Brittany joined Team Stanley this year as a dental assistant to Dr. David Baranowski. Brittany married her husband, John, in 2009 and together they moved to North Carolina from Florida in 2014. She officially entered the dental field in 2015. Together they have two cats, a dog, and multiple chickens.
Brittany is an extremely hard working and loves challenging herself in and out of the office to accomplish new things. When she is not in the office, Brittany enjoys taking road trips, going on hiking adventures, and spending time with her animals.
Brittany loves animals, especially her chickens!


analyzing the appropriations and revisions of Indian identification first conducted by way of Anglo-American engravers and later by means of early Anglo-American ladies writers, Cathy Rex exhibits the ways that iconic photos of local figures tell not just an rising colonial/early republican American identification but in addition the authorial identification of white girls writers. ladies equivalent to Mary Rowlandson, Ann Eliza Bleecker, Lydia Maria baby, and the pseudonymous Unca Eliza Winkfield of the feminine American, Rex argues, co-opted and revised pictures of Indianness similar to these present in the Massachusetts Bay Colony seal and the varied diversifications of Pocahontas's snapshot according to Simon Van de Passe's unique 1616 engraving. Doing so allowed them to posit their very own identities and presumed superiority as American girls writers. occasionally gruesome, sometimes not easy, and sometimes patently racist, the Indian writings of those girls however query the masculinist and Eurocentric discourses governing an American identification that has continually had Indianness at its middle. instead of treating early American pictures and icons as ancillary to literary works, Rex areas them in dialog with each other, suggesting that those famous narratives and photographs are together constitutive. the result's a brand new, extra textually inclusive point of view at the box of early American studies.
Quantity II covers the poems of Dryden from 1682 to 1685. including quantity one, the paintings types the 1st a part of the main informative and available version of Dryden's poetry, offering a useful source for college kids of recovery culture.
Ce nouveau quantity de Calvini Opera Omnia Denuo Recognita donne l'édition critique des deux traités de Jean Calvin contre les libertins spirituels, publiés respectivement en 1545 et en 1547, et de son libelle contre les nicodémites, adressé en 1562 à Coornhert. Les libertins menacent les fondements même du christianisme : Calvin vilipende leur critique de l'autorité de los angeles Bible ; il leur reproche l. a. récusation de l'existence du diable et le déni de l. a. résurrection des morts.
This can be a choice of twenty-nine of the main influential articles and papers approximately medieval musical tools and their repertory. The authors speak about the development of the tools, their enjoying method, the events for which they played and their repertory. Taken as a complete, they paint a really large, in addition to distinct, photo of instrumental functionality through the medieval interval.


For a (Very) brief moment I thought Episode 3 was the best.
Then I realised it was the worst after some guy had slapped me.
Nothing is wrong with Ep.3 i loved it and it is in second place right now....and for me, it took 1st for awhile also.
Yeah, same here, right after I see an action movie, it gets put in my top 5 for some reason?
Our school was selling roses for Valentines Day that were going to be delivered to our classes. Someone sent me one from "Jango Fett."
JH3!!! CLEANOUT YOUR INBOX!!! Thanx!
Thats the coolest dream i ever heard lol!!
"But Eli. I am santa."
If only Boba were Santa. Like on the Santa Fett wallpaper from TFN, who goes flying around on his jetpack to deliver toys to good little Corellians and Alderaanians.
He might shoot you for getting drool on his boots.
I'll feed him cookies and cake, and then watch in fascination as he drinks milk through a straw.
I have never found Jar-Jar amusing....and aren't we off subject?
Yes we are off the subject........but one last statemant.
WHY DID JAR JAR BECOME A SENATOR?!! I dont get it!! I dot think any person who could get his tounge stuck in a visable laser could ever become a senator!!
Gosh that really bugs me!! Im gonna put it in the Anger management thread.
Technically Jar Jar is not a senator. Padme is the senator for Naboo, she represents the planet Naboo as a whole. Naboo has two species, Humans and Gungans, both the humans and the Gungans need representatives in the Senate, and since the humans already have a senator, the Gungans still need their representative, but the role of senator is already filled. So Jar Jar is only a Gungan Representative, and Padme's substitute.
I never really liked Boss Nass. The guard was okay in my opinion.


