambda^2=4.8\times 10^{-2}$, which
is consistent with the experimental facts $\Delta m_{12}^2/\Delta m_{23}^2\simeq 3.1\times 10^{-2}$ \cite{PDG} up to the combination of ${\cal O}(1)$ coefficients.

\subsection{MNS matrix}

We can also calculate the MNS matrix in our model.
First, charged lepton Yukawa matrix is given \cite{Ishiduki:2009vr} as
\begin{equation}
Y_e=\left(\begin{array}{ccc}
[\frac{bg-af}{ac-b^2}(f'+\frac{bg'}{a})-\frac{gg'}{a}]\beta_He^{2i\delta}\lambda^6 & \frac{3}{2}d_l\lambda^5 & 0\\
0 & \beta_Hf'e^{i\delta}\lambda^{4.5} & \beta_Hg'e^{i\delta}\lambda^{2.5}\\
-\frac{3}{2}d_l\lambda^5 & (\frac{ac-b^2}{a}+\frac{bg-af}{g}\frac{b}{a})\lambda^4 & \frac{bg-af}{g}\lambda^2
\end{array}\right).
\end{equation}
Then we can calculate MNS matrix.
Following the diagonal procedure given in \cite{King:2002nf}, it is computed, at the leading order,
\begin{equation}
V_{\rm{MNS}}=\left(\begin{array}{ccc}
1 & v_{12}\lambda^{0.5} & v_{13}\lambda\\
-v_{12}^\ast\lambda^{0.5} & 1 & v_{23}\lambda^{0.5}\\
(v_{12}^\ast v_{23}^\ast -v_{13}^\ast)\lambda & -v_{23}^\ast\lambda^{0.5} & 1
\end{array}\right),
\end{equation}
where $v_{12}, v_{13}$, and $v_{23}$ are written as
\begin{equation}
v_{12}=\frac{\frac{3}{2}d_l}{\beta_H}\frac{1}{1-gg'\frac{bf+c}{bg-af}}-\frac{y_{12}y_{33}-y_{13}y_{23}}{y_{22}y_{33}-y_{23}^2},
\end{equation}
\begin{equation}
v_{13}=-\frac{y_{13}}{y_{33}}-v_{23}^\ast\frac{y_{12}y_{33}-y_{13}y_{23}}{y_{22}y_{33}-y_{23}^2},
\end{equation}
\begin{equation}
v_{23}=\frac{\beta_Hgg'}{bg-af}-\frac{y_{23}}{y_{33}}.
\end{equation}

This result can be compared with experimental values.
The model says $\tan\theta_{12}=V_{12}/V_{11}\sim \lambda^{0.5}=0.47$, $\tan\theta_{23}=V_{23}/V_{33}\sim \lambda^{0.5}=0.47$ up to the combination of ${\cal O}(1)$ coefficients.
These are consistent with experiment $\tan\theta_{12}\simeq 0.68$, $\tan\theta_{23}\geq 0.747$ \cite{PDG}.
It is also interesting that recent T2K result \cite{Abe:2011sj} $0.087<\sin\theta_{13}<0.275$ (assuming $\delta_{CP}=0$) supports our result $\sin\theta_{13}=|V_{13}|\sim \lambda=0.22$, up to the combination of ${\cal O}(1)$ coefficients.

\subsection{The role of the $\Psi\bar{H}H\Psi H$ terms}

As we have seen, the terms $\Psi^a\bar{H}H\Psi_a H$ played the important role for the
non-vanishing second generation neutrino mass.
Here we show that this type of higher-dimensional operators do not affect other structures of this model, for example, the quark masses and charged lepton masses.

First, we classify $SO(10)$ invariant Yukawa interaction derived from $E_6$ invariant Yukawa term $\Psi_i\Psi_jH$ (or $\Psi_i\Psi_jC$):
\begin{equation}
\bm{27}_i\bm{27}_j\bm{27}_{H,C}=\bm{16}_i\bm{16}_j\bm{10}_{H,C}+\bm{10}_i\bm{10}_j\bm{1}_{H,C}+\bm{16}_i\bm{10}_j\bm{16}_{H,C}+\bm{10}_i\bm{1}_j\bm{10}_{H,C}.
\label{eq:E6toSO(10)}
\end{equation}
Note that these terms have common ${\cal O}(1)$ coefficients, and all terms are symmetric between $i$ and $j$, although at $SO(10)$ level, the coefficients of the terms
$\bm{16}_i\bm{10}_j\bm{16}_{H,C}$ and $\bm{10}_i\bm{1}_j\bm{10}_{H,C}$ do not have to be taken as symmetric.

