text:
Board index Playing Men's UK Southern
SEMLA Structure for the 2012/13 Season
Play in the Southern Divisons? Post Here.
A full list of men's rules can be found here
Postby fudge Fri Mar 23, 2012 1:13 am
Forgive me if i've missed the thread if there is one - but what's the deal with the structure of SEMLA next season? Anyone know? Want to know the situation with promotions/relegations, 1 or 2 teams etc as I know there is serious talk of an East Div 4?
Last edited by fudge on Fri Mar 23, 2012 11:48 am, edited 1 time in total.
Maidstone Red Wolves #26, 2014 - Present
Canterbury Christ Church University #1, 2009-12
Re: Structure for the 2012/13 Season
Postby Chilli Fri Mar 23, 2012 9:38 am
There has been no discussion of next year's structure yet at the Committee meetings.
As is now standard practice, we will see which new clubs will apply before the AGM and which clubs will not continue into next season, e.g. Penarth and RAF Marham are definitely out.
Then we'll discuss the best format according to actual numbers and any other relevant factors.
All open and transparent discussion at the monthly meetings, all clubs welcome by audio-conference or written submissions.
Contact Ash
Postby Ash Fri Mar 23, 2012 9:41 am
Don't think there has been a thread. Formal talk normally happes in april and may time each year. I am doubtful that there will be any significant change unless there are substantial numbers of new clubs in the leagues and i haven't heard many rumours.
Oxford City is likely. I haven't heard a lot of other realistic rumours but there may well be other teams in the works. So unless there are loads of other teams numbers remain about the same!
The west divisions have 4/5 free spots (dependent on Pernarth) the east divisions have 4 free spots (Marham are apparently out for next year).
But my guess is that there won't be any significant change to structures or the promotion format next season as it sounds like we have the same number of teams roughly!
Reading Wildcats (#13) 2010 - Present
Southampton City (#13) 2008-2010
Reading Wildcats 2007-2008
Southampton University (#13) Pre - 2007
Postby fudge Fri Mar 23, 2012 11:50 am
Ash wrote: Don't think there has been a thread. Formal talk normally happes in april and may time each year. I am doubtful that there will be any significant change unless there are substantial numbers of new clubs in the leagues and i haven't heard many rumours.
Chilli wrote: There has been no discussion of next year's structure yet at the Committee meetings.
Cheers guys. So it's still 2 up, 2 down?
Re: SEMLA Structure for the 2012/13 Season
Postby Chilli Fri Mar 23, 2012 12:25 pm
Yes, as per the byelaws on the SEMLA website www.southlacrosse.org.uk
Postby Tree13 Thu Apr 05, 2012 12:42 pm
I think, given the amount of concessions and rearranged fixtures this year, it is fair to assume that while we remain a winter sport we will be at the mercy of winter weather. This being the case, I think that OUTSIDE the prem we need to do one of two things:
a) lengthen the season so that more weekends are available to play the fixtures
b) reduce the number of teams per division. Ten is too many given the current number of weekends available, and other divisions only have seven teams. This imbalance helps no-one.
There is a problem with option a, as proven by Cambridge and Brighton Uni both struggling to get teams out for the first week of October, the last week before Christmas and the first after new year. Add in varsity matches and tours, and exam season.... however, extending the season might not provide the answer if the extra dates are outside university term times.
Option b I think is better, and I would point to the expansion of East 1 from last season (8 teams) compared to this season (10 teams), and the consequential conceded fixtures - I don't know if there was a rise, if it was proportionate or disproportionate, but I have a gut feeling that going to an eight- or nine-team division limit is a better idea. A nine-team limit means that one team is off every week, allowing players to plan time away to coincide with their "bye week"; it also (in theory) makes a couple more basic level refs available every week to travel and officiate in other games.
Tree13's posts only reflect Tree13's personal opinions. They do not represent the views of any other person, team or club. Any interpretation to the contrary is invalid.
Brighton #18 2008 - 2011; 2012 - 2014
EG #41 2011 - 2012
ILL Allstars #26 2011
Bristol #13 2005 - 2007
Postby Ash Thu Apr 05, 2012 10:45 pm
East 1 has been significantly better this season than last year in my opinion. In terms of having good club teams and an improving standard!!
There have only been 1 or 2 unreliable teams, the main ones are Brighton and Cambridge who are university teams and have had a number of issues outside of their control, mainly most of their squad leaving or very short terms (so its no major criticism of them).
Both these teams have been relegated, and next season Hillcroft a and Epsom/eg a (maybe both if eg go up and Purley don't go down) will be moving up. That will make easy 1 an entirely club division (only Colchester are partially Uni reliant).
Cambridge and Brighton will move into a sMaller division that is more compatible with their term dates. Problem solved.
10 teams is perfect for this division.
I wish having an off week meant people planned to go away that weekend! Normally when we have a game I have a few unavailable! When we have a weekend off I have most of the squad texting me demanding a friendly!! Ha
babyant
Postby babyant Fri Apr 06, 2012 8:52 pm
Ash wrote: (only Colchester are partially Uni reliant).
Unfortunately Colchester are somewhat more than partially uni reliant and I think that will be even more the case next year... I live in hope that ten graduates will move back to Colchester over the summer though!
Winning isn't everything, wanting to is
Contact J-Lo
Postby J-Lo Sun Apr 08, 2012 9:42 am
Tree13 wrote: I think, given the amount of concessions and rearranged fixtures this year, it is fair to assume that while we remain a winter sport we will be at the mercy of winter weather. This being the case, I think that OUTSIDE the prem we need to do one of two things:
A) is a bad idea. East 3 already has too many weekends without a game. It causes teams players to lose focus and interest in the league.
If it was my call i would run a summer league (not the Arch level way, they don't have much love) and slowly reduce the winter league. University teams wouldn't play, no problem, the players can join their respective club teams. Teams who use cricket grounds have a problem, no worries, hire a school pitch for £30-50. There are enough clubs that don't use cricket grounds for a league to be successful without them.
http://www.sportsfanpanel.co.uk
Postby Tree13 Wed Apr 11, 2012 11:03 am
Ash wrote: East 1 has been significantly better this season than last year in my opinion. In terms of having good club teams and an improving standard!!
Hasn't East 1 just been as predicted? EG spanked everyone and Brighton and Cambridge tumbled to the bottom having lost too many players to graduation. Of the remaining teams, has there been a marked improvement upon last year's standard of play?
All of which is besides the point, as I was referring to the impression I had formed that perhaps the return to a ten-team format, and the resultant extra fixtures needing to be played during a period of the year when foul weather is predictable and prevalent, had led to more fixtures being conceded. I'm not certain, but the maths will soon be available to confirm or refute.
Ash wrote: There have only been 1 or 2 unreliable teams, the main ones are Brighton and Cambridge who are university teams and have had a number of issues outside of their control, mainly most of their squad leaving or very short terms (so its no major criticism of them).
The very short terms were the same length as last year - the playing season was extended which, when taken together with the previously-mentioned term lengths, posed a problem for those two teams.
Ash wrote: Both these teams have been relegated, and next season Hillcroft a and maidstone/eg a (maybe both if eg go up and Purley don't go down) will be moving up. That will make east 1 an entirely club division (only Colchester are partially Uni reliant).
Am I right in interpreting this to mean that you are happy for SEMLA to adopt a league format that uni teams will struggle with? Not trying to stir, just wanting to understand. East 1 is POTENTIALLY only a couple of years away from being a division comprised solely of second teams from club sides; with the rules as they stand that would mean no promotion from E1 to prem. Furthermore, it will leave East 3 with several free weekends as they have had this year which, as J-Lo has pointed out, is far from perfect.
Ash wrote: 10 teams is perfect for this division.
Provided you are happy for Uni sides to be at a competitive disadvantage, yes. Provided you are happy with foul weather annually frustrating attempts to play games, yes. Provided you are happy handling a fixture pile-up at the end of the season, yes. I'm not convinced, personally.
Ash wrote: I wish having an off week meant people planned to go away that weekend! Normally when we have a game I have a few unavailable! When we have a weekend off I have most of the squad texting me demanding a friendly!! Ha
The league format can't make your players more intelligent, it can only provide them with an opportunity to make intelligent decisions ;o) In all seriousness, if your "bye weeks" were known further in advance (by their nature, a bye week is very different to a week were an ooponent cries off at the last minute, or the pitch is deemed unplaybale on the morning of the fixture), do you not think your players would plan around them?
J-Lo wrote: If it was my call i would run a summer league (not the Arch level way, they don't have much love) and slowly reduce the winter league. University teams wouldn't play, no problem, the players can join their respective club teams. Teams who use cricket grounds have a problem, no worries, hire a school pitch for £30-50. There are enough clubs that don't use cricket grounds for a league to be successful without them.
I doubt we'd have to go forward without them. I suspect that if the switch to a summer league was made official people would just get on with it and make it work, unless they actually preferred cricket to lacrosse.
If you propose it as a motion to the appropriate SEMLA meeting, I'll second it.
laxambition
Postby laxambition Wed Apr 11, 2012 1:35 pm
A quick look at Brighton's results show (assuming all 10-0 losses were conceded games and not the coincidental final score of a fixture which was fulfilled) they conceded games on:
8th October, 7th January, 4th February, 18th Feb, 3rd March, 17th March, 24th March, and that they postponed a game on 11th Feb which they subsequently conceded the rearranged fixture on 25th March
It is disingenuous to suggest therefore that their fate is related to the length of the season/ term dates
In 4 of the last 5 years East 1 has had 10 teams, and on two of those occasions Cambridge have finished 2nd in the league. So once again, it is a convenient fallacy that season length/ term dates are the be-all and end-all of why Cambridge find themselves in the relegation spot this season.
So if East 1 gets re-structured to (say) 8 teams, does the league prevent promotion from East 2 (which will surely not please Hillcroft A and EG A), or do 4 teams get relegated which will surely not be popular with Welwyn 2s or Colchester?
Provided you are happy for Uni sides to be at a competitive disadvantage
If the alternative is to write the entire league structure and fixture list based on the available dates for 2 teams out of 50 or so, then yes.
The opinions expressed herein are those of the author and do not necessarily represent Reading Wildcats Lacrosse Club, SEMLA or, indeed, anybody else......but that doesn't mean that it's not what they're all thinking!
Postby rr53 Wed Apr 11, 2012 2:19 pm
I think you should keep structure of this year. Otherwise there is no real point of fighting for promotion when it keeps getting restructured. If thats the case, there wouldnt be much point in starting up new clubs who wants to get promoted - would be easier to just join a big club who is in the top league, which to be fair isnt a bad idea anyway lol
Postby Chilli Wed Apr 11, 2012 3:34 pm
Just to add a little background to this debate, for many years there were only three or four Unis active in SEMLA and Oxford and Cambridge only had games to fit their very short terms.
The other couple of Unis happily played a full schedule without comment.
The argument from time immemorial was that the prestige of keeping lax in Oxbridge was worth the complications it caused the fixture schedule.
Not my personal opinion at all and it led to unjustifiable results when the Oxbridge games were sometimes played for double points and sometimes not, so if you got a good result against them on a double pointer it was better than the poor sods who had to travel and play two games.
Then probably ten years ago Cambridge had a good squad and asked for full fixture schedules.
The SEMLA Committee took the decision that agreement to a full schedule would be a condition of joining SEMLA for all teams, Uni or Club.
No dispensations, no special conditions, all equal.
This hasn't stopped any new team from joining and has never been an issue.
The creation of BUCS gives all Unis an alternative and as we have seen some have left SEMLA and then come back, some use SEMLA as their development league and that's all good for the game.
University teams will inevitably wax and wane, always have. always will. They are the very last teams around which it would be in any way sensible to create a stable structure.
However, we have allowed both Unis and Clubs to make a case for voluntary demotion if their circumstances demand it.
It is clearly in the long term interests of the team, the Uni, the Club, SEMLA and the game as a whole to vary the structure when it is justified.
It may very well happen that a Uni has a strong team for three or four years and blasts through into the Premiership and then slumps dramatically back down as they graduate, but that's all part of the excitement.
The key thing is to ensure that those players move into Club teams once they graduate.
Contact Steely Dan
Postby Steely Dan Wed Apr 11, 2012 3:56 pm
To add to Chillis post: a few years ago I was heavily involved with the Herts Comets uni team, we had a tough couple of seasons building a squad and did reasonably well in that short period. Hertfordshire as a University were very accomodating at the time and allowed non-uni or alumni members to continue to train and this helped the club grow.
However it became apparent to a number of us that were no longer university students that the nature of the university squad would always be cyclical and that it made more sense from a personal, club and regional perspective to join a club team (in our case we were fortunate to have a close relationship with Welwyn Warriors).
The result was that when Herts Comets withdrew from SEMLA to concentrate on BUCS, Welwyn also added a new squad to the club. Now Herts players have the ability to play SEMLA with an established club team and they get to play BUCS as well.
I persoanlly feel the flexibility of SEMLA has a lot to do with the success of Lax in the area and I'm sure whatever structure that is voted on will be the best for the times (as long as we don't get demoted )
Herts Comets Founder 04-08
Welwyn Warriors 04/05. 08 -->
Return to "UK Southern"


text:
import { SlackEvent } from "../../slack/interfaces";
import { Team } from "../../teams/team";
import { SlackApiClient } from "../api/client";

import { Message } from "./message";

export interface Handler {
    match(event: SlackEvent): boolean;
    handle(team: Team, event: SlackEvent, apiClient: SlackApiClient): void;
}

const handlers: Array<Handler> = [
    Message
];

export default handlers;