text:
Photo credit: Jo Zimny Photos / Flickr (CC BY-NC-ND 2.0)
DC, 3 States Sue Google, Saying It Invades Users' Privacy
Whowhatwhy Editors 01/26/22
PICKS are stories from many sources, selected by our editors or recommended by our readers because they are important, surprising, troubling, enlightening, inspiring, or amusing. They appear on our site and in our daily newsletter. Please send suggested articles, videos, podcasts, etc. to picks@whowhatwhy.org.
DC, 3 States Sue Google, Saying It Invades Users' Privacy (Maria)
The author writes, "The District of Columbia and three states are suing Google for allegedly deceiving consumers and invading their privacy by making it nearly impossible for them to stop their location from being tracked. In the lawsuit filed Monday in a District of Columbia court, D.C. Attorney General Karl Racine alleges Google has 'systematically' deceived consumers about how their locations are tracked and used. He also says the internet search giant has misled users into believing they can control the information the company collects about them. 'In reality, consumers who use Google products cannot prevent Google from collecting, storing and profiting from their location,' the lawsuit says."
Is Ginni Thomas a Threat to the Supreme Court? (DonkeyHotey)
From The New Yorker: "The claim that the Justices' opinions are politically neutral is becoming increasingly hard to accept, especially from [Clarence] Thomas, whose wife, Virginia (Ginni) Thomas, is a vocal right-wing activist. She has declared that America is in existential danger because of the 'deep state' and the 'fascist left,' which includes 'transsexual fascists.' Thomas, a lawyer who runs a small political-lobbying firm, Liberty Consulting, has become a prominent member of various hard-line groups. Her political activism has caused controversy for years. For the most part, it has been dismissed as the harmless action of an independent spouse. But now the Court appears likely to secure victories for her allies in a number of highly polarizing cases — on abortion, affirmative action, and gun rights."
Ethics Office Says Reps. Newman, Lamborn May Have Broken Law (Reader Steve)
The author writes, "A congressional ethics watchdog has concluded that U.S. Reps. Marie Newman of Illinois and Doug Lamborn of Colorado may have violated federal law, prompting reviews from the House Ethics Committee. Separate investigative reports from the Office of Congressional Ethics released Monday detailed a 'substantial reason to believe' that Newman, a Democrat, promised federal employment to a political opponent and that Lamborn, a Republican, misused official resources for personal purposes."
Lawmakers Ramp Up Bills That Would Affect LGBTQ+ Students (Dana)
From the South Florida Sun Sentinel: "As lawmakers in Florida take aim at prohibiting instruction around racial equality in classrooms, some are now also trying to limit conversation about gender and sexual orientation in schools with a bill that will be voted upon later this spring. The bill's sponsors, including Sen. Dennis Baxley, a Republican from Central Florida, present it as a mechanism to preserve parents' rights in education, but critics say it would ultimately police what students and teachers can discuss in classrooms regarding gender and sexuality. It was one of five bills filed during the first week of Florida's 2022 legislative session that would affect LGBTQ+ students in school, and those seeking medical care."
Why Pay TV Operators Are Dropping Trump-Loving Cable Networks (Reader Steve)
The author writes, "Before One America News Network host Dan Ball finished an interview with guest Jim Jordan last week, he asked the Ohio Republican congressman for a favor. 'Please put some pressure on AT&T and DirecTV for us,' said Ball, whose nightly program Real America airs nightly on the right-wing cable channel. 'OAN would love to continue broadcasting on that platform and we know for a fact it is all political behind the scenes on why they're doing that to us.' … The desperate calls for help — which would be considered unseemly on a traditional cable news outlet — follow DirecTV's Jan. 15 announcement that it will drop the San Diego-based OAN from its service in April."
What Is the 'Lunar Effect,' and What Does It Have to Do With Shark Attacks? (Mili)
The author writes, "When the full Moon rises, strange things can happen here on Earth. Oysters snap close. Corals spawn. Zooplankton dive deeper. Seabirds stick to the shore. And lions hunt less. Several of these behaviors are tied to moonlight; others, to tides. But some have no clear explanation at all. More than 50 years' worth of shark attack data, for instance, has now found that sharks bite humans more when the Moon is fuller."
I Spent Hundreds of Hours Working in VR. Here's What I Learned (Sean)
The author writes, "Hello from low-earth orbit! I have spent hundreds of hours working here in virtual reality. Even as I write this to you, I have Facebook's Oculus strapped to my face and am in an aptly named app called Immersed. It puts me in this orbiting spaceship where there's just me, the computer screen in front of me, and — let me look out the window — Ecuador. I'm not sure where Facebook's Metaverse begins or ends; perhaps I am in it right now. But I am primarily a writer of English text and computer code, a solitary profession that rarely requires real-time meetings like those in the Metaverse demos. When I was a kid, I wrote homework essays on a manual typewriter. What I do now is not much different, except I don't need to use that white correction tape stuff to erase typos — and I'm in space."
Whowhatwhy Editors
After Roe, Dems Seek Probe of Tech's Use of Personal Data
Sheriff, Group Sue to Block Strict Oregon Gun Control Law
Google to Pay Indiana $20M to Resolve Privacy Suit