This property changes if we include higher-dimensional operators like $\Psi_i\bar{H}H\Psi_jH$ or $\Psi_i\bar{H}H\Psi_jC$.
Each terms in the right-hand-side of (\ref{eq:E6toSO(10)}) receives extra contribution, which generically differs from each other.
Therefore, they cannot have common ${\cal O}(1)$ coefficients, and the number of parameters increases.

Fortunately, in our model, only (1,2) and (2,1) elements of $Y^H$ have room of $U(1)_A$ charge for including $\bar{H}H$, and in other Yukawa elements, SUSY-zero forbids such higher-dimensional operators.
Since these elements are anti-symmetric due to $SU(2)_F$, the extra contributions $\bm{16}_i\bm{16}_j\bm{10}_H$ and $\bm{10}_i\bm{10}_j\bm{1}_H$ vanish.
Therefore, the higher-dimensional operator including $\bar{H}H$ only affects the Dirac neutrino mass through $\bm{10}_i\bm{1}_j\bm{10}_H$, while the quark sector and charged lepton sector is unchanged.

According to the previous paper \cite{Ishiduki:2009vr}, the model has characteristic predictions $V_{ub}\sim \lambda^4$ and $V_{cb}y_b=y_c$ at the GUT scale.
We will show in Appendix B that these predictions are not spoiled even if the model generically contains such higher-dimensional operators. Sufficient conditions for these
predictions are $\langle A\rangle\propto Q_{B-L}$ and that the (2,2), (2,3), (3,2), and (3,3)
components of $Y^C$ are vanishing. Such conditions are satisfied in more general $E_6$ GUTs
with family symmetry. The former condition should be satisfied to solve the doublet-triplet
splitting problem, and the latter can be satisfied by the SUSY zero mechanism if the
anomalous $U(1)_A$ charge of $C$ is smaller than that of $H$.
The discrete symmetry for solving the SUSY CP problem is not necessary.
Therefore, these two predictions are rather general ones. The first prediction
$V_{ub}\sim \lambda^4$ has been tested by B-factory experiments, and the second
prediction $V_{cb}y_b=y_c$ can be tested in future experiments by measuring
the $\tan\beta\equiv \langle H_u\rangle/\langle H_d\rangle $.

\section{Summary and discussion}

In this paper we conducted a detail calculation of the neutrino sector in $E_6\times SU(2)_F$ SUSY GUT with spontaneous CP violation.
Originally, $E_6$ GUT can explain the realistic neutrino sector as well as quark and charged lepton sector.
However, the previous paper reported the problem about the neutrino mass because of the new discrete symmetry, which is introduced in order to solve the SUSY CP problem.
We computed the neutrino masses and the MNS matrix explicitly and found that the term like $\Psi_i\bar{H}H\Psi_jH$, which have not been considered in the previous paper, is important to make the second generation massive.
These higher dimensional operators only contribute in the neutrino sector, so the structures of quarks and charged leptons, which calculated in the previous paper, are kept valid.

Our result reproduces experimental value well.
$\Delta m_{12}^2/\Delta m_{23}^2$, $\tan\theta_{12}$, $\tan\theta_{23}$ and $\sin\theta_{13}$ are all consistent with experimental values up to the combination of ${\cal O}(1)$ coefficients.
Combining the previous paper and our result, the concrete model reproducing realistic masses and mixings for all the SM fermions is constructed. Note that even if the model has the
``modified universal sfermion mass spectrum", we have no SUSY CP problem.

In this model, because of the strong constraint of Yukawa structure, there are characteristic predictions $V_{ub}\sim \lambda^4$ and $V_{cb}y_b=y_c$ at the GUT scale \cite{Ishiduki:2009vr}.
These predictions are valid even if we generically include the higher-dimensional operators $\Psi_i\bar{H}H\Psi_jH$ and $\Psi_i\bar{H}H\Psi_jC$.
Unfortunately, we could  get no characteristic prediction in the neutrino sector because of huge number of parameters in the Majorana neutrino mass terms.

\section*{Acknowledgments}
N.M. is supported in part by Grants-in-Aid for Scientific Research from
MEXT of Japan.
This work was partially supported by the Grand-in-Aid for Nagoya
University Global COE Program,
``Quest for Fundamental Principles in the Universe:
from Particles to the Solar System and the Cosmos'',
from the MEXT of Japan.

\section{Diagonalization procedure of the superheavy Yukawa matrix}

In this appendix, we derive the expression for the two matrices $U^0_{10}$ (\ref{eq:U10}) and $U^0_{16}$ (\ref{eq:U16}) which describe the massless $\bar{\bm{5}}^0_i$ as the combination of $\bar{\bm{5}}_i$ and $\bar{\bm{5}}'_i$ as (\ref{eq:massless}).
All calculation is performed at the leading order.