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}
\label{sec:int}
Most peculiar
properties of transition metal oxides that attract a lot of attention
are believed to result from strong electronic correlations. A great variety of
physical phenomena has been evidenced \cite{Ima98}, with prominent examples
being the
striking metal-to-insulator transitions in vanadium sesquioxide
\cite{McW73,Hel01,Lim03,Gry07}, high-$ {\rm T_c} $ superconductivity in the
cuprates \cite{Bed86,Sch93}, non-Fermi liquid behavior in the vanadates
\cite{Ina95}, stripes in nickelates~\cite{Sac95n,Tra17} and
cuprates~\cite{Tra95c,Tra17b}, or the colossal magnetoresistance observed in the
manganites \cite{Hel93,Tom95,Rav95,Mai95}. In addition, a whole series of
promising materials for thermoelectric applications has been discovered
\cite{Ter97,Mas00,Mat01,Mic07,Ohta07,Mai09b,Wang13}.

The infancy of the microscopical modeling of strongly correlated systems
dates to the early sixties with the introduction of the so-called one-band
Hubbard Model \cite{Hub63,Hub64,Kan63,Gut63},
\begin{equation}
H = -t \sum_{\langle i,j\rangle ,\sigma}  f_{i\sigma}^{\dagger}
f^{\phantom{\dagger}}_{j\sigma}  +
U \sum_i n_{i\uparrow}^{\phantom{\dagger}} n_{i\downarrow}^{\phantom{\dagger}} \,,
\end{equation}
that describes interacting fermions hopping on a lattice between nearest
neighbor sites with amplitude $-t$. The screened Coulomb interaction is
assumed local, and its strength on each site $i$ is given by $U$. It was later
on extended by Ole\'s to multiband systems to better embrace the diversity of
transition metal oxides \cite{Ole83}. A fundamental consequence of strong
correlations was already recognized by Hubbard, who showed that they split the
non-interacting tight-binding band  and give rise to additional features in
the excitation spectra including the upper Hubbard band (UHB)
\cite{Hub63,Hub64}. In fact, more recent investigations of the one-band
Hubbard Model within dynamical mean-field theory revealed that its
one-particle excitation spectra generically consist of lower and upper Hubbard
bands, together with a quasi-particle peak \cite{Geo96,Bul01}. These genuine
interaction-driven features are reflected in two-particle excitation
spectra. For instance, as shown in Fig.~\ref{fig:fs} the charge excitation
spectra consist of a continuum, a zero-sound collective mode, and a
high-frequency collective mode originating from the upper Hubbard band
\cite{Dao17}. The latter escapes a description within perturbation theory.

\begin{figure}[h]
  \includegraphics[clip=true, width=0.48\textwidth]{fig-Im_Chi_c.eps}
  \caption{(Color online) Spectrum of the inelastic charge response function
    ${\rm Im} \chi_c$ at low temperature $T$ for different momenta along the
    path linking $\Gamma=(0,0)$ to ${\rm M}=(\pi,\pi)$, at coupling $U=10t$
    and doping from half-filling $\delta=\pm 0.5$. Note the peak of the
    zero-sound collective mode above the upper edge of the continuum, and the
    UHB mode peak at higher energy.
  Parameter: $T=t/100$.}
  \label{fig:fs}
\end{figure}

The Kotliar and Ruckenstein slave-boson representation of the Hubbard model
\cite{Kot86} is a convenient tool to obtain these spectra at one-loop order in
the paramagnetic phase \cite{Dao17}. Such a symmetry-breaking free calculation
may be performed in the thermodynamical limit. It thus allows to resolve the
full momentum dependence of the spectra. Since incommensurate magnetic
instabilities are strongly suppressed with increasing temperature, neglecting
magnetic instabilities does not severely constrain the parameter range where
the calculation may be meaningfully performed. For instance, on the square
lattice, they essentially disappear for $T\approx t/6$ \cite{Dao17}. The
Gutzwiller approximation, which entails the interaction driven Brinkman-Rice
metal-to-insulator transition~\cite{Bri70}, is reproduced on the saddle-point
level by the Kotliar and Ruckenstein slave-boson
representations~\cite{Kot86,FW}.

The zero-temperature Brinkman-Rice metal-to-insulator transition is second
order~\cite{Bri70}.
It turns first order at finite temperature as the latter may destabilize a poorly
coherent Fermi Liquid \cite{Doll3, FK}. It is located in a coexistence region between
a metallic and an insulating phase. Furthermore this first order transition extends
to finite doping, where it is replaced by a transition from a good metal (with large
quasi-particle residue) to a poor metal (with small quasi-particle residue). It
extends up to a critical endpoint that depends on temperature \cite{Dao17, Mez17}.
In contrast, a zero-temperature first order transition has been found in the two-band
model in the vicinity of half-filling \cite{Fre02}.
The role of the lattice geometry on the metal-to-insulator transition
was also investigated~\cite{Kot00}. In particular, a very good agreement
on the location of the metal-to-insulator transition has been found with
Quantum Monte Carlo simulations on the honeycomb lattice~\cite{Doll3}.
Further comparisons of groundstate energies
to existing numerical solutions have also been carried out for the square
lattice. Regarding groundstate energies, for instance for $U=4t$, it could
be shown that the slave-boson result is larger than its counterpart by less
than 3\%~\cite{Fre91}. For larger values of $U$, the slave-boson groundstate
energy exceeds the exact diagonalization data by less than
4\% (7\%) for $U=8t$ ($20t$) and doping larger than
15\%. The discrepancy increases when the doping is lowered~\cite{Fre92}.
The saddle-point approximation is exact in the large degeneracy limit,
and the Gaussian fluctuations provide $1/N$ corrections~\cite{FW}.
Moreover it obeys a variational principle in the limit of large spatial
dimensions where the Gutzwiller approximation becomes exact for the
Gutzwiller wave function~\cite{Met89,Met88,Met89b}.
Let us finally emphasize that a quantitative agreement was established
between the charge structure factors calculated from Gaussian fluctuations
within the slave-boson approach and quantum Monte Carlo
simulations~\cite{Zim97}.

Numerous valuable results have been obtained with Kotliar and
Ruckenstein~\cite{Kot86} and related slave-boson representations~\cite{Li89,FW}. Special
attention has been paid to anti-ferromagnetic~\cite{Lil90}, spiral~\cite{Fre91,Igo13,Fre92,Doll2}, and
striped~\cite{SeiSi,Fle01,Sei02,Sei03,Sei05,Rac06,Rac07,RaEPL} phases. In addition,
the competition between the latter two has been addressed as
well~\cite{RaEPL}. It has also been obtained that the spiral order
continuously transforms to the ferromagnetic order in the large $U$ regime ($U
\gtrsim 60t$)~\cite{Doll2} so that its experimental realization is unlikely.
Furthermore, in the two-band model on the square lattice, ferromagnetism was predicted
as a possible groundstate in the doped Mott insulating regime only~\cite{Fre02}.
However, the ferromagnetic instability line could be brought down to the intermediate
coupling regime when taking into account a ferromagnetic exchange
coupling~\cite{lhoutellier15}. A sufficiently large next-nearest-neighbor hopping
amplitude~\cite{FW98}, as well as going to the fcc lattice~\cite{Igo15}, results in a
similar effect. In addition, this formalism extended to the Hubbard model with inter-site
Coulomb interaction has been applied to address the strongly inhomogeneous
polaronic states observed in correlated heterostructures~\cite{Pav06}.
Most recently the possibility to enhance the capacitance by strong
correlation effects in the metallic plates of a capacitor has been investigated
within this approach~\cite{Ste17}.

Yet it needs to be verified that the approximate analytical expression used to
calculate the charge excitation spectra complies with the
symmetries of the model. Clearly, translational invariance and spin-rotational
invariance are satisfied in a paramagnetic phase. However the less obvious
particle-hole symmetry remains to be established.
Furthermore, there is a certain degree of arbitrariness inherent to
this representation as to how to perform the one-loop calculation: While the
internal gauge symmetry group of the representation allows to simplify the
problem, as the phase of three of the four slave-boson fields may be gauged
away by promoting the Lagrange multipliers to time-dependent fields, there is
no prescription to determine which one of them must remain a complex field. In
this paper, we not only show that the charge excitation spectra computed in
\cite{Dao17} are indeed particle-hole symmetric, but also that they do not
depend on whether the selected complex slave-boson field describes doubly
occupied sites or empty sites.

\section{Model and method} \label{sec:method}
In the spin-rotation invariant (SRI) Kotliar and Ruckenstein slave-boson
representation~\cite{Kot86,fresard12} the Hubbard Hamiltonian is expressed with
pseudo-fermion operators $f_{i\sigma}$ and auxiliary boson operators
$e_i$, $p_{i\mu}$, $d_i$ (for atomic states with respectively zero, single and
double occupancy) as
\begin{equation} \label{eq:model}
 H = -t \sum_{\langle i,j\rangle} \sum_{\sigma, \sigma', \sigma''} z_{i\sigma'' \sigma}^{\dagger}
 f_{i\sigma}^{\dagger} f_{j\sigma'} z_{j\sigma' \sigma''} + U \sum_i d_i^{\dagger} d_i.
\end{equation}
In this form the on-site Coulomb interaction has the advantage to
be bilinear in bosonic operators. The canonical operators $p_{i\mu}$
build a $2\times2$ matrix in spin space in order to preserve spin rotation
symmetry~\cite{Li89,FW}. It is expanded into the identity matrix
$\underline{\tau}^0$ and the Pauli matrices as
${\underline p}_i = \frac{1}{2} \sum_{\mu=0}^3 p_{i\mu} {\underline \tau}^{\mu}$.
The operator $\underline{z}_i$ takes into account the occupancy change that occurs during
a hopping process. In the spin space it is also a matrix defined as
\begin{equation}
 {\underline z}_i = e_i^{\dagger} {\underline L}_i M_i {\underline R}_i \,
 {\underline p}_i + {\underline {\tilde{p}}}_i^{\dagger} {\underline R}_i M_i
 {\underline L}_i \, d_i
\end{equation}
with
\begin{eqnarray}
& M_i & = \Big[ 1 + e_i^{\dagger} e_i + \sum_{\mu=0}^3 p_{i\mu}^{\dagger} p_{i\mu}
+  d_i^{\dagger} d_i \Big]^{1/2}, \nonumber \\
&{\underline L}_i & = \Big[ (1 -d_i^{\dagger} d_i) {\underline \tau}^0
- 2 {\underline p}_i^{\dagger} {\underline p}_i \Big]^{-1/2}, \nonumber \\
& {\underline R}_i & = \Big[ (1 - e_i^{\dagger} e_i) {\underline \tau}^0
- 2 {\tilde{\underline p}}_i^{\dagger} {\tilde{\underline p}}_i \Big]^{-1/2}
\end{eqnarray}
where  $\tilde{\underline p}_i = \frac{1}{2} ( p_{i0} {\underline \tau}^0
- {\bf p}_i \cdot \boldsymbol{\underline \tau} )$.