redpajama_set_name: RedPajamaCommonCrawl


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In the market of cosmetic products are much of creams for skin nutrition from expensive to affordable, from import to domestic, from classic to innovative. Nourishing cream should be in a arsenal of each mature young woman, let alone what it was he be up to you.Vitamin nourishing fluid «Matis», France (50 mL, ok. 2200 rub.) Fluid is designed to supply dry face, suffering with a lack of lipids. When applied on the face forms a highly thin protective film, making a feeling of comfort. Contains natural efficacious ingredients (sunflower extract, nut a butter Bass, corn butter, shea butter, vitamins E), however comfortably so a range of anti-aging substances. The cream nourishes the facial skin while rejuvenating it and acts barrier means from a harmful effects of external aggression.Cream «Ahava», softening and nourishing, Israel (50 mL, ok.
Packs of parsley good soothe irritation and soothe the skin. You just soak in a broth of parsley gauze, put on facial skin and keep 20 min. After compression, It is possible to not sluice.You can as well do compresses decoction of hop cones. It is indispensable to brew bumps (TWO tbsp) glass of stewing h2o, drain and use in a configuration of heating, how correctly however a decoction of parsley.Like posts: Masks for skin after biorevitalisation Masks at night Masks for fase and body treatments at home. . .
Moisturizing skin care covers are vital for dry, dehydrated, sensitive and flaky facial skin, however it instantly hydrate a face and restore organic moisture balance and facial skin however good how soften and restore facial skin elasticity and suppleness. Hydrating mask made with organic products (dairy, plum, raw vegetables, etc.) and are the perfect addition to creams. You saturate the skin with vitamins and other nutrients. Their treatment is valuable for all skin types. But they are essential for mature, aging face that needs a unique ingredients that can erase a traces of time: cut wrinkles, restore and renew a facial skin, to charge her extra energy. Hydrating mask from a generator recommended 3-4 times a week, home hydrating mask - every time.Similar articles: Face care acne Facials summer Skin care in a cold season.
Moisturizing face care covers are vital for very dry, dehydrated, sensitive and flaky facial skin, how it instantly hydrate a skin and restore organic moisture balance and skin as well as soften and restore skin elasticity and suppleness. Hydrating mask made from organic products (dairy, melon, raw vegetables, etc.) and are a perfect addition to creams. You saturate the face with vitamins and other nutrients. A treatment is healthy for all face types. But they are essence for mature, aging face that demands a unique ingredients that can erase a traces of time: reduce skin wrinkles, restore and renew the facial skin, to charge her extra energy. Hydrating mask from a manufacturer recommended 3-4 times a week, home hydrating cover - each day.Similar articles: Facials at home in winter Facial face is dry Anti-Aging Masks and skin care.
Packs of parsley good soothe irritation and soothe a face. You just soak in a broth of parsley gauze, put on facial skin and keep 20 min. Of the compression, you can not wash.It is possible to also make compresses decoction of hop cones. It is necessary to brew bumps (TWO tbsp) glass of boiling h2o, drain and apply in the configuration of warmth, however well so a decoction of parsley.Same posts: Masks and skin care in 50 years Skin care in 50 years Masks and face care in 40 years. . .