First, we show the strategy of finding $U$ which diagonalize the superheavy Yukawa matrix as (\ref{eq:diagonalization}). In the following, we assume that $M_1$ has rank 3, and therefore
we have a inverse matrix $M_1^{-1}$.
Then we calculate $M_1^{-1}M_2$ and parametrize it as
\begin{equation}
M_1^{-1}M_2\equiv C\equiv \left(\begin{array}{ccc}
c_{11}\lambda^{0.5} & c_{12}\lambda^{-0.5} & c_{13}\lambda^{-2.5}\\
c_{21}\lambda^{1.5} & c_{22}\lambda^{0.5} & c_{23}\lambda^{-1.5}\\
c_{31}\lambda^{3.5} & c_{32}\lambda^{2.5} & c_{33}\lambda^{0.5}
\end{array}\right).
\end{equation}
Here $c_{ij}$ are the combination of ${\cal O}(1)$ coefficients.
After expressing $U^0_{10}$ and $U^0_{16}$ in terms of $c_{ij}$, we will substitute concrete parameters in them.
Then we rotate $M_1^{-1}(M_1\ M_2)=(1_{3\times 3}\ C)$ as
\begin{equation}
(1_{3\times 3}\ C)U'=(C'\ 0_{3\times 3}),
\end{equation}
where $U'$ is a $6\times 6$ unitary matrix
\begin{equation}
U'\equiv\left(\begin{array}{cc}
U_1 & U_3\\
U_2 & U_4
\end{array}\right)
\end{equation}
and $C'$ is a $3\times 3$ matrix.
If we find unitary matrices $V$ and $V'$ which diagonalize $M_1C'$ as
\begin{equation}
V^\dagger M_1C' V'=M_H^{\rm{diag}},
\end{equation}
then we can express the matrix $U$ as
\begin{equation}
U\equiv \left(\begin{array}{cc}
U_{10}^H & U_{10}^0\\
U_{16}^H & U_{16}^0
\end{array}\right)
=U'\left(\begin{array}{cc}
V' & 0\\
0 & T
\end{array}\right)
=\left(\begin{array}{cc}
U_1V' & U_3T\\
U_2V' & U_4T
\end{array}\right).
\end{equation}
Here $T$ is a unitary matrix which corresponds to the degree of freedom of the rotation for the three 0's with keeping (\ref{eq:diagonalization}).