The subspace of physical states in the augmented Fock space generated by the
auxiliary fermion and boson operators is the intersection of the kernels of
operators
\begin{eqnarray}\label{eq:const}
 & {\cali A}_i &= e_i^{\dagger} e_i + \sum_{\mu=0}^3 p_{i\mu}^{\dagger} p_{i\mu}
 +  d_i^{\dagger} d_i - 1,  \nonumber\\
 & {\cali B}_{i0} & = \sum_{\mu=0}^3 p_{i\mu}^{\dagger} p_{i\mu} + 2 d_i^{\dagger} d_i
 - \sum_{\sigma} f_{i \sigma}^{\dagger} f_{i \sigma}, \\
 & \pmb{\cali B}_i & =  p_{i0}^{\dagger} {\bf p}_i + {\bf p}_i^{\,\dagger} p_{i0}
 - \ii {\bf p}_i^{\,\dagger} \times {\bf p}_i  - \sum_{\sigma, \sigma'}
 \boldsymbol{ \tau}_{\sigma \sigma'} f_{i\sigma'}^{\dagger} f_{i\sigma}, \nonumber
\end{eqnarray}
{\it i.e.} in this subspace ${\cali A}_i = 0$ that is the constraint of one
atomic state per site, and ${\cali B}_{i\mu} = 0$ which equates the
number of fermions to the number of $p$ and $d$ bosons.

Functional integration is used to calculate the partition function~\cite{li91,Zim97}
with the effective Lagrangian
${\cal L} = {\cal L}^{\rm B} + {\cal L}^{\rm F}$. Here the purely
bosonic part is
\begin{eqnarray}
 {\cal L}^{\rm B} = \sum_i  \bigg[  e_i^{\dagger} \partial_{\tau} e_i
 & + & \sum_{\mu=0}^3 p_{i\mu}^{\dagger} \partial_{\tau} p_{i\mu}
 + d_i^{\dagger} (\partial_{\tau} + U) d_i  \nonumber \\
 & + & \alpha_i {\cali A}_i + \sum_{\mu=0}^3 \beta_{i\mu}  {\cali B}_{i\mu}^{\rm B} \bigg]
\end{eqnarray}
with ${\cali B}_{i\mu}^{\rm B}$ being the bosonic part of the operator
${\cali B}_{i\mu}$. After the integration of the fermion fields the mixed fermion-boson
part may be written as
\begin{eqnarray}
{\cal L}^{\rm F} = & - {\rm tr} \Big\{ \ln \Big[ (\partial_{\tau} - \mu +  \beta_{i0})
\delta_{\sigma\sigma'} \delta_{ij} + \boldsymbol{\beta}_i \cdot
\boldsymbol{\tau}_{\sigma\sigma'} \delta_{ij} \nonumber \\
 & + t_{ij} \sum_{\sigma_1} z_{j\sigma\sigma_1}^{\dagger} z_{i\sigma_1\sigma'} \Big] \Big\},
\end{eqnarray}
with $\mu$ the chemical potential.
 The constraints that define the physical states are enforced
with Lagrange multipliers $\alpha_i$ and $\beta_{i\mu}$. The problem may be simplified
thanks to the internal gauge symmetry group of the representation. Indeed
by promoting the Lagrange multipliers to time-dependent fields~\cite{FW}, the
phases of $e$ and $p_{\mu}$ can be gauged away. This leaves us with radial
slave-boson fields~\cite{Fre01}. Their saddle-point values may be viewed as
an approximation to their exact expectation values that are
generically non-vanishing~\cite{Kop07}. In fact, disproving earlier
claims~\cite{Ras88,Lav90,Li94}, the slave-boson field
corresponding to double occupancy $d_i = d'_i + {\rm i} d''_i$ however
has to remain complex as emphasized by several authors~\cite{Jol91,Kot92,FW}.
Furthermore the dynamics of the, now, real $e_i$ and $p_{i\mu}$ fields drops out of
${\cal L}^{\rm B}$ due to the periodic boundary conditions on boson fields.

Within the approximation of Gaussian fluctuations, the action is
expanded to second order in field fluctuations
\begin{eqnarray}
&\psi(k) = \big(\delta e(k),\delta d'(k),\delta d''(k),\delta p_{0}(k),
\delta \beta_{0}(k), \delta \alpha(k), \nonumber \\
& \delta p_{1}(k),\delta \beta_{1}(k),\delta p_{2}(k),\delta \beta_{2}(k),
\delta p_{3}(k), \delta \beta_{3}(k) \big)
\end{eqnarray}
around the paramagnetic saddle-point solution
\begin{equation}
\psi_{\rm MF} = (e, d, 0, p_0,\beta_0,\alpha, 0,0,0,0,0,0)
\end{equation}
as
\begin{equation}
 \int d\tau {\cal L}(\tau) = {\cal S}_{\rm MF} + \sum_{k,\mu,\nu} \psi_{\mu}(-k)
 S_{\mu\nu}(k) \psi_{\nu}(k)
\end{equation}
(the matrix $S$ is given in Appendix~A of \cite{Dao17}). We have introduced the
notation $k=({\bf k},\nu_n)$, with the Matsubara frequencies $\nu_n=2\pi nT$,
and $\sum_k = T \sum_{\nu_n} L^{-1} \sum_{{\bf k}}$ with $L$ the number of
lattice sites. The correlation functions of boson fields are then
Gaussian integrals which can be obtained from the inverse of the fluctuation
matrix $S$ as
$\langle \psi_{\mu}(-k) \psi_{\nu}(k) \rangle = \frac{1}{2} S^{-1}_{\mu\nu}(k)$.
Using the density fluctuation
$\delta {\cali N} = \delta(d^{\dagger} d - e^{\dagger} e) $,
the charge susceptibility is
\begin{eqnarray}
 \chi_c(k) & = & \langle \dd {\cali N}(-k) \dd {\cali N}(k) \rangle \nonumber \\
 &  = & 2 e^2 S_{1,1}^{-1}(k) - 4 e d S_{1,2}^{-1}(k) + 2 d^2  S_{2,2}^{-1}(k) .
 \label{eq:chi_c-def}
\end{eqnarray}
Dynamical response functions are eventually evaluated within analytical
continuation ${\rm i} \nu_n \rightarrow \omega + {\rm i} 0^+$.

\section{Symmetry of the saddle-point solution}

The Hubbard model possesses the particle-hole symmetry on a bipartite
lattice. We show below that the symmetry is preserved at the saddle-point
level in the specific case of the square lattice.

At first we present the general results of the paramagnetic
solution, which do not presume any property of the lattice. At the
saddle-point level, the boson values can be expressed with
the hole doping from half-filling $\delta$ and the variable $x =e +d$ as
\begin{equation}\label{eq:boson}
 e = \frac{x^2 + \delta}{2x}, \quad d = \frac{x^ 2 - \delta}{2 x} ,
\quad p_0^2 = 1 - \frac{x^4 + \delta^ 2}{2 x^2}.
\end{equation}
The bare quasiparticle dispersion $t_{\bf k}$ is renormalized as
\begin{equation}
 E_{{\bf k}} = z_0^2 t_{{\bf k}} - \mu_{\rm eff}
\end{equation}
with the factor
 \begin{equation}\label{eq:z0}
 z_0^2= \frac{2 p_0^2 (e+d)^2}{1-\delta^2},
 \end{equation}
and $\mu_{\rm eff}$ the effective chemical potential.

The paramagnetic solution for fixed values of doping $\delta$ and
coupling $U$ is found by determining the chemical potential
$\mu_{\rm eff}$ via the filling condition
\begin{equation}
  \frac{2}{L} \sum_{{\bf k}} n_F(E_{{\bf k}}) = 1 - \delta
\end{equation}
 and the solution $x$ of the saddle-point equation
\begin{equation}\label{eq:saddle-point}
\frac{(1-x^2) x^4}{x^4 - \delta^2}  =  \frac{U}{U_0}.
\end{equation}
Here the coupling scale
\begin{equation}
 U_0 = - 8 \varepsilon_0/(1-\delta^2)
\end{equation}
has been introduced in terms of the semi-renormalized kinetic energy
 \begin{equation}
 \varepsilon_0 =  \frac{2}{L} \sum_{{\bf k}}  t_{{\bf k}} n_F(E_{{\bf k}})
 \end{equation}
 and the Fermi function $n_F(\epsilon) = 1/(\exp(\epsilon/T) + 1)$.

 Solving the saddle-point equation (Eq.~\ref{eq:saddle-point}) at half-filling yields
$z_0^2=1-(U/U_0)^2$, in which case the effective mass of the quasiparticles
diverges when $U$ reaches $U_0$. This is the Brinkman-Rice mechanism of the
metal-to-insulator transition, as it also arises in the Gutzwiller
approximation~\cite{Bri70,Vol84,Vol87}.

In order to establish the particle-hole symmetry of the saddle-point
approximation, we show that the solution for the opposite doping
is obtained by swapping the values of the empty and double occupancy, $e$
and $d$, and reversing the sign of the effective chemical potential
$\mu_{\rm eff}$, while keeping unchanged $p_0$. Hence the saddle-point
value $x$ and the renormalization factor $z_0$ are even functions of
$\delta$. The boson expressions~(\ref{eq:boson}) comply with the
transformation, so it remains to check that the latter (i) leaves invariant
the saddle-point equation and (ii) yields the filling condition for the
opposite doping.  This can be achieved using the parity of the quasiparticle
density of state $N(-\epsilon) = N(\epsilon)$.
Alternatively, the dispersion on
the square lattice
\begin{equation}
t_{{\bf k}} = -2t(\cos k_x +\cos k_y)
\end{equation}
yields the property $t_{{\bf k}+{\bf Q}} = - t_{\bf k}$, with ${\bf Q} =
(\pi,\pi)$, that will be used in the next section.

For (i) one can remark
that both sides of Eq.~(\ref{eq:saddle-point}) are even in $\delta$ since
\begin{eqnarray}
 \varepsilon_0(-\delta) & = &\frac{2}{L} \sum_{{\bf k}}  t_{{\bf k}} n_F(z_0^2 t_{\bf k}
 + \mu_{\rm eff})  \\
 & = &\frac{2}{L} \sum_{{\bf k'}}  t_{{\bf k'}+{\bf Q}} n_F(z_0^2 t_{{\bf k'}+{\bf Q}}
 + \mu_{\rm eff}) \nonumber \\
 & = & \frac{2}{L} \sum_{{\bf k'}} t_{\bf k'} \big[n_F(z_0^2 t_{{\bf k'}} - \mu_{\rm eff}) - 1\big]
  = \varepsilon_0(\delta) \nonumber
\end{eqnarray}
(the last equality results from the vanishing of $\sum_{\bf k} t_{\bf k}$ over the Brillouin zone)
so the saddle-point equation is invariant.
 As for (ii), the density of the transformed solution
\begin{eqnarray}
 \frac{2}{L} \sum_{{\bf k}} n_F(z_0^2 t_{{\bf k}} + \mu_{\rm eff})
 & = & \frac{2}{L} \sum_{{\bf k'}} n_F(z_0^2 t_{{\bf k'}+{\bf Q}} + \mu_{\rm eff}) \nonumber \\
 & = & \frac{2}{L} \sum_{{\bf k'}} \big[ 1 - n_F(z_0^2 t_{{\bf k'}} - \mu_{\rm eff}) \big] \nonumber \\
 & = & 2 - (1 - \delta) = 1 + \delta
\end{eqnarray}
indeed corresponds to the opposite doping.