We have teamed up with Swedish electro-dub duo Cazzette to give away some dope, unique gear you will be hard-pressed to find anywhere. One piece of the giveaway is one of those sweet necklaces that you see in the "Run For Cover" video, though I cannot speak to whether or not it will get you attacked by a giant flock of pigeons, hopefully not. Also included is a poster and some stickers to add to your collection and tag your computer, wall, loved one or whatever. See pics of what you will win after jump, including the now famous "Beam Me Up Video". You will win one special edition necklace, a "Run For Cover" poster and a batch of "Run For Cover" stickers. Enter the punchtab widget below to win.


text:
What is a Green Card (And How Do I Get One)?
Home/What is a Green Card (And How Do I Get One)?
Many people have heard the term green card, but what is it? Does it make you a legal permanent resident of the U.S., and what are the benefits of having a green card?
What is a Green Card?
A green card is an identification card that makes a person a lawful permanent resident of the U.S. If you have one, it shows that you have official permission to reside in the U.S. and to take employment here.
How Do I Get a Green Card?
There are different ways to obtain a green card, depending on your situation.
Typically, you can get a green card:
Through family
Through a job
Through refugee or asylee status
Obtaining a Green Card Through Family
You may be eligible to get a green card if you are:
An immediate relative of a current U.S. citizen, which can include spouses, unmarried children under the age of 21, and parents of U.S. citizens over the age of 21
A family member of a U.S. citizen who fits into a "preference" category, including unmarried children over the age of 21, married children of any age, and siblings of U.S. citizens aged 21 or over
A family member of a green card holder, including spouses and unmarried children of the green card holder
A member of a special category, such as battered spouses or children, a K nonimmigrant, a V nonimmigrant, a person born to a foreign diplomat in the U.S., or a widow or widower of a U.S. citizen
Obtaining a Green Card Through a Job
You could be eligible for a green card based on an offer of permanent employment in the U.S., through investments that create new U.S. jobs, or through self-petition as an "Alien of Extraordinary Ability." You may also apply based on your current job if it fits in a special category, such as:
Afghan/Iraqi interpreter
Employee of an international organization
Iraqi who assisted the U.S. government
Nato-6 nonimmigrants
Panama Canal employee
Religious Worker
Obtaining a Green Card as a Refugee or Asylee
If you're here as a refugee or you're a qualifying family member of an asylee (someone who has been granted asylum in the U.S.), you may be eligible to apply for a green card.
Do You Need to Talk to a Waukesha Immigration Lawyer?
If you need to talk to a Wisconsin immigration lawyer who may be able to help you apply for a green card, call us at 414-383-6700 right away.
By Carlos Gamino|2021-07-25T15:30:06-05:00November 23rd, 2019|Immigration Law|Comments Off on What is a Green Card (And How Do I Get One)?


text:
\section{Introduction}

Quantum dots, routinely made by electrostatically confining a two-dimensional electron gas \cite{Davies}, have been extensively studied in recent
years \cite{Thierry_book}. The interest in these low-dimensional structures stems from the fact that their physics is controlled by quantum effects.
Furthermore, while sharing many similarities with real atoms, quantum dots manifest intriguing low-energy quantum phenomena, which are specific to them.
This is because their properties can be influenced by external factors such as the geometry or the shape of the confining potential and the application
of external fields. Clearly some of these features are not accessible in real atoms. Research in the past has been motivated by the possibility of developing
novel quantum dot based devices in both the fields of quantum cryptography/computing \cite{Zipper} and spintronic \cite{Foldi}, as well as by the simple
curiosity of exploring the properties of many-electron systems in reduced dimensions.

Quantum rings represent a particular class of quantum dots \cite{Lorke, Fuhrer}, where electrons are confined in circular regions \cite{Garcia, Lorke2}.
The circular geometry can sustain an electrical current, which in turns can be induced by threading a magnetic flux across the ring itself. Such a
magnetic flux produces exciting effects like Ahanorov-Bohm (AB) oscillations \cite{Aharonov, Levy} and persistent currents \cite{Buttiker},
effects that were anticipated as early as the late 60's \cite{Bloch1, Bloch2}. In one dimension (1D) the persistent currents have been thoroughly
studied \cite{Buttiker, Buttiker2}. These, as many other physical properties of the ring, are a periodic function of the magnetic flux quantum,
$\Phi_0=hc/e$ ($h$ is the Planck's constant, $c$ the speed of light and $e$ the electron's charge).