Since we are only interested in $U^0_{10}$ and $U^0_{16}$ in this paper, our task is to find the matrix $U'$.
After tedious calculation, we can find $C'$ and $U'$ as
\begin{equation}
(1_{3\times 3}\ C)U'=\left(\begin{array}{ccc|ccc}
c_{31}\lambda^{-2.5} & 0 & 0 & 0 & 0 & 0\\
c_{32}\lambda^{-1.5} & 1 & 0 & 0 & 0 & 0\\
c_{33}\lambda^{0.5} & (c_{22}-\frac{c_{12}c_{23}}{c_{13}})(c_{32}-\frac{c_{12}c_{33}}{c_{13}})\lambda^{3} & 1 & 0 & 0 & 0
\end{array}\right),
\end{equation}
\[
U'=\left(\begin{array}{ccc|}
\frac{1}{c_{13}}\lambda^{2.5} & -\frac{c_{23}}{c_{13}}\lambda & -\frac{c_{33}}{c_{13}}\lambda^3\\
0 & 1 & -(c_{22}-\frac{c_{12}c_{23}}{c_{13}})(c_{32}-)\lambda^3\\
0 & 0 & 1\\
\hline
\frac{c_{11}}{c_{13}}\lambda^3 & (c_{21}-\frac{c_{11}c_{23}}{c_{13}})\lambda^{1.5} & (c_{31}-\frac{c_{11}c_{33}}{c_{13}})\lambda^{3.5}\\
\frac{c_{12}}{c_{13}}\lambda^2 & (c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^{0.5} & (c_{32}-\frac{c_{12}c_{33}}{c_{13}})\lambda^{2.5}\\
1 & -\frac{c_{12}}{c_{13}}(c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^{2.5} & -\frac{c_{12}}{c_{13}}(c_{32}-\frac{c_{12}c_{33}}{c_{13}})\lambda^{4.5}
\end{array}\right.
\]
\begin{equation}
\left.\begin{array}{|ccc}
\frac{c_{23}}{c_{13}}(c_{21}-\frac{c_{11}c_{23}}{c_{13}})\lambda^{2.5} & 1 & 0\\
-(c_{21}-\frac{c_{11}c_{23}}{c_{13}})\lambda^{1.5} & \frac{c_{23}}{c_{13}}\lambda & -(c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^{0.5}\\
-(c_{31}-\frac{c_{11}c_{33}}{c_{13}})\lambda^{3.5} & \frac{c_{33}}{c_{13}}\lambda^3 & -(c_{32}-\frac{c_{12}c_{33}}{c_{13}})\lambda^{2.5}\\
\hline
1 & 0 & 0\\
-(c_{21}-\frac{c_{11}c_{23}}{c_{13}})(c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^2 & \frac{c_{23}}{c_{13}}(c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^{1.5} & 1\\
-\frac{c_{11}}{c_{13}}\lambda^3 & -\frac{1}{c_{13}}\lambda^{2.5} & -\frac{c_{12}}{c_{13}}\lambda^2
\end{array}\right).
\end{equation}
We choose a basis which $(U^0_{16})_{12}$,  $(U^0_{16})_{13}$ and  $(U^0_{16})_{22}$ are zero by the rotation
\begin{equation}
T=\left(\begin{array}{ccc}
1 & 0 & 0\\
0 & 1 & \frac{c_{23}}{c_{13}}(c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^{1.5}\\
0 & -\frac{c_{23}}{c_{13}}(c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^{1.5} & 1
\end{array}\right).
\end{equation}
After that, we can get $U^0_{10}$ and $U^0_{16}$ in terms of $c_{ij}$ as
\begin{equation}
U_{10}^0=\left(\begin{array}{ccc}
\frac{c_{23}}{c_{13}}(c_{21}-\frac{c_{11}c_{23}}{c_{13}})\lambda^{2.5} & 1 & \frac{c_{23}}{c_{13}}(c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^{1.5}\\
-(c_{21}-\frac{c_{11}c_{23}}{c_{13}})\lambda^{1.5} & \frac{c_{23}}{c_{13}}\lambda & -(c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^{0.5}\\
-(c_{31}-\frac{c_{11}c_{33}}{c_{13}})\lambda^{3.5} & -\frac{c_{33}}{c_{13}}\lambda^{3} & (c_{32}-\frac{c_{12}c_{33}}{c_{13}})\lambda^{2.5}
\end{array}\right),
\end{equation}
\begin{equation}
U_{16}^0=\left(\begin{array}{ccc}
1 & 0 & 0\\
-(c_{21}-\frac{c_{11}c_{23}}{c_{13}})(c_{22}-\frac{c_{12}c_{23}}{c_{13}})\lambda^2 & 0 & 1\\
-\frac{c_{11}}{c_{13}}\lambda^{3} & -\frac{1}{c_{13}}\lambda^{2.5} & -\frac{c_{12}}{c_{13}}\lambda^{2}
\end{array}\right).
\end{equation}
We can check these matrices satisfy the relation (\ref{eq:diagonal_condition}) at the leading order.
Finally, we obtain (\ref{eq:U10}) and (\ref{eq:U16}) by substituting the concrete expressions in $c_{ij}$:
\begin{equation}
c_{11}=\frac{bg-af}{a\alpha d_5}, \ c_{12}=\frac{ac-b^2}{\alpha d_5^2}\frac{f}{a}, \ c_{13}=\frac{ac-b^2}{\alpha d_5^2}\frac{g}{a}
\end{equation}
\begin{equation}
c_{21}=0, \ c_{22}=\frac{f}{\alpha d_5}, \ c_{23}=\frac{g}{\alpha d_5}
\end{equation}
\begin{equation}
c_{31}=\frac{g}{a}, \ c_{32}=-\frac{bf}{a\alpha d_5}, \ c_{33}=-\frac{bg}{a\alpha d_5}
\end{equation}

\section{The condition of the predictions}

In section 3, we obtained the realistic neutrino sector by introducing the higher-dimensional operator $\Psi^a\bar{H}H\Psi_aH$, and saw that such operators cannot be written in other
 elements of $Y^H$ and $Y^C$ because of the SUSY zero mechanism.
In this appendix, we will clarify the conditions of the characteristic predictions $V_{ub}\sim \lambda^4$ and $V_{cb}y_b=y_c$, and show that the conditions can be satisfied even if we generically include the higher-dimensional operators $\Psi_i\bar{H}H\Psi_jH$ and
$\Psi_i\bar{H}H\Psi_jC$.

In order to see the essence of the predictions, let us choose the basis where the up-type Yukawa matrix $Y_u$ is diagonal.
In this basis, $V_{ub}$ is simply written only by the down-type Yukawa matrix as $V_{ub}\sim (Y_d)_{13}/(Y_d)_{33}$.
The relation $V_{cb}y_b=y_c$ is also simplified as $(Y_d)_{23}=(Y_u)_{22}$.
Therefore, we focus on the quantities $(Y_d)_{13}$ and $(Y_d)_{23}$.