\section{Symmetry of the quasiparticle response functions}
On the square lattice the quasiparticle response function is transformed
under the reversal of the doping sign as
\begin{equation}
 \chi_m^-(k) = (-1)^m \chi_m^+(k).
\end{equation}
Here we have introduced the notation for the generalized quasiparticle
response functions at doping $\pm\delta$
\begin{equation}
 \chi_m^{\pm}(k) = \frac{2}{L} \sum_{{\bf q}}  (t_{{\bf q} + {\bf k}} + t_{\bf q} )^m
 \frac{n_F(E_{{\bf q} + {\bf k}}^{\pm}) - n_F(E_{\bf q}^{\pm})}{\omega -
 (E_{{\bf q} + {\bf k}}^{\pm} - E_{\bf q}^{\pm}) }
\end{equation}
with $E_{\bf q}^{\pm} = z_0^2 t_{\bf q} \mp \mu_{\rm eff}$.
The relation between the expressions at opposite dopings can be derived by
summing instead on ${\bf p} = -{\bf q} - {\bf k} + {\bf Q}$. This yields
\begin{eqnarray}
 \chi_m^-(k) & = &\frac{2}{L} \sum_{{\bf p}}  (t_{{\bf -p} + {\bf Q} }
 + t_{-{\bf p}-{\bf k}+ {\bf Q}} )^m \\
 & & \times \frac{n_F(E_{-{\bf p}+ {\bf Q}}^-) - n_F(E_{-{\bf p}-{\bf k}+ {\bf Q}}^-)}
 {\omega - (E_{-{\bf p}+ {\bf Q}}^- - E_{-{\bf p}-{\bf k}+ {\bf Q}}^-) } \nonumber \\
 & = & \frac{2}{L} \sum_{{\bf p}}  (- t_{{\bf p}} - t_{{\bf p}+{\bf k}} )^m
 \frac{n_F(- E_{{\bf p}}^+) - n_F(-E_{{\bf p}+{\bf k}}^+)}
 {\omega - (- E_{{\bf p}}^+ + E_{{\bf p}+{\bf k}}^+) } \nonumber
\end{eqnarray}
wherein we have used the equalities $t_{-{\bf p} + {\bf Q}} = -t_{\bf p}$
and $E_{-{\bf p} + {\bf Q}}^{-} = -z_0^2 t_{\bf p} + \mu_{\rm eff} = - E_{\bf p}^{+}$.
Finally the sum can be written as
\begin{equation}
 \chi_m^-(k) = (-1)^m \frac{2}{L} \sum_{{\bf p}}  (t_{{\bf p}+{\bf k}} + t_{\bf p} )^m
 \frac{n_F(E_{{\bf p}+{\bf k}}^+) - n_F(E_{{\bf p}}^+)}
 {\omega - (E_{{\bf p}+{\bf k}}^+ - E_{{\bf p}}^+) }
\end{equation}
since $n_F(-\epsilon) = 1 - n_F(\epsilon)$.

{\it En passant} the above relation shows the particle-hole symmetry of the RPA charge
response function
\begin{equation}
\chi_{\rm RPA}(k) = \frac{\chi_0^{(0)}(k)}{1 + \frac{U}{2} \chi_0^{(0)}(k)}
\end{equation}
where $\chi_0^{(0)}(k)$ is the charge response function of a Fermi gas,
{\it i.e.} $\chi_0^{(0)}(k) = \chi_0(k)|_{z_0 = 1}$.

\section{Symmetry of the slave-boson charge response}

The charge dynamical response function has been given in Ref.~\cite{Dao17}. In
order to demonstrate its particle-hole symmetry, we cast it into an expression
which is explicitly invariant under the transformation $\{ \delta \mapsto
-\delta, e \mapsto d, d \mapsto e, \chi_m(k) \mapsto (-1)^m \chi_m(k) \}$
undergone when reversing the doping sign. After a lengthy but straightforward
expansion, it can be written as
\begin{equation}\label{eq:chi_c}
 \chi_c(k) = \frac{A(k) + B(k)  \omega^2}{C(k) + D(k)
 \omega^2}
\end{equation}
where
\begin{align}\label{eq:coeff}
& A(k) = \frac{ 2  p_0^2 \varepsilon_0 }{1 - \delta^2}  \bigg[ \Big( p_0^2(d^2 S_{11} + e^2 S_{22}) + 4 e^2 d^2 S_{44} \nonumber \\
& \qquad \qquad \quad + 2edp_0^2 S_{12} - 4edp_0(d S_{14} + e S_{24})  \Big) \chi_0(k) \nonumber \\
& \qquad \qquad \quad  + 2 \big( e \Delta_1 - d \Delta_2 \big)^2 \bigg], \nonumber \\
& B(k) = ed p_0^2 \chi_0(k), \nonumber \\
& C(k) = \frac{ 2  p_0^2 \varepsilon_0 }{1 - \delta^2}   \bigg[
\bigg( p_0^2 S_{11} S_{22} - (p_0 S_{12} - d S_{14} - e S_{24})^2  \nonumber \\
& \qquad \qquad \quad + 4 ed S_{14} S_{24} - 2 p_0( d S_{11} S_{24} + e S_{22} S_{14})  \nonumber \\
& \qquad \qquad \quad + (d^2 S_{11} + e^2 S_{22} - 2ed S_{12}) S_{44} \bigg) \frac{\chi_0(k)}{2} \nonumber \\
& \qquad \qquad \quad + S_{11} \Delta_{1}^2 + S_{22} \Delta_{2}^2 + S_{44} \Delta_{4}^2  + 2 S_{12} \Delta_{1} \Delta_{2}
 \nonumber \\
& \qquad \qquad \quad -  2 S_{14} \Delta_{1} \Delta_{4} - 2 S_{24} \Delta_{2} \Delta_{4} \bigg], \nonumber \\
& D(k) = \frac{ed}{(e+d)^2} \bigg[ \quad \bigg( p_0^2 (S_{11} + S_{22}) + (e-d)^2 S_{44} \nonumber \\
& \qquad \qquad \quad - 2 p_0^2 S_{12} + 2 (e-d) p_0 (S_{24} - S_{14}) \bigg) \frac{\chi_0(k)}{2} \nonumber \\
& \qquad \qquad \quad + \big( \Delta_1 + \Delta_2 \big)^2 \quad \bigg].
\end{align}
Here the elements of the fluctuation matrix are
\begin{align}
S_{11} & = -\varepsilon_0 \frac{z_0}{e} \frac{\partial z}{\partial e} + s_{11}(k), \nonumber \\
S_{22} & = -\varepsilon_0 \frac{z_0}{d} \frac{\partial z}{\partial d'} + s_{22}(k), \nonumber \\
S_{44} & = -\varepsilon_0 \frac{z_0}{p_0} \frac{\partial z}{\partial p_0} + s_{44}(k), \nonumber \\
S_{\mu \nu} & = s_{\mu\nu}(k) \;\;  \text{for $\mu,\nu=1,2,4$ with $\mu\neq \nu$}
\nonumber \\
\end{align}
where
\begin{equation}
 s_{\mu\nu}(k) = \varepsilon_0 z_0 \frac{\partial^2 z}{\partial \psi_{\mu} \partial \psi_{\nu}}
 + \frac{\partial z}{\partial \psi_{\mu}} \frac{\partial z}{\partial \psi_{\nu}}
 \left[ \varepsilon_{{\bf k}} - \frac{z_0^2}{2}  \chi_2(k) \right]
\end{equation}
with \begin{equation}
 \varepsilon_{\bf k} = \frac{2}{L} \sum_{{\bf q}} t_{{\bf q}+{\bf k}} n_F(E_{\bf q}),
 \label{eq:epsk}
\end{equation}
and
\begin{align}
& \Delta_{1} =  d p_0 + \left( p_0 \frac{\partial z}{\partial d'} - d \frac{\partial z}{\partial p_0} \right)
\frac{z_0}{2} \chi_1(k), \nonumber \\
 & \Delta_{2} =  e p_0 - \left( p_0 \frac{\partial z}{\partial e} - e \frac{\partial z}{\partial p_0} \right)
 \frac{z_0}{2} \chi_1(k),  \nonumber \\
 & \Delta_{4} = 2 e d + \left( e  \frac{\partial z}{\partial d'} - d \frac{\partial z}{\partial e} \right)
 \frac{z_0}{2} \chi_1(k).
\end{align}

The expressions of the derivatives of $z$ may be gathered from Ref.~\cite{li91,Zim97}.
The first-order derivatives are
\begin{align}
 \frac{\partial z}{\partial e}  & = \sqrt{2} \eta p_0 \left( 1 + \frac{2 x e}{1-\delta} \right),  \nonumber \\
 \frac{\partial z}{\partial d'} & = \sqrt{2} \eta p_0 \left( 1 + \frac{2 x d}{1+\delta} \right), \nonumber \\
 \frac{\partial z}{\partial p_0} & = \sqrt{2} \eta x \left( 1 + \frac{2 p_0^2}{1-\delta^2} \right),
\end{align}
with $\eta =1/\sqrt{1-\delta^2}$. The second-order derivatives are
\begin{align}
 \frac{\partial^2 z}{\partial e^2} & = \frac{2\sqrt{2}\eta p_0}{1-\delta} \left( x + 2e
 + \frac{6 x e^2}{1-\delta} \right), \\
  \frac{\partial^2 z}{\partial d'^2} & = \frac{2\sqrt{2}\eta p_0}{1+\delta} \left( x + 2d
 + \frac{6 x d^2}{1+\delta} \right), \nonumber \\
 \frac{\partial^2 z}{\partial p_0^2} & = 2\sqrt{2}\eta^3 x p_0 \Big(3 + (6\eta^2 - 2) p_0^2 \Big), \nonumber \\
 \frac{\partial^2 z}{\partial e \partial d'} & = 2\sqrt{2}\eta p_0 \left( \frac{e}{1-\delta}
 + \frac{d}{1+\delta} + 2 \eta^2 x e d \right), \nonumber \\
 \frac{\partial^2 z}{\partial e \partial p_0} & = \sqrt{2}\eta \left( 1 + 2\eta^2 p_0^2 (1 + x e)
 + \frac{2 x e}{1-\delta} + \frac{6 x e p_0^2}{(1-\delta)^2} \right), \nonumber \\
 \frac{\partial^2 z}{\partial d' \partial p_0} & = \sqrt{2}\eta \left( 1 + 2\eta^2 p_0^2 (1 + x d)
 + \frac{2 x d}{1+\delta} + \frac{6 x d p_0^2}{(1+\delta)^2} \right). \nonumber
\end{align}

It should be emphasized that due to the symmetry of the saddle-point solution,
{\it i.e.}
$e({-\delta}) = d({\delta})$ and $p_0(-\delta) = p_0(\delta)$, the values of the partial
derivatives of $z$ by $e$ are interchanged with those by $d'$ when reversing
the sign of the doping, {\it e.g.} $(\partial^2 z/\partial e\partial p_0) (-\delta) = (\partial^2 z/\partial
d'\partial p_0) (\delta)$. The values of the fluctuation matrix
elements $S_{\mu\nu}$ with indices $1$ and $2$ are thus interchanged, {\it e.g.}
$S_{11}(-\delta) = S_{22}(\delta)$ or $S_{14}(-\delta)= S_{24}(\delta)$.
Furthermore one can check that $\Delta_4(-\delta) = \Delta_4(\delta)$ and
$\Delta_{1}(-\delta) = \Delta_{2}(\delta)$. As a result, the coefficients~(\ref{eq:coeff}),
and then the response function, are actually invariant.