A number of earlier theoretical studies \cite{Giancarlo, Kirchner, Molina, SKMaiti2004, Thierry2} on persistent currents focused on unveiling
the role of electron correlations and disorder over the electron transport. This line of research is inspired by the fact that electronic correlation in 1D
always leads to non-fermionic low-energy quasiparticle excitations. In fact, even in the presence of weak interaction, 1D fermions
behave differently from a Fermi liquid and their ground state is generally referred to as Luttinger liquid. This possesses specific collective
excitations \cite{Kolomeisky}.

There are two theoretical frameworks commonly used to study finite 1D rings \cite{Viefers}. The first is based on the continuum model, where electrons
move in a uniform neutralizing positive background and interact via Coulomb repulsion, $e^2/4\pi\varepsilon_0r$ ($\varepsilon_0$ is the
vacuum permittivity, $e$ the electron charge, $r$ the distance between two electrons). The second is populated by lattice models, where the electronic
structure is written in a tight-binding form and the electron-electron
interaction is commonly described at the level of Hubbard Hamiltonian \cite{Hubbard1, Hubbard2}. In both frameworks exact diagonalization (ED)
has been the preferential solving strategy for small systems (small number of sites and electrons) \cite{SKMaiti2004,Bouzerar}. Additional methods
used to study quantum rings over lattice models include Bethe Ansatz (BA) \cite{Bethe, LiebWu}, renormalization group \cite{Meden} and
density matrix renormalization group \cite{Dias}. In contrast the continuum model has been tackled with self-consistent Hartree Fock
techniques \cite{Cohen}, bosonization schemes \cite{Gogolin}, conformal field theory \cite{Jaimungal}, current-spin density functional theory
\cite{Viefer2} and quantum Monte Carlo \cite{Emperador}.

Many of the methods developed for solving lattice models for interacting electrons suffer from a number of intrinsic limitations connected either to
their large computational overheads or to the need of using a drastically contracted Hilbert space. Density functional theory (DFT) can be a natural
solution to these limitations. DFT is a highly efficient and precisely formulated method \cite{HK, KS}, originally developed for the Coulomb
interaction (this is commonly known as {\it ab initio} DFT), and then extended to lattice models \cite{Gunnarsson, Schonhammer, Capelle3}.
Lattice DFT (LDFT) is based on the rigorously proved statement that the ground state of an interacting electron system is a universal functional
of the local site occupation. The functional, as in {\it ab initio} DFT, is unknown explicitly. However all the many-body contributions to the total energy
can be incorporated in a single term, the exchange and correlation (XC) energy, for which a hierarchy of approximations can be constructed.

The most commonly used approximation for the XC energy in {\it ab initio} DFT is probably the local density approximation (LDA) \cite{KS,Densityfunctional},
where the exact (unknown) XC energy is replaced by that of the homogeneous electron gas. The theory is then expected to work best in situations
close to those described by the {\it reference} system, i.e. close to the homogeneous electron gas. Since in 1D Fermi liquid theory breaks down, the homogeneous
electron gas is no longer a good reference. For the homogeneous Hubbard model it was then proposed \cite{Capelle3, Capelle1} to use instead the BA
construction of Lieb and Wu \cite{LiebWu}. Such a scheme was then applied successfully to a wide range of situations \cite{Capelle2, Silva, Campo, Xianlong1,
Xianlong2, Xianlong3,Akin} and more recently it has been extended to time-dependent problems \cite{Xianlong3, Verdozzi, Kurth,Stefanucci}
and to the 3D Hubbard model \cite{Karlsson}.

LDFT can be further extended to include the action of a vector potential,  i.e. it can be used to tackle problems where a magnetic flux is relevant. This
effectively corresponds to the construction of current-LDFT (CLDFT). Such an extension of LDFT was proposed recently for one-dimensional spinless
fermions with nearest-neighbor interaction \cite{Schenk} and it is here adapted to the repulsive Hubbard model. The newly constructed functional is then
used to investigate total energies, persistent currents and Drude weights of a mesoscopic repulsive Hubbard ring threaded by a magnetic flux.