Let us determine the third generation of massless $\bar{\bm{5}}$ combination $\bar{\bm{5}}^0_3$, which is mainly $\bar{\bm{5}}_2$, in this basis.
Since we can choose the basis where $\bar{\bm{5}}^0_3$ does not contain $\bar{\bm{5}}_1$ and $\bar{\bm{5}}'_1$, we parametrize
\begin{equation}
\bar{\bm{5}}^0_3\equiv\frac{1}{\sqrt{1+|\alpha|^2+|\beta|^2+|\gamma|^2}}(\bar{\bm{5}}_2+\alpha\bar{\bm{5}}'_2+\beta\bar{\bm{5}}'_3+\gamma\bar{\bm{5}}_3).
\end{equation}
As we saw in Section 3.2, the massless modes are determined by diagonalizing the $3\times 6$ mass matrix $(M_1\ M_2)$.
Both $Y_u$ and $M_1$ is obtained from $Y^H$, but here we consider general case where these two matrices cannot be diagonalized simultaneously.
In this case, $M_1$ is the form
\begin{equation}
M_1\sim
\left(\begin{array}{ccc}
1 & \lambda & \lambda^3\\
\lambda & 1 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\left(\begin{array}{ccc}
\lambda^6 & \lambda^5 & \lambda^3\\
\lambda^5 & \lambda^4 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\left(\begin{array}{ccc}
1 & \lambda & \lambda^3\\
\lambda & 1 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\sim
\left(\begin{array}{ccc}
\lambda^6 & \lambda^5 & \lambda^3\\
\lambda^5 & \lambda^4 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right).
\end{equation}
On the other hand, $M_2$ is obtained from $Y^C$.
Again, we consider general case
\begin{equation}
M_2\sim \lambda^{0.5}
\left(\begin{array}{ccc}
1 & \lambda & \lambda^3\\
\lambda & 1 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\left(\begin{array}{ccc}
\lambda^6 & \lambda^5 & \lambda^3\\
\lambda^5 & \lambda^4 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\left(\begin{array}{ccc}
1 & \lambda & \lambda^3\\
\lambda & 1 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\sim
\left(\begin{array}{ccc}
\lambda^{6.5} & \lambda^{5.5} & \lambda^{3.5}\\
\lambda^{5.5} & \lambda^{4.5} & \lambda^{2.5}\\
\lambda^{3.5} & \lambda^{2.5} & \lambda^{0.5}
\end{array}\right).
\end{equation}
Then we can obtain the massless combination of $\bar{\bm{5}}^0_3$ by solving
\begin{equation}
(M_1\ M_2)\left(\begin{array}{c}0\\ \alpha\\ \beta\\ 0\\ 1\\ \gamma\end{array}\right)=0.
\end{equation}
The solution becomes generically
\begin{equation}
\alpha\sim\lambda^{0.5}, \ \beta\sim\lambda^{2,5}, \ \gamma\sim\lambda^2.
\label{eq:5bar_solution}
\end{equation}