As an example we plotted the numerical evaluation of Eq.~(\ref{eq:chi_c}) in
Fig.~\ref{fig:fs}, where the characteristic features of the inelastic charge
response function are clearly visible. While neither the continuum nor the
zero-sound collective mode above the upper edge of the continuum could be
brought into a simple analytical form, an approximate expression of the
UHB pole for all momenta applicable in the strong coupling regime could be
derived \cite{Dao17}. It reads
\begin{equation}
 \omega_{\rm UHB}({\bf k}) \approx U \sqrt{1 - \frac{U_0}{2U} \left( 1-3|\delta|
 + (1-|\delta|) \frac{\varepsilon_{\bf k}}{\varepsilon_0}\right)}\,.
  \label{eq:wuhb2}
\end{equation}
In Fig.~\ref{fig:wid} we compare the evaluation of Eq.~(\ref{eq:chi_c}) with
the approximation Eq.~(\ref{eq:wuhb2}) for $U=20t$ and $40t$. The smallest
energy of the UHB mode peak is obtained for ${\bf k} = (0,0)$, and the highest
one for ${\bf k} = (\pi,\pi)$. The dispersion of this mode is approximately
given by $-2 (1-|\delta|) \varepsilon_{\bf k}$, and is accordingly largest at
half-filling and vanishingly small in the limit of empty/full
system. Furthermore, the difference between the approximation
Eq.~(\ref{eq:wuhb2}) and Eq.~(\ref{eq:chi_c}) tends to vanish already for
$U=40t$.

\begin{figure}[h]
  \includegraphics[clip=true, width=0.48\textwidth]{fig-UHB.eps}
  \caption{(Color online) Dispersion of the UHB mode following from
    Eq.~(\ref{eq:chi_c}) (shaded area) as a
    function of the doping for $U=20t$ and $40t$. The dashed boundaries are
    obtained from the strong-coupling approximation Eq.~(\ref{eq:wuhb2}).
  Parameter: $T=t/100$.}
  \label{fig:wid}
\end{figure}

Let us finally mention an alternative derivation of Eq.~(\ref{eq:chi_c}). We
recall that there is some arbitrariness to its derivation as we chose here to
gauge away the phase of the $e$-boson (on top of the one of the
$p_{\mu}$-bosons). Alternatively one may chose to gauge away the phase of the
$d$-boson while keeping the $e$-boson as a complex field. This obviously leads
to a $S$-matrix that differs from the one derived in \cite{Dao17} and used
here. Yet, tedious work shows that $\chi_c(k)$ obtained this way is
nevertheless given by Eq.~(\ref{eq:chi_c}), thereby overcoming the above
mentioned arbitrariness and putting Eq.~(\ref{eq:chi_c}) on a firmer ground.

\section{Conclusion}

Summarizing, the particle-hole symmetry of the charge response function
obtained for the Hubbard model using various approximations has been
considered. It has first been established that this symmetry is obeyed in the
random phase approximation for a bipartite lattice such as the square lattice
that we explicitly addressed. We then considered the expression of $\chi_c$
resulting from the SRI Kotliar and Ruckenstein slave boson representation
calculated to one-loop order again on the square lattice. In this case we
succeeded to cast its rather involved expression into a form that is manifestly
particle-hole symmetric. The latter also applies to the Kotliar and
Ruckenstein representation. Our arguments can easily be extended to other
bipartite lattices with one atom in the unit cell, such as the simple cubic one.

\section*{Acknowledgments}

The authors acknowledge the financial
support of the French Agence Nationale de la Recherche (ANR), through
the program Investissements d'Avenir (ANR-10-LABX-09-01), LabEx EMC3, the
R\'egion Basse-Normandie, the R\'egion Normandie, and the Minist\`ere de la
Recherche.

\section*{Bibliography}

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text:
2012 IPC Athletics European Championships
IPC Athletics European Championships
Stadskanaal, Netherlands
Nations participating
Athletes participating
23 – 28 June
Main venue
Stadskanaal Stadium
< 2005 Espoo
2014 Swansea >
The 2012 IPC Athletics European Championships was a track and field competition for athletes with a disability open to International Paralympic Committee (IPC) affiliated countries within Europe. It was held in Stadskanaal, Netherlands and lasted from 23 to 28 June. The event was held in the Stadskanaal Stadium and was the last major European disability athletics event before the forthcoming 2012 Summer Paralympics in London. Approximately 550 athletes from 38 countries attended the games.[1] Several countries used the Championships to finalise the remaining places for the Paralympics.[2]
1 Venue
3 Coverage
4.1 Opening ceremony
4.2 Classification
5 Medal table
5.1 Multiple medallists
6 Highlights
7 Participating nations
The event was held at the Stadskanaal Stadium.
The 2012 IPC Athletics European Championships was an invitational tournament taking in track and field events. No combined sports were included in the 2012 Championships. Not all events were open to all classifications, with several throwing and jumping events being contested between classifications, which were then decided on a points system. The men's 100m relay was the only event to use mixed classifications as a team, with each leg of the relay contested by a different classification athlete. There were no women's relay events. In total there were 144 events held over 17 disciplines.
Athletes finishing in first place are awarded the gold medal, second place the silver medal and third place the bronze. If only three competitors are available to challenge for an event then no bronze medal is awarded. Some events were classed as 'no medal' events.
This section is empty. You can help by adding to it. (August 2013)
Main article: Disability sport classification
To ensure competition is as fair and balanced as possible, athletes are classified dependent on how their disability impacts on their chosen event/s. Thus athletes may compete in an event against competitors with a different disability to themselves. Where there are more than one classification in one event, (for example discus throw F54/55/56), a points system is used to determine the winner.[3]
F = field athletes
T = track athletes
11-13 – visually impaired, 11 and 12 compete with a sighted guide
20 – intellectual disability
31-38 – cerebral palsy or other conditions that affect muscle co-ordination and control. Athletes in class 31-34 compete in a seated position; athletes in class 35-38 compete standing.
41-46 – amputation, les autres
51-58 – wheelchair athletes
● Opening ceremony Events ● Closing ceremony
Date →
100 m Men
Details T11
T42 T34
T46 T51/53
T12 T34/52/53 T42
Details T44 T46
T34/52/53
T54 T12 T44
1500 m Men
4×100 m relay Men
Details T11-T13
Long jump Men
Details T37/38 F36 F11 F20
F13 F42/44
Details F13 F20
F38 F42/44/46
Shot put Men
Details F20
F52/53 F56/57/58 F40
Details F37 F35/36
F57/58 F20 F40/42/44
F11/12 F34
Details F51/53/53
F57/58 F40/44
Details F51/52/53 F35/36 F37
Javelin throw Men
Details F12/13
F44 F33/34/52/53 F54
Details F57/58 F12/13 + F37/38 F52/53/33/34 F46
Club throw Men
Ceremonies ● ●
The medal table at the end of Day 5 (28 June).
* Host nation (Netherlands)
Ukraine (UKR)
Germany (GER)
Poland (POL)
Spain (ESP)
Greece (GRE)
Netherlands (NED)*
Great Britain (GBR)
Bulgaria (BUL)
Serbia (SRB)
Belarus (BLR)
Italy (ITA)
Finland (FIN)
Sweden (SWE)
Azerbaijan (AZE)
Switzerland (SUI)
Czech Republic (CZE)
Portugal (POR)
Lithuania (LTU)
Cyprus (CYP)
Croatia (CRO)
Slovakia (SVK)
Turkey (TUR)
Ireland (IRL)
Romania (ROU)
Austria (AUT)
Iceland (ISL)
Slovenia (SLO)
France (FRA)
Hungary (HUN)
Belgium (BEL)
Bosnia and Herzegovina (BIH)
Totals (34 nations)
Source: paralympic.org
Multiple medallists
Participating nations
Below is the list of countries who agreed to participate in the Championships and the requested number of athlete places for each.
^ "IPC Athletics European Championships Open". paralympic.org. 23 June 2013. Retrieved 31 July 2013.
^ "IPC Athletics European Championships 2012 Stadskanaal". disgames.org. Archived from the original on 4 March 2016. Retrieved 31 July 2013.
^ "Classification". paralympic.org. Retrieved 22 July 2013.
Official web-site

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New Music: Remy Shand (@RemingtonShand) - "WhereAreWeGoing?"
Man, have I missed this dude's music!
So apparently he's been releasing music on his YouTube page, and this one's a new track coming from his indie label, Remy Records. Sounds like a modern day, retro "What's Going On".
Im so happy you are releasing music!!


text:
Q: custom AppBar The element type 'List' can't be assigned to the list type class BottomOfAppBar extends StatelessWidget implements PreferredSizeWidget {
  BottomOfAppBar({Key? key, required this.tabs}) : super(key: key);
  List tabs;
  @override
  Widget build(BuildContext context) {
    return Obx(() => Container(
          child: ColoredBox(
            color: Colors.white,
            child: Column(
              children: [
                widget.tabbarenable
                    ? TabBar(
                        labelColor: Colors.purple[100],
                        indicatorColor: Colors.purple,
                        isScrollable: true,
                        labelPadding:
                            const EdgeInsets.symmetric(horizontal: 8.0),
                        tabs: <Widget>[tabs])
                    : Container()
              ],
            ),
          ),
        ));
  }

  @override
  Size get preferredSize => const Size.fromHeight(55.0);
}

Hello,
I am trying to use tab variables in customAppBar class but I am getting this error. tabs: tabs line gives this error.
any help

A: Replace List tabs; with List<Widget> tabs; and provide tabs like
tabs: tabs,
 TabBar(
      labelColor: Colors.purple[100],
      indicatorColor: Colors.purple,
      isScrollable: true,
      labelPadding: const EdgeInsets.symmetric(horizontal: 8.0),
      tabs: tabs,
    );

does it solve your issue?

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Coupons valid until December 31, 2018. Pick up starting December 18, 2018. May redeem multiple coupons per person. Open Monday to Sunday from 5:30 AM till 11:00 PM. Valid at Achrafieh branch only. Reservation required on 01 202 743, quote Gosawa coupon. Coupons must be printed. No carry over. VAT included in price. Standard terms & conditions apply.
Christmas is all about enjoying a delicious feast with the whole family! Get this 4 Kg Turkey & 40-cm Bûche de Noël & Karabij from Fouad el Jer el Doueihy, only $100 instead of $200.
Have yourself a delicious treat!


Atlanta –The Young Harris College women's tennis opened its fall season Friday at the SCAD-Atlanta Invitational.
The Mountain Lion netters had some mixed results, but overall head coach Jacob Turner was pleased with some of the positive results.
In the Women's A Flight Singles Main Draw, Sara Rodgers lost to Sadia Mayou, 6-0, 6-0 and Sarah Deese fell to Mary Claire Sliade, 6-0, 6-0. In the consolation bracket, Deese dropped a 6-0, 6-0 decision to Dahbi.
In the Women's B Flight Singles Main Draw, Mary Beth Maxwell was topped by Asia Boyd, 6-0, 6-0, but Herndon defeated Rebecca Swindall, 6-1, 6-2. In the consolation bracket, Maxwell fell to Adreina Gomez, 6-4, 2-6, 13-11.
In doubles play, the team of Deese and Maxwell lost to Slaide and Mayou, 8-0. Rodgers and Herndon beat Boyd and Gomez, 8-4.
Atlanta — The Young Harris College men's tennis team opened its fall season Friday at the SCAD-Atlanta Invitational.The Mountain Lion netters had some mixed results, but overall head coach Jacob Turner was pleased with some of the positive results.
In the Men's A Flight Singles Main Draw, Mitchell Midkiff fell to Salif Kante, 6-0, 6-0 and Koren Gottenbos lost to Jack Anton, 6-1, 6-0. Martin Harach dropped a hard-fought match to Ismail Lemtoni, 7-5, 7-5. In the consolation bracket, Gottenbos lost to Harach, 6-3 and then retired. Akeen Bryon topped Midkiff 6-1, 6-4.
In the Men's B Flight Singles Main Draw, Jacob Greene was blanked by Christian Beling, 6-0, 6-0 and Jacon Scarborough fell to Ali Vazin Homedani, 6-0, 6-0. Hamala won his match over Nathan Singleton, 6-3, 7-6 (7-2). In consolation play, Singleton topped Scarborough, 6-3, 6-1.
In men's doubles play, Scarborough and Green lost to Konte and Bryan, 8-0 and Harach and Gottenbos defeated Beling and Singleton, 8-5. Midkiff and Hamala dropped a hard-fought 8-5 decision to Lemtouri and Homedani.