The paper is organized as follows. Section II reviews the theoretical foundations leading to the construction of CLDFT and to its LDA. Then we present
our results for both homogeneous and defective rings, highlighting the main capabilities and limitations of our scheme, and finally we conclude.

\section{Theoretical Formulation of Current Lattice DFT}

Current-DFT (CDFT) is a generalization of time-dependent density functional theory \cite{Gross} to include in the Hamiltonian an external vector potential
\cite{thebook}. In this case the theory is constructed over two fundamental quantities, namely the electron density, $n$, and the paramagnetic
current density, $\vec{j}_p$. The Hohenberg-Kohn theorem \cite{HK} is thus expanded to the statement that the ground state $n$ and
$\vec{j}_p$ uniquely determine the ground-state wave-function and consequently the expectation values of all the operators \cite{Vignale1, Vignale2}.
Equally important is the fact that the standard Kohn-Sham construction can also be employed for CDFT, so that the many-body problem can be
mapped onto a fictitious single-particle one, with the two sharing the same ground state $n$ and $\vec{j}_p$ \cite{Vignale1, Vignale2}. Practically
one then needs to solve self-consistently a system of single-particle equations. Also for CDFT all the unknown of the theory are incorporated in the
XC energy, which then needs to be approximated.

The scope of this section is to describe how {\it ab initio} CDFT has been translated to lattice models and how a suitable approximation for the
XC energy associated to the Hubbard Hamiltonian can be constructed. Our description follows closely the one previously given by Dzierzawa
et al. \cite{Schenk}. In general a vector potential, $\vec{A}$, enters into a lattice model via Peierls substitution \cite{Peir,Vogel}, where the matrix
elements of the $\vec{A}$-dependent Hamiltonian, $H(\vec{r},\vec{p}+\frac{e}{c}\vec{A})$, can be written in terms of those for $\vec{A}=0$ as
\begin{equation}
\langle\vec{R}^\prime|H(\vec{r},\vec{p}+\frac{e}{c}\vec{A})|\vec{R}\rangle=
\langle\vec{R}^\prime|H(\vec{r},\vec{p})|\vec{R}\rangle
\mathrm{e}^{-\frac{ie}{\hbar c}\int_{\vec{R}}^{\vec{R}^\prime}\vec{A}\cdot\mathrm{d}\vec{s}}\:,
\end{equation}
where $c$ is the speed of light and $|\vec{R}\rangle$ is the generic orbital located at the position $\vec{R}$ and belonging to the basis set (here
assumed orthogonal) used to construct the tight-binding Hamiltonian.

When the Peierls substitution is applied to the construction leading to the 1D Hubbard model the only term in the Hamiltonian that gets
modified is the kinetic energy $\hat{T}$. This takes the form
\begin{equation}
\hat{T}=-t \sum_{\sigma,\:l=1}^{L}(e^{-i{\Phi_{\sigma l}/L}}\:\hat{c}^\dagger_{\sigma\:l+1}\hat{c}_{\sigma\:l}+hc)\:,
\label{Ekin}
\end{equation}
where we have considered a system comprising $L$ atomic sites (note that the ring boundary conditions imply $L+1=1$).
In the equation (\ref{Ekin}) $\hat{c}^\dagger_{\sigma l}$ ($\hat{c}_{\sigma l}$) is the creation (annihilation) operator for an electron
of spin $\sigma$ ($\sigma=\uparrow, \downarrow$) at the $l$-site, $t$ is the hopping integral and $\Phi_{\sigma l}$ is the phase
associated to the $l$-th bond, which effectively describes the action of $\vec{A}$. The remaining terms in the Hamiltonian
are unchanged so that the 1D Hubbard model in the presence of a vector potential is defined by
\begin{equation}\label{Hint}
\hat{H}^\Phi_\mathrm{Hubbard}=\hat{T}+\hat{U}+\sum_l^Lv_l^\mathrm{ext}\hat{n}_{l}\:,
\end{equation}
where \{$v_l^\mathrm{ext}$\} is the external potential ($v_l^\mathrm{ext}$ is the on-site energy of the $l$-site), while the Coulomb
repulsion term is $\hat{U}=U\sum_{l=1}^L \hat{n}_{\uparrow l} \hat{n}_{\downarrow l}$, with $U$ being the Coulomb repulsion energy
and $\hat{n}_{\sigma l}=\hat{c}^\dagger_{\sigma l}\hat{c}_{\sigma l}$. Throughout this work we always consider the diamagnetic
(non-spin polarized) case so that $\Phi_{\uparrow l}=\Phi_{\downarrow l}=\Phi_l$ and $n_{\uparrow l}=n_{\downarrow l}=n_l$.