Let us evaluate $(Y_d)_{13}$ and $(Y_d)_{23}$ to obtain the conditions for
$V_{ub}\sim \lambda^4$ and $V_{cb}y_b=y_c$.
The down-type Yukawa matrix $Y_d$ consists of two types of interaction: one is the interaction between $\bm{10}$ and $\bar{\bm{5}}$ via $Y^H_{\rm{down}}$, the other is between $\bm{10}$ and $\bar{\bm{5}}'$ via $\lambda^{0.5}Y^C$. Here we denote the matrix $Y^H$ appearing in the
down-type quark Yukawa matrix as $Y^H_{\rm{down}}$.
$Y^C$ is written in this basis as
\begin{equation}
Y^C\sim
\left(\begin{array}{ccc}
1 & \lambda & \lambda^3\\
\lambda & 1 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\left(\begin{array}{ccc}
\lambda^5 & \lambda^4 & \lambda^2\\
\lambda^4 & \lambda^3 & \lambda\\
\lambda^2 & \lambda & \lambda^{-1}
\end{array}\right)
\left(\begin{array}{ccc}
1 & \lambda & \lambda^3\\
\lambda & 1 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\sim
\left(\begin{array}{ccc}
\lambda^{5} & \lambda^{4} & \lambda^{2}\\
\lambda^{4} & \lambda^{3} & \lambda\\
\lambda^{2} & \lambda & \lambda^{-1}
\end{array}\right).
\end{equation}
For example, the leading contributions for
$(Y_d)_{13}$ are $(Y^H_{\rm{down}})_{12}$, $\gamma(Y^H_{\rm{down}})_{13}$,
$\alpha\lambda^{0.5}(Y^C)_{12}$, and $\beta\lambda^{0.5}(Y^C)_{13}$. They are of order $\lambda^5$, and therefore $V_{ub}$ becomes ${\cal O}(\lambda^3)$. In order to obtain
$V_{ub}\sim \lambda^4$, all the leading contributions must vanish. The first two contributions
vanishes if $\langle A\rangle$ is proportional to $Q_{B-L}$,
which plays an important role in solving the doublet-triplet splitting problem.
This is because $Y^H_{\rm{down}}$ is the same as $Y_u$ and therefore off-diagonal elements
of $Y^H_{\rm{down}}$ are vanishing in the basis in which $Y_u$ is diagonal.
Another important point is that the $U(1)_A$ charge of $C$ is smaller than that of $H$ by one.
This nature forbids the (2,2), (2,3), (3,2) and (3,3) elements (before rotating the basis) of $Y^C$ by the SUSY-zero mechanism\footnote{In our model, the (1,1) entry of $Y^C$ is also forbidden by the discrete symmetry.}.
Therefore, after rotating, $Y^C$ becomes
\begin{equation}
Y^C\sim
\left(\begin{array}{ccc}
1 & \lambda & \lambda^3\\
\lambda & 1 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\left(\begin{array}{ccc}
0 & \lambda^4 & \lambda^2\\
\lambda^4 & 0 & 0\\
\lambda^2 & 0 & 0
\end{array}\right)
\left(\begin{array}{ccc}
1 & \lambda & \lambda^3\\
\lambda & 1 & \lambda^2\\
\lambda^3 & \lambda^2 & 1
\end{array}\right)
\sim
\left(\begin{array}{ccc}
\lambda^{5} & \lambda^{4} & \lambda^{2}\\
\lambda^{4} & \lambda^{5} & \lambda^{3}\\
\lambda^{2} & \lambda^{3} & \lambda^{5}
\end{array}\right).
\label{eq:YC_small}
\end{equation}
This changes the determination of massless $\bar{\bm{5}}^0_3$ composition (\ref{eq:5bar_solution}) into
\begin{equation}
\alpha\sim\lambda^{2.5}, \ \beta\sim\lambda^{4,5}, \ \gamma\sim\lambda^2,
\end{equation}
so the terms containing $\alpha$ and $\beta$ become smaller.
The above two points are the essential points for $V_{ub}=0$ at the leading order.

Next, we see $(Y_d)_{23}$.
The main contributions are from $\gamma(Y^H_{\rm{down}})_{23}$, $(Y^H_{\rm{down}})_{22}$, $\alpha\lambda^{0.5}(Y^C)_{22}$ and $\beta\lambda^{0.5}(Y^C)_{23}$, but the first contribution
is vanishing if $\langle A\rangle$ is proportional to $Q_{B-L}$\footnote{
If the adjoint Higgs $A$ couples only to the (1,2) (and (2,1)) components as in the model we
are considering, then this condition that  $\langle A\rangle$ is proportional to $Q_{B-L}$
is not necessary, because $Y^H_{\rm{down}}$ is almost $Y_u$ and therefore
$\gamma(Y^H_{\rm{down}})_{23}$ becomes very small in the basis in which $Y_u$ is diagonal.
}.
The second term is nothing but $(Y_u)_{22}$, so the relation $V_{cb}y_b=y_c$ is realized
when $\alpha$ and $\beta$ become smaller due to the SUSY-zero mechanism as noted above.

How does above discussion changed if we generically include the higher-dimensional operators $\Psi_i\bar{H}H\Psi_jH$ and $\Psi_i\bar{H}H\Psi_jH$?
First, $Y_u$ and $Y^H_{\rm{down}}$ are derived from same expression $\bm{16}_i\bm{16}_j\bm{10}_H$ at $SO(10)$ level, therefore simultaneous diagonalizability of $Y_u$ and $Y^H_{\rm{down}}$ does not affected by the higher-dimensional operators.
Second, the form of $Y^C$ with the SUSY-zero mechanism (\ref{eq:YC_small}) does not changed because adding $\bar{H}H$ ($\bar{h}+h<0$) cannot revive the terms which was forbidden by the SUSY-zero mechanism.
Therefore, the characteristic predictions $V_{ub}\sim\lambda^4$ and $V_{cb}y_b=y_c$ do not affected whether or not we include such higher-dimensional operators.