Hear the latest from RNZ's flagship music show.
Nick Bollinger lends a critical ear to current new releases (pictured here with Toumani and Sidiki Diabate).
Emerging artists present their fresh sounds.
See live performances from the RNZ Music studios.
Musical guests compile a C60, and talk us through their selections.
Join seasoned industry insider, Trevor Reekie (pictured here with Michael Kiwanuka).
Hear the weekly Music 101 Podcast.
Browse playlists from Radio NZ Music producers.
Journey through musical places, cultures, and artists.
Hear stories from people in musical industries.
Profiles of New Zealand musicians, in their own words.


One of the foods that I really, and I mean really really miss after going vegan is a classic cream cheese bagel. As a kid I would absolutely load cream cheese onto my bagels. Definitely not healthy. There is something about the creamy and tangyness of the cream cheese that I really missed. I was craving a cream cheese bagel recently and had one for brunch at a cute smoothie bar. It was good, but I knew it could have been better. I knew that the secret was to actually culture the cheese. There are a lot of recipes for vegan cream cheese that just require you to blend all of the ingredients and it's good to go, but to me it's just not the real thing. That method is great if you just want to whip up a quick bagel, but it still yields a sweet cream cheese due to sweetness from the cashews.
If you want a vegan cream cheese that literally tastes like the real thing, then look no further. I'm so proud of this recipe because my favourite recipes are the ones that you can easily re-create into a vegan version, without any bad ingredients, while still yielding a perfect result. Most store-bought vegan cream cheese is filled with refined oils, processed soy, and other nasty ingredients. And really, they just don't taste like real cream cheese. So please enjoy this recipe for easy, simple, and super healthy vegan cream cheese, and make sure to let me know what you think!
Use a good quality vegan probiotic. I used 2 50 billion cfu capsules, and this is all that I experimented with. You very well may be able to get away with using a small cfu count, so feel free to experiment.
Use a wooden or plastic spoon to mix the cream cheese, because there is a chance that using a metal spoon may cause a reaction with the probiotics and, preventing your cheese from culturing!
Blend the cashews, water, lemon juice, salt, and pepper in a high-powered blender for a few minutes until perfectly smooth.
Transfer the cashew mixture to a small glass dish. Break open the probiotic capsules and mix them in with a wooden or a plastic spoon. Using a metal spoon can possibly cause a reaction with the probiotics, preventing your cheese from culturing, so avoid using one! Mix until the probiotics and the cheese is well combined.
Cover the dish with a cheese cloth and allow the cheese to sit for 24 hours in a room temperature or warm location.
After 24 hours, the cheese will have turned slightly tangy. Mix in the finely chopped herbs and refrigerate the cheese until it is cold and firm.
Serve on top of bagels, with veggies, and much more. Enjoy!


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Google takes Android One to Africa with the ¢370 Infinix Hot 2
by Qwesi GyanSeptember 29, 2015
Today Google has announced that the Android One program has entered a new continent: Africa. So far, the company's affordable smartphone initiative has been contained to certain Asian markets.
However, with the Infinix Hot 2 handset, Android One will debut in Nigeria, Ghana, Ivory Coast, Kenya, Egypt, and Morocco. These countries have combined populations of 379 million people. Infinix, Google's partner this time around, is apparently "one of the hottest, fastest growing smartphone brands in Africa".
The Infinix Hot 2 comes with a 5-inch 720p touchscreen, an 8 MP rear camera with LED flash, a 2 MP selfie snapper, a 1.3 GHz quad-core MediaTek processor, 16GB of storage, dual-SIM support, an FM radio, and a 2,200 mAh battery. There's a version with 1GB of RAM, and this is offered in black, white, red, or blue, and another with 2GB of RAM, which is only out in gold.
The smartphone runs Android 5.1.1 Lollipop from the get-go, and it's also guaranteed to receive an update to Android 6.0 Marshmallow at some point in the future.
The Hot 2 is available today in Ghana for ¢370 (with 1GB of RAM),or ¢450 (with 2GB of RAM). These prices currently translate into $99 and $120, respectively. The device will make its way to the other African countries mentioned above "over the next few weeks", presumably with similar pricing.
Buyers Guide, Cellphones, Guides, News
Editor's Pick, hot 2, infinix, infinix hot 2, Latest Headlines, Top Stories
Editor's PickinfinixLatest HeadlinesTop StoriesBuyers GuideCellphonesGuidesNews
Airtel Ghana Launches the First ever Tap and Pay Mobile Money Payment Service...
Google and LG's 5X is the Nexus for the rest of us


COMPASS® Bacillus cereus Agar is a rapid method for the enumeration of presumptive Bacillus cereus in human and animal food products within 24 hours.
COMPASS® Bacillus cereus Agar is a solid medium used for the detection and the enumeration of spores and vegetative forms of presumptive species belonging to the group Bacillus cereus in products destined for human and animal consumption.
Detection or enumeration can be performed directly on this medium without purification steps, biochemical confirmation (glucose fermentation, Voges-Proskauer, nitrate reduction and hemolysis testing) and/or microscopic examination normally done within the confines of standardized methods.
COMPASS® Bacillus cereus Agar for the enumeration of presumptive Bacillus cereus is officially certified by AFNOR Certification, under the reference number BKR 23/06-02/10.
This entry was posted in Latest News and tagged BioKar, COMPASS® Bacillus, Microbiological Media.


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101 Dalmatians + Friends for Cath Kidston
At 7am, Shelton Street, nestled in the heart of Covent Garden, is usually a quiet and tranquil place, with commuters walking to the tube in the early morning sunshine, a couple of joggers pounding the pavements and coffee shops just opening up their shutters; however, here at PetLondon Models we knew this wouldn't be the case as we were tasked in providing 25 dogs for the launch of Cath Kidston's brand new 101 Dalmatian range in collaboration with Disney.
Queuing up to Checkout
Our assignment was to provide 6 Dalmatians to be stars of the show, with 20 other dogs of varying sizes, ages and breeds to support them. Even though not close to the 101, it sure felt like it, as it was possibly a record number of dogs in one location at one time in recent history for PetLondon Models.
Forming an orderly queue…
The 6 Dalmatian stars rose very early with their owners to get over to Covent Garden. For the participants it was a great experience. "We as owners, were a little nervous on arrival not really knowing what to expect!" said Celia, the owner of Suzy and Bebe. "We were put at ease immediately by the warm welcome to both ourselves and the dallies and was impressed with Adams professional handling of all the dogs."
The Dalmatians came from near and far, very reminiscent of the film, to partake in the earlier part of shoot taking place in the store itself. Below from left to right we have the six superstars: Roo, Bebe, Suzy, Dolly, Mylo & Domino. We had a truly magical tear-jerking Disney moment, as Mylo & Domino found out they were siblings and have been reunited years later on this shoot. After the shoot was done, they were seen walking side-by-side to go for some brunch and a paw-to-heart.
Mylo and Domino litter siblings united after years apart!
The goal of the shoot was to get some amazing shots of the Dalmatians in store and outside the store in some fun and candid setups. This included Bebe placing her paws on the counter pretending to pay for her goods, Roo walking out the shop happy as can be with a shopping bag in this mouth and a couple of the models sniffing around the shop itself looking at the Dalmatian emblazoned merchandise.
The Disney range itself is very varied with different designs and motives across a wide range of products; from tote bags to umbrellas, purses to socks, pyjamas to aprons each is classically Dalmatian themed, both for adults and kids alike. The range is available across all stores and online for the UK, and in selected international outlets. Please check here.
Whilst this was taking place, in a courtyard just around the corner, the rest of the supporting cast and crew arrived. Not only did we have twenty dogs, but also one human model for every animal. The cast included a range of typical dogs seen out shopping on your local high-street, so we had a varied collection of supporting cast including: Poodles, French bulldogs, Pugs, Jack Russell, Sausage Dogs, Spaniels and a lot more aside! The models were to each have a canine companion for the duration of the shoot. The dogs definitely chose their new pet parent for that morning and after a lot tail wagging and sniffing , we were ready to start the second part of the shoot taking place outside the store.
Lolly, Bix, Peggy, Lola and Milo chilling out on set
Models getting to know their new pet parents
The aesthetic was to line them up along the shop front with the Dalmatians at the front of the line, with each dog and their model forming a somewhat orderly queue behind. It was a very high energy set with so many models both human and canine together, but some amazing shots were taken. Lots of squeaking, clapping, barking and cheering to get the attention of the dogs. After some readjustments and repositioning of certain dogs, the camera team was able to snap some fantastic shots.
Getting the pawww-fect shot
The hallmark of any successful job is finishing early, and this assignment finished a full 60 minutes ahead of schedule. All the dogs were pawfectly awesome and were as good as gold considering all the excitement.
#CatsOnaPlane
A recent and very top secret project we have been working on a PetLondon Models HQ was a multi-cat job involving some very unusual requests! The assignment involved a large group of friendly felines needed for filming on actual airplanes at an Airport.
This job was for both Thomas Cook Airlines and its sister Airline, Condor. The airlines wanted some cats to test out the comfort of their new Airbus 330 and Boeing 767 and to create entertaining, promotional viral videos. The resulting footage and images were to become part of the #CatsOnAPlane campaign. The campaign, which launches as part of a wider advertising initiative for Thomas Cook Airlines in both the UK and Germany, aims to highlight the airline's belief that customers "deserve better" when flying on their hard-earned holidays.
Travelling with animals by air, especially with cats is very difficult when you live in the UK so this was a unique and one-off experience for some of our models to try out being in the actual cabin of a plane!
The initial brief was very detailed. There were ten roles up for casting and PetLondon Models was asked to help suggest cats for each position. Each character we had to fill had a brief about their individual personalities. We studied the storyboards and cross-checked these against our books to see who would be fitting for each role. In the end a variety of options went over to the client for each of the characters to be cast and they then had the difficult decision of selecting the final few. For many jobs there is strong competition for each position and behind the scenes the clients are often choosing between a few animals for each role.
Once word was in of the clients final choices, the excitement began for many of our cats and handlers. The filming schedule spanned nearly a full 24-hour period. Travel arrangements and schedules had to be carefully planned in advance and practise began for each cat to get used to what they would need to do on set.
First up we had Starina. She was chosen for the role of "Princess Pamper". Having worked with Starina on many previous occasions we certainly agree this was the perfect character for her to play! "Princess Pamper (Pamps to her friends) is a lover of the finer things in life.She was chosen because she's renowned for her demanding demeanor.For Pamps to be happy she requires a certain set of guidelines to be adhered to. If all her needs are met, it's a smooth ride for everyone"
Starina is a very easy-going cat who is used to going on lots of outdoor adventures. It was her first time on a plane but she took everything in her stride and took some time to select her favourite seat!
Starina Settles Into Her Preferred Seat
Starina enjoyed looking out the window and meeting all the crew on set. Once it was time to get filming, she was as ever, ready to perform for the camera! This sweet girl has the most stunning eyes, one blue and one green.
Here is the final footage of Starina's filming that we are delighted to be able to share with you. The online ad shows Starina relaxing on Thomas Cooks newly refurbished A330 and has subtitles to show what she might be thinking.
Next, was the role of "The Stray Siblings". There were several litters in the running for this position but in the end it was six adorable Chausie brothers and sisters who were selected by the client. Only three were used in the footage but they took the filming in turns and this enabled the babies to get some rest in between the swaps. They loved all the excitement though and could not get enough of their first big adventure!
"Ben, Jane and Alice Stray are 3 siblings. They're well known as the toughest, most challenging and rowdy bunch of testers… and they know it. They know how to push the buttons of cabin crew and how to truly stress test the friendly customer service."
The Chausie Kittens enjoyed all the excitement of exploring somewhere new
Here is their final footage. As you will see, these babies truly enjoyed themselves, having time to explore and play, watch some in-flight entertainment and then after all that excitement, taking a nap with their teddy bear!
Next was the very distinguished Zinedine. Zinedine (nickname Zinny) was cast as "Quality Ken". "Quality Ken is a total cynic, he's hard to impress and he knows it. He plays his cards close to his chest – he hates to show anyone what he's really thinking… even if it's good!Ken's lived a quiet life, he's the eldest of 18 brothers and sisters…always the most reliable. He doesn't often let his hair down. Ken is one of those cats who's ashamed of his feline instincts. Behaving cat-like demeans the air of authority he has worked so hard to achieve."
Zinny is a six year old male Persian from London. He is very confident with being an actor and enjoys meeting new people or trying new experiences. Arriving at the airport he was not phased by the hangar but did appreciate a cosy blanket to snuggle up in.
Waiting Patiently for the Camera Crew to get ready….
Sweet Zinny is a most expressive cat and his film reel certainly demonstrates this and entertains viewers about the airlines newly refurbished fleet. He was so cosy and happy in his seat that he was quite miffed when it was time to leave!
Finally we had brothers Orpheus and Ryder. These Norwegian Forest Cats are the best of friends. They enjoy to do everything together and so this was a perfect opportunity for them to be side by side. They were both working on the Condor Plane.
Orpheus played the role of "Captain". Captain is a more senior role and he is a well versed flyer who has flown with Condor for a lifetime. He enjoys the welcome and warmth hwereceives on every flight. Orpheus performed like a true pro as he quickly settled into the new environment and relaxed into his comfortable seat.
One lucky cat was chosen to travel business class and this was Ryder! With his stunning pure white coat he looked very elegant in his oversized and reclining seat and was able to fully stretch out. He even managed to operate the controls himself.
This project was a delight to work on for all the handlers, crew and animals involved. As a special sneak peak we have some behind the scenes footage to be able to share with you if you have have ever wondered how on earth his all gets put tougher
The fabulous collection of viral ads are currently being promoted across Facebook, Instagram and Twitter.
Tom Morey, senior group marketing manager at Thomas Cook Airlines, said: "No-one can assess comfort like a cat. They're the hardest customers to please, which is why we wanted to test our new interiors with the best. And the results left the cautious kitties feline great."
Harvey Nichols Menswear Launch
A dozen PetLondon Model dogs descended upon Knightsbridge to promote the launch of department store Harvey Nichols new menswear department that is selling clothes by 270 designers in Central London.
Harvey Nichols, founded in 1831, is a British department store chain with a flagship store in Knightsbridge, London. It sells fashion collections for men and women, fashion accessories, beauty products, wine and food.
To celebrate the grand opening of the newly refurbished and relaunched menswear department some talented dogs were called in from us. A total of three different breeds all in groups of four; Bulldogs, Greyhounds and Afghan Hounds. At PetLondon HQ there was a lot of preparatory work needed. We set to task putting together some quads who would be happy working together and also had to take a series of measurements that would be used to create some custom-made outfits for each dog.
Since some of these breeds were especially tricky shapes, this called for some of the owners to get creative with their sketch pads and we were especially impressed with some of the submissions.
The event called for a very early start and some of our models set off very early in order to make it in time for the 7am meet and greet. This was a chance for all the dogs to get familiar with each other and for the male model appointed to each group to get acquainted with his animals. All the dogs were in high spirits and excited by all the fuss and extra attention they were recieving.
First on the schedule was a photoshoot with a photographer outside the stores main entrance and also on the square to the side of the store. The dogs posed in their groups of four of a breed with the male models.
From Left to Right, The Bulldogs; Queenie, Louie, Coco and Olive
Each dog's outfit co-ordinated with what the human model was wearing. The Bulldogs that included sisters Coco and Olive, along with Louie and Queenie were wearing raspberry pink polo shirts and navy gilets.
From Left to Right; Norman, Suki, Lurch & Jet
The Greyhounds' outfit was our personal favourite, they were wearing tailored suits complete with shirt collars and ties. All of the dogs in this group were especially charming and friendly. They looked so professional and dapper and the colour scheme suited them perfectly.
From Left to Right; Iraida, Lucca, Trieze & Louis
Finally, the Afghan Hounds in their bright orange cashmere. These girls and boys were from different owners but all related in that they all shared the same father. It was a great chance for a family reunion and there was much excitement all round. These dogs are show-stoppers, with their elegant flowing locks that were blowing in the wind, they were impossible to miss.
A variety of fabulous shots were taken of all the dogs, both static and on the move. Many of these made it onto social media and into the evening press with a great response from the public.
After the still shots next was a promotional walk around the perimeter of the store to hand out Harvey Nichols goody bags to the surprised but exceed passers-by.
PetLondon Models also took some behind the scenes footage. Here you can see the Greyhound group doing one of their walks outside the Knightsbridge store. A lot of passers-by did a few double-takes. Its not every day you see such a sight, even in London!