The first step in the construction of a CLDFT is the formulation of the problem in a functional form.
The basic variables of the theory are the site occupation $n_l=\langle\Psi|\hat{n}_l|\Psi\rangle$ and bond paramagnetic current,
$j_l=\langle\Psi|\hat{j}_l|\Psi\rangle$, where $|\Psi\rangle$ is the many-body wavefunction and the bond paramagnetic current
operator is defined as
\begin{equation}\label{paraJ}
\hat{j}_l=-it(e^{-i{\Phi_l/L}}\:\hat{c}^\dagger_{\sigma\:l+1}\hat{c}_{\sigma\:l}-hc)
\end{equation}
In complete analogy to {\it ab initio} CDFT we can write the total energy, $\mathcal{E}$, of the Hamiltonian (\ref{Hint}) as a functional
of the local external potentials and phases
\begin{equation}\label{LF1}
\mathcal{E}=\mathcal{F}[n_l,j_l]+\sum_lv_l^\mathrm{ext}n_l+\sum_l\Phi_lj_l,
\end{equation}
so that
\begin{equation}
\begin{aligned}\label{LF2}
n_l=\langle\hat{n}_l\rangle&=\frac{\partial \mathcal{E}}{\partial v_l^\mathrm{ext}}\:,\\
j_l=\langle\hat{j}_l\rangle&=\frac{\partial \mathcal{E}}{\partial \Phi_l}\:.
\end{aligned}
\end{equation}
$\mathcal{F}[n_l,j_l]$ is a universal functional, whose functional derivatives with respect to $\{n_l\}$ and $\{j_l\}$ satisfy the following two equations
\begin{equation}\label{LF3}
\begin{aligned}
v_l^\mathrm{ext}=&-\frac{\partial \mathcal{F}}{\partial n_l}\\
\Phi_l=&-\frac{\partial \mathcal{F}}{\partial j_l}.
\end{aligned}
\end{equation}
Note that equations (\ref{LF1}) through (\ref{LF3}) follow directly from the properties of the Legendre transformation.

In order to make the theory practical one has now to introduce the auxiliary single-particle Kohn-Sham system. This is described by a single-particle
Hamiltonian, $\hat{H}^\mathrm{s}$, whose ground state site occupations and bond paramagnetic currents are identical to those of the interacting
system [described by equation (\ref{Hint})]. $\hat{H}^\mathrm{s}$ reads
\begin{equation}\label{Hs}
\hat{H}^\mathrm{s}=\hat{T}^\mathrm{s}+\sum_l^Lv_l^\mathrm{s}\hat{n}_{l},
\end{equation}
where $\hat{T}^\mathrm{s}=-t \sum_{\sigma,l=1}^{L-1}(e^{-i{\Phi_l^\mathrm{s}/L}}\:\hat{c}^\dagger_{\sigma\:l+1}\hat{c}_{\sigma l}+hc)$ and the
associated local effective potentials and phases are $v_l^\mathrm{s}$ and $\Phi_l^\mathrm{s}$ respectively. The single-particle Schr\"{o}dinger
equation is then
\begin{equation}
 \hat{H}^\mathrm{s}|\Psi^\mathrm{s}_\alpha\rangle=\epsilon_\alpha|\Psi^\mathrm{s}_\alpha\rangle,
\end{equation}
and the site occupation is defined as
\begin{equation}\label{occup}
n_l^\mathrm{s}=\sum_\alpha f_\alpha\langle\Psi^\mathrm{s}_\alpha|\hat{n}_l|\Psi^\mathrm{s}_\alpha\rangle\:,
\end{equation}
where $f_\alpha$ is the occupation number. An analogous expression can be written for $j^\mathrm{s}_l$.

The energy functional associated the Kohn-Sham system, $\mathcal{F}^\mathrm{s}$, can be constructed by performing again a Legendre
transformation
\begin{equation}\label{fs}