What becomes obvious in this appendix is that the conditions for $V_{ub}\sim \lambda^4$ and
$V_{cb}y_b=y_c$ can be satisfied in the more general $E_6$ GUTs with family symmetry.
The discrete symmetry for solving the SUSY CP problem is not necessary. One prediction
$V_{ub}\sim \lambda^4$ has been already tested by the B-factory experiments.
The other prediction $V_{cb}y_b=y_c$ at the GUT scale means that comparably small
$\tan\beta\equiv \langle H_u\rangle/\langle H_d\rangle $, which can be tested in future
experiments.

redpajama_set_name: RedPajamaArXiv


Saigon's fashionable crowd love this sophisticated art-café that evokes French elegance and old-world glamour. A cosy setting for business lunches or afternoon tea with friends and family, either indoors or out on the shady terrace.
Travellers can take a well-deserved break in the Café des Beaux Arts. To the gentle sound of music coming from the grand piano in the Arts Room, they can settle back in a comfortable armchair and read a book from the library. Friendly waiters serve tea, cocktails, light lunches and gourmet delights throughout the day from 7am to 10pm.
Have a wonderful time immersing yourself in the Jazz music beautifully performed by our the talented pianist from 2:30PM to 5:00PM, from Mon to Sun.


the use of iBeacon technology in an easy and cost efficient way.
and managing the web database yourself.
send you the iBeacons that are linked to your pages.
Setup your portal page and order your beacons from Beacon Portals.
Turn on the beacons at your business.
Your customers will discover your beacons and view the information at your portal page on their smart phones.
Do you sell goods and services while on the move? Do you need to let your potential customers know that you are in the area, and what you are carrying to sell?
iBeacon is a high tech solution in lieu of holding out big signs on the street and advertising your business.
Interested in trying the latest retail technology at your store like the big chain stores do? But not ready to commit yet without knowing the benefits, while at the same time, you don't want to be left behind from the latest retail technology?
You can set up a few beacons from Beacon Portals without paying the upfront costs for the IT setup.


ChemIDplus - 11054-63-0 - BYWOWQCRVFUOLF-AQZAFBPESA-N - Tsushimycin - Similar structures search, synonyms, formulas, resource links, and other chemical information.
mouse LD50 intraperitoneal 50mg/kg (50mg/kg) "CRC Handbook of Antibiotic Compounds," Vols.1- , Berdy, J., Boca Raton, FL, CRC Press, 1980Vol. 4(1), Pg. 318, 1980.
mouse LD50 intravenous 50mg/kg (50mg/kg) "CRC Handbook of Antibiotic Compounds," Vols.1- , Berdy, J., Boca Raton, FL, CRC Press, 1980Vol. 4(1), Pg. 318, 1980.
mouse LD50 subcutaneous 50mg/kg (50mg/kg) "CRC Handbook of Antibiotic Compounds," Vols.1- , Berdy, J., Boca Raton, FL, CRC Press, 1980Vol. 4(1), Pg. 318, 1980.


Being a beginner caller can be extremely overwhelming. There are so many things you have to keep in mind when you are calling, such as formation, arrangement, sequence, and relationship, not to mention timing, rhythm, clarity of your voice, etc. Anything that can be done to simplify the task so you can concentrate on fewer things at once is highly welcome!
Here are some cheats sheet that will help you learn to resolve any square from normal (non-sashayed) two-faced lines (boys on the ends).
These cheat sheet let you think primarily about getting your square into a normal two-faced line. Then, you just follow the instructions to resolve the square. I am currently using this as my go-to resolution method so I can practice calling extemporaneously based on formation. I watch to see what formation appears (ideally, I should be able to guess accurately ahead of time, but that doesn't always work!) and then call something "legal" from that formation. When I have played enough, I put the couples into normal two-faced lines and resolve.
I learned these methods from Richard Reel's All8.com site.


Documents filed this week in a lawsuit over housing near the University of Akron exposed a fight involving one of the nation�s largest charitable foundations, Akron leaders and the former director of the University Park Alliance.
The president and Akron program director of the Miami-based John S. and James L. Knight Foundation, a $2 billion charitable organization funded by the former owners of the Akron Beacon Journal and Knight Newspapers, accused management of the UPA of deception and raised concerns about the ability of city leaders sitting on the board to oversee UPA.
An amended complaint in a lawsuit by businessman Roger Carter against UPA contains emails among Knight Foundation officials and members of the UPA board, a nonprofit group working on the redevelopment of 50 city blocks around UA.
The suit alleges that UPA in late 2012 was deceptive � specifically former executive director Eric Anthony Johnson � in securing a $6 million grant and $1.9 million loan from Knight by withholding information that UA had dropped its involvement in a key component of the project, jeopardizing its success.
The foundation canceled the grant in April 2013. Carter sued, placing in jeopardy Carter�s investment with UPA in the University Square Brown Street housing project.
In a notation to herself on Sept. 8, 2013, Knight�s Akron program director Jennifer Thomas raised questions about Johnson: �No one to reign him in. There are many points along this path where the board could have spotted this,� and she later suggested he was running a Ponzi-like scheme.
Board members named in the suit are Johnson, Thomas, UA president Luis Proenza, Mayor Don Plusquellic, Children�s Hospital president William Considine, Summa Health System CEO Thomas Strauss and vice president Patrice Lange, County Executive Russ Pry, Akron Metropolitan Housing Authority director Tony O�Leary, Akron School Superintendent David James, Akron Chamber CEO Dan Colantone, former Beacon Journal publisher Andrea Mathewson, attorney J. Bret Treier, First National Bank vice president John Falatok and community leaders Ann Gates and Ethel Chambers.
Knight Foundation and University of Akron officials declined comment. James, UPA board chairman, also declined comment, saying he could not comment on pending litigation and had not reviewed the complaint. Calls to Considine and Treier were not returned. Thomas, who recently resigned from the foundation, said she could not comment.
In Summit County Common Pleas Court, Carter says he contributed two Brown Street student-rental properties to UPA in exchange for a 5 percent stake in University Park Village, a UPA venture.
Carter�s attorney, Bradley S. LeBoeuf, on Thursday said the amended complaint includes documents and other information obtained during the discovery process.
Treier shared the information that month with Johnson, but no one else on the board, and the Knight Foundation approved the grant and loan in December 2012 not knowing about the change, according to Carter�s complaint.
The funding fell apart quickly.
Knight Foundation Vice President, Chief Financial Officer and Treasurer Juan J. Martinez, in an April 2, 2013, email to Johnson and UPA board chair James, said UPA funding was cut off.
�As part of Knight�s monitoring of the grant Knight staff became aware that UPA management had been notified by UA prior to Knight�s approval of the grant, that UA would not partner in the development and management of student housing at University Square,� Martinez wrote.
Johnson resigned as UPA�s executive director three days later.
The suit also references an email from Thomas to the Knight Foundation on Sept. 6, saying Plusquellic �has commenced a �private investigation� of defendant Eric Johnson.� Plusquellic was out of town and did not return a call seeking comment.
Johnson, reached at his new job in Charlotte, N.C., said he had not seen the amended complaint and, reacting to portions read to him over the phone, vehemently denied all allegations.
�I don�t even know where to begin. That is not accurate information,� said Johnson, who is now chief development officer of Horizon Development, a nonprofit subsidiary of the Charlotte Housing Authority.
�They are trying to destroy my career is what they�re trying to do. I came into a situation where it was wrought with sheer competition amongst those anchor institutions. Everybody wanted a piece of the funds,� said Johnson.
Johnson denied that he was told by Treier that Proenza changed the scope of the university�s project and believed at the time of his resignation that the project was intact.
Cheryl Powell can be reached at 330-996-3902 or cpowell@thebeaconjournal.com. Betty Lin-Fisher can be reached at 330-996-3724 or blinfisher@thebeaconjournal.com. Follow her on Twitter at www.twitter.com/blinfisherABJ and see all her stories at www.ohio.com/betty.


text:
Last edited by JoJot
Wednesday, October 21, 2020 | History
4 edition of Age of Aquarius found in the catalog.
by Alek Sander
Published December 5, 2005 by PublishAmerica .
Adventure / thriller,
Fiction - General,
Action & Adventure,
Fiction / Adventure
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Somerset Light Infantry (Prince Alberts) (the 13th Regiment of Foot).
Vitamin and mineral content of certain foods as affected by home preparation
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text:
Madonna Will Come to Russia on the Tour of Her New Album MDNA
Madonna will come to Russia on the tour of her new album MDNA. Madonna's MDNA tour will include Moscow and St. Petersburg. In Moscow, Madonna will perform in the Olympic stadium, and in St. Petersburg, Madonna will perform in SKK arena. The dates are August 7th and August 9th respectively.
The album will be released in March, but the tour starts off on May 29th in Tel Aviv, and will be completed in 2013 in Australia. Madonna will have 90 concerts on her tour, making it the most extensive tour in her history of travelling.
In December, Madonna signed with Interscope Records for 40 million dollars, on a three-disk agreement. The 53-year-old actress has her first album MDNA, coming out in March, and the MDNA album was first started in July last year.
Madonna's last studio album was Hard Candy. The album was released in 2008. Her tour was called Sticky & Sweet, and it brought in more than $400 million. The singer had a concert on Palace Square in St. Petersburg during the Sticky & Sweet tour. Subsequently, the name, "Hard Candy", was taken by a fitness center network, in which one was opened in Moscow in late December.
Besides music, Madonna is taking part in films. Last week, Russia premiered her film WE Believe in Love. The film is dedicated to the British king who abdicated for the love of a twice-divorced American woman.