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Gov. Whitmer Announces 50 New Jobs as Global Building Products Manufacturer LP Building Solutions Expanding in Dickinson County
Kathleen Achtenberg
LANSING, Mich. – Today, Governor Gretchen Whitmer joined the Michigan Economic Development Corporation (MEDC) to announce that global building products manufacturer LP Building Solutions is expanding its operations in Sagola Township with support from the Michigan Strategic Fund (MSF). The company's $194 million investment is one of the largest projects ever supported by the MSF in the Upper Peninsula.
The project is expected to create at least 50 jobs and retain the 151 jobs currently at the site, supported by a $325,000 Michigan Business Development Program performance-based grant. Michigan was chosen for the project over competing sites in the U.S. and Canada.
"This transformational investment by LP Building Solutions – one of the largest ever supported by Michigan's economic development fund in the U.P. – will create at least 50 good-paying manufacturing jobs in Sagola Township and underscores the strength of our talented manufacturing workforce and the attractiveness of our business climate," said Governor Whitmer. "Together, we will continue growing Michigan's economy by empowering our hardworking people and innovative businesses. I will work with anyone to build on our momentum, and investments like this one by LP Building Solutions will help us continue moving our state forward."
LP Building Solutions, headquartered in Nashville, Tenn., is an international leader in high-performance engineered wood building products for new construction, repair and remodeling, and outdoor structures that meet the demands of builders, remodelers, and homeowners worldwide. The company has operated in Sagola Township in Dickinson County since 1988 and currently employs 151 people at that location.
To meet growing customer demand for LP's engineered wood home siding products, LP plans to convert its Sagola Township operations from the manufacture of oriented strand board to LP® SmartSide® Trim & Siding, a large-scale conversion project that will create at least 50 new positions and has the potential for future expansion of a second processing line, which would create additional investment and employment opportunities in the region. The expansion will include 134,000 square feet of new construction as well as new machinery and equipment.
For more than 20 years, LP SmartSide Trim and Siding has provided customers with an innovative approach to home siding that combines the beauty of traditional wood and the durability of engineered wood. In that time, SmartSide siding products have experienced tremendous success and become one of the fastest-growing siding brands in the U.S.
"This project is an exciting win for the Upper Peninsula and further demonstrates Team Michigan's commitment to supporting economic opportunities throughout all regions of the state. We appreciate LP Building Solutions' vote of confidence in Michigan and our talented workforce," said Quentin Messer, Jr., CEO of the MEDC and President and Chair of the Michigan Strategic Fund. "We are grateful to the Governor and legislators for the continued support of the Michigan Business Development Program. We're proud to join our partners at Invest UP, Sagola Township, and the Dickinson Area Economic Development Alliance as we celebrate LP Building Solutions' expansion and look forward to working together to grow, add jobs and provide greater opportunity for our friends and neighbors in the Upper Peninsula."
This will be a transformational project for the Upper Peninsula and will have a profound ripple effect of positive economic impact on Sagola Township as well as the surrounding region. In addition, the company will be contracting with local suppliers and contractors, creating additional investment and employment opportunities. LP offers competitive wages and full benefits to its employees and is also an active contributor to the local community.
"Customer demand for LP SmartSide Trim and Siding is at an all-time high," said Executive Vice President, General Manager of Siding Jason Ringblom. "To ensure our customers have the product they need to build beautiful, durable homes and structures, capacity expansion projects like our conversion of LP Sagola to the manufacture of LP SmartSide are incredibly important to LP. In addition to supplying the increased demand for SmartSide, converting LP Sagola to a siding facility positions the mill for years of growth and improved stability, which will benefit our local employees, their families, and the broader community. We are thrilled to welcome LP Sagola to LP's SmartSide family of mills."
Sagola Township anticipates approval of a property tax abatement in support of the project, and the MEDC also authorized a State Education Tax abatement to be used with the local abatement. Individuals interested in careers with LP should visit here.
"We are excited to see this significant investment in the LP Sagola facility," said Dickinson Area Economic Development Alliance Executive Director Lois Ellis. "The project will align the plant to produce a high-value product and provide 50 additional family-sustaining jobs with excellent wages and benefits for area residents."
About LP Building Solutions
As a leader in high-performance building solutions, Louisiana-Pacific Corporation (LP Building Solutions, NYSE: LPX) manufactures engineered wood building products that meet the demands of builders, remodelers, and homeowners worldwide. LP's extensive offerings include innovative and dependable building products and accessories, such as Siding Solutions (LP® SmartSide® Trim & Siding, LP® SmartSide® ExpertFinish® Trim & Siding, LP BuilderSeries® Lap Siding, and LP® Outdoor Building Solutions®), LP Structural Solutions (LP® TechShield® Radiant Barrier, LP WeatherLogic® Air & Water Barrier, LP Legacy® Premium Sub-Flooring, and LP® FlameBlock® Fire-Rated Sheathing, LP NovaCore™ Thermal Insulated Sheathing, and more), LP® TopNotch® Sub-Flooring, and oriented strand board (OSB). In addition to product solutions, LP provides industry-leading customer service and warranties. Since its founding in 1972, LP has been Building a Better World™ by helping customers construct beautiful, durable homes while our shareholders build lasting value. Headquartered in Nashville, Tennessee, LP operates 22 plants across the U.S., Canada, Chile, and Brazil. For more information, visit LPCorp.com.


Rainforest Mist bath spray can be used daily on the birds. Rainforest mist will cleanse your bird and relieve dry, itchy skin while helping to prevent feather plucking and unnecessary molting. This product helps rid lice and mites. Has a nice Hawaiian Hibiscus Scent.
All small birds, Finches, Canaries, Parakeets, Lovebirds, Cockatiels.
Shake well and spray on bird 12 inches away until feathers are visibly wet. Do not spray near open food, or water, or directly into birds face. Keep bird out of drafty areas during use to prevent the bird from chills.
Do not spray sick birds with this product unless other wise directed by a veterinarian, as this may make the bird get chilled.
Does not contain alcohol,will not discolor plumage.


Li Keqiang vows #China-#ASEAN "diamond decade"
Premier Li Keqiang called for an "upgraded version" of the free trade area (FTA) between #China and #the Association of Southeast Asian Nations (#ASEAN), pledging economic and trade cooperation of "greater scope and higher quality."
Xi Jinping says #China #ASEAN trade surged from 7B to 362.8B. Average annual growth of over 20%.
Xi Jinping and Thai Deputy Prime Minister meet at #China #ASEAN Expo and pledge further development of ties.
Xi Jinping inspected Guangxi Zhuang Autonomous Region.
Wen Jiabao visited Guangxi Zhuang Autonomous Region.
Li Keqiang addressed the opening ceremony of the 6th China-ASEAN Business and Investment Summit (CABIS).
Hui Liangyu inspected Guangxi Zhuang Autonomous Region.
Zhou Yongkang attended the presentation ceremony of the Treasure Ding-Tripod of Ethnic Unity, on accasion of celebrating the 50th founding anniversary of the Guangxi Zhuang Autonomous Region.
Wang Qishan met with leaders of ASEAN countries who are here to attend the fifth China-ASEAN Expo.
Wen Jiabao inspected Guangxi Zhuang Autonomous Region.
Ma Biao was appointed acting chairman of Guangxi Zhuang Autonomous Region.
Zeng Peiyan addressed the opening ceremony of the 4th China-ASEAN Business & Investment Summit.
Jia Qinglin met with Former Laotian President Khamtay Siphandone.
Li Changchun inspected Guangxi Zhuang Autonomous Region.
Wen Jiabao met with Philippine President Gloria Macapagal Arroyo, Singaporean Prime Minister Lee Hsien Loong, Indonesian President Susilo Bambang Yudhoyono, Cambodian Prime Minister Hun Sen and Malaysian Prime Minister Abdullah Ahmad Badawi.
Wen Jiabao and heads of ten ASEAN countries attended the opening ceremony of the Commemorative Summit marking the 15th Anniversary of ASEAN-China Dialogue Relations.
Zeng Qinghong inaugurated the opening ceremony of the second China-Association of South East Asian Nations (ASEAN) Exposition.
Zeng Qinghong met with Cambodian Prime Minister Hun Sen.
Zeng Qinghong met with Thailand deputy Prime Minister Somkid Jatusripitak.
Zeng Qinghong met with Myanmar Prime Minister General Soe Win.
Zeng Qinghong met with Laotian Vice President Choummali.
Zeng Qinghong met with Vietnamese Deputy Prime Minister Nguyen Tan Dung.
Huang Ju made remarks at a work conference of the People's Bank of China (PBC), the central bank.
Huang Ju inspected Guangxi province.
Zeng Peiyan made remarks at the opening of the Western Forum of China 2004.
Wu Yi held meetings with Cambodian Prime Minister Hun Sen, Laotian Prime Minister Boungnang Vorachit and Myanmar Prime Minister Soe Win, who were in the city to attend the First China-ASEAN Expo.
Zeng Qinghong inspected Guangxi Zhuang Autonomous Region.
Hui Liangyu inspected Guangxi province.
Jia Qinglin made an inspection tour in Guangxi Zhuang Autonomous Region.


Our close proximity to Philadelphia, King of Prussia and the Blue Route makes Fleming's of Radnor a convenient location for exceptional social and business affairs. Available for lunch and dinner, our four Private Dining Rooms can easily accommodate a wide range of events, from corporate meetings and business presentations to rehearsal dinners and intimate family gatherings. Each Private Dining Room is equipped with a Cisco® conferencing system for video connection with all our other Fleming's locations and up to five satellite sites.


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Political Law Briefing
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U.S. Supreme Court Allows Expanded Donor Disclosure Rules to Take Effect
By Lawrence H. Norton, Janice M. Ryan & Sean Wright on September 20, 2018
Posted in 501(c)(4), Disclosure, FEC, Super PACs
The U.S. Supreme Court this week left in place a lower court ruling that expands donor disclosure for advocacy groups that fund independent expenditures. While the full effect of the ruling may not be known for some time, groups in the throes of an election season suddenly have to reconsider their electoral spending plans and fundraising practices, and donors to politically active 501(c)(4) social welfare organizations or 501(c)(6) business leagues have to account for an increased risk that their donations will be publicly disclosed.
What Does the Ruling Do?
Groups that are not registered with the Federal Election Commission (FEC) as campaign committees, party committees, or PACs are nonetheless required to file reports if they make an expenditure of more than $250 that expressly supports or opposes a federal candidate. These "independent expenditure" reports must itemize disbursements to each vendor involved in the creation and distribution of an ad (or other public communication), and identify the election involved and whether the organization supports or opposes the featured candidate.
In addition, a long-standing FEC rule requires that these reports identify donors who gave more than $200 to the organization in the calendar year for the purpose of funding the particular ad that is being reported. As a practical matter, donors seldom know that their funds will be used to pay for a specific ad, and thus donors have rarely been disclosed.
The district court struck down the FEC donor-disclosure rule, concluding that it applied the statutory disclosure requirement too narrowly. The court concluded that independent expenditure reports filed by groups that are not registered political committees must identify all donors who (1) give to the organization for the purpose of influencing a federal election, or (2) give for the purpose of funding the group's independent expenditures, whether tied to a specific ad or not. The court stressed, however, that contributors to an organization's "general programs" need not be identified.
The court deferred the effective date of the ruling for 45 days, giving the FEC time to adopt a new donor disclosure rule. That period came and went with no new rule or interpretive guidance. Crossroads GPS, which intervened in the case, has appealed the ruling to the D.C. Circuit.
Continue Reading U.S. Supreme Court Allows Expanded Donor Disclosure Rules to Take Effect
Pre-Election Year Housekeeping to Boost Your Government Affairs Program and Help You Stay out of Trouble
By Lawrence H. Norton & Lyndsay E. Steinmetz on December 21, 2017
Posted in Compliance, Contributions, Lobbying, PAC Compliance, State, Super PACs
With an election year just weeks away, there are steps you can take now to boost the effectiveness of your government affairs program, and help your organization and its principals avoid legal trouble. This is a particularl y good time to fill the coffers of your PAC, develop a political contribution plan for next year,…
Federal Government Contractor Fined for Super PAC Contribution
By Lawrence H. Norton & Ronald M. Jacobs on October 3, 2017
Posted in Campaign Finance, Contributions, Super PACs
The Federal Election Commission has fined a federal contractor for making $200,000 in contributions to a Super PAC that supported a candidate in the 2016 presidential election. This is the first time the FEC has fined a government contractor for contributing to a Super PAC.
Federal contractors are prohibited from making contributions to federal candidates…
A Guide to Supporting the 2016 Presidential Nominating Conventions: From Hosting Events to Writing a Check
By Lawrence H. Norton, Ronald M. Jacobs & William Powers on June 3, 2016
Posted in Gift laws, Lobbying, Super PACs
By White House/Chuck Kennedy (White House (P090612CK-0875)) [Public domain], via Wikimedia Commons
Thinking about sponsoring or hosting an event at the presidential nominating conventions in Cleveland and Philadelphia? Or considering giving free items to attendees?
Venable's client alert summarizes recent guidance on convention events from the House and Senate ethics committees,…
Setting Up and Operating a Super PAC
By Lawrence H. Norton, Ronald M. Jacobs & Janice M. Ryan on May 31, 2016
Posted in Campaign Finance, FEC, Super PACs
Interested in what it takes to set up a federal Super PAC? Take a look at Venable's recently released white paper summarizing the key rules of the road, including:
Steps for creating a federal Super PAC
Avoiding illegal coordination with candidates
FEC and IRS reporting obligations
Advertising disclaimers
For those interested in Maryland elections, please…
Super PAC or Super Fraud: What to do when a super PAC raises money off a candidate's name but doesn't actually do anything to support the candidate
By Ronald M. Jacobs on May 29, 2015
Posted in State, Super PACs
Some candidates have a cozy relationship with super PACs that support them (as close as they can, given rules about coordination). Others are surprised and excited when a super PAC shows up to help out. But sometimes a super PAC raises money using a candidate's name or picture, but doesn't do much to help the candidate. In those cases, the candidate may be concerned the super PAC is taking donations that might otherwise go directly to the campaign or to super PACs that are actively supporting the candidate. 2013 Virginia gubernatorial candidate Ken Cuccinelli faced such a situation and decided to sue over it.
The lawsuit, which was filed in federal court, was not based on any campaign finance laws, but on the federal Lanham Act, which is a false advertising statute, and state law claims of false advertising, breach of contract, and unauthorized use of Mr. Cuccinelli's name and picture. Mr. Cuccinelli sued not only the super PAC, but also all of the individuals associated with the super PAC. The case settled on interesting terms.
First, the Super PAC and its principals agreed to pay Mr. Cuccinelli $85,000. They also agreed to turn over their solicitation lists to Mr. Cuccinelli so he can use them either to raise money for future campaigns or to rent the lists to others. The Super PAC and the company that ran it will also undertake certain "best practices" in future campaigns. These include honoring a request from a candidate to stop using the candidate's name or picture and maintaining contact information on their website. These terms make clear they apply to other PACs that are clients of the defendant's company. In this respect, Mr. Cuccinelli may have helped future candidates that find themselves in his spot. …
Continue Reading Super PAC or Super Fraud: What to do when a super PAC raises money off a candidate's name but doesn't actually do anything to support the candidate
Please Join Us: WEBINAR – Ramping up for the 2016 Cycle: Make Compliance a Priority for Lobbying and Political Activity
By Ronald M. Jacobs & Lawrence H. Norton on March 11, 2015
Posted in Contributions, FEC, Lobbying, Pay-to-Play, State, Super PACs
1:30 p.m. – 2:30 p.m. ET – Webinar
The Justice Department recently announced its first criminal prosecution for coordination. States like Virginia are revamping their ethics laws and California recently imposed new restrictions on lobbyists. Although the IRS has yet to issue regulations for 501(c)(4)s, many states have created new disclosure requirements for politically active nonprofit groups. Maryland has imposed tough new disclosure requirements on state contractors that make campaign contributions. …
Continue Reading Please Join Us: WEBINAR – Ramping up for the 2016 Cycle: Make Compliance a Priority for Lobbying and Political Activity
Back to the Future: FEC issues regulations for Citizens United
By Ronald M. Jacobs on March 11, 2015
Posted in Campaign Finance, Contributions, FEC, Super PACs
In January 2010 – as almost everyone already knows by now – the Supreme Court struck down major portions of campaign finance laws, allowing corporations to make independent expenditures in support of, or opposition to, candidates for federal office. Super PACs that could accept unlimited individual and corporate contributions soon followed based on lower court…
Justice Department Brings First Criminal Case for Campaign, Super PAC Coordination
By Lawrence H. Norton & Ronald M. Jacobs on February 17, 2015
Posted in Campaign Finance, Super PACs
The U.S. Department of Justice has announced the first criminal prosecution for a violation of federal laws prohibiting outside groups from coordinating their activities with the candidates and campaigns they support.
The six-member Federal Election Commission, which is primarily responsible for interpreting and enforcing federal campaign finance laws, has deadlocked repeatedly over whether to investigate complaints of coordination. But with this announcement, the Justice Department, which may pursue knowing and willful violations of the same laws, has stepped into the breach.
In the plea agreement, a Virginia-based political consultant admitted serving as campaign manager for a U.S. candidate for Congress, while at the same time operating a Super PAC that spent $325,000 on ads attacking that candidate's opponent. No one else has been charged in the case. Interestingly, there is no indication in the charging documents that the candidate knew about the work the consultant was doing for the Super PAC. However, the coordination rules apply not just to candidates, but also to their staff, and in some circumstances, their volunteers. Violations may be established even if the candidate is unaware of a representative's unlawful activity. …
Continue Reading Justice Department Brings First Criminal Case for Campaign, Super PAC Coordination
Naming Your PAC
By Ronald M. Jacobs on February 10, 2015
Posted in Campaign Finance, Rulemaking, Super PACs
The Washington Examiner recently wrote about the art of naming a PAC, pointing out that the name must "balance patriotic with practical considerations." The Examiner talked about making sure the name is not too long if the PAC will have to include "paid for by" statements on its ads. But there are some other legal considerations as well. Let's look at some of the FEC's naming rules.
If the PAC is a connected PAC, meaning it is supported by a company, union, nonprofit, or trade or professional association, then it must include the full name of the connected organization. We have seen registrations rejected by the FEC for failing to include "Inc." or "Company" if that full legal name of the entity includes those signifiers. Thus, Widget Manufacturing Company of Our Town, Inc. must include all of those words in the name of the PAC. That name must appear in all legal disclaimers.
Continue Reading Naming Your PAC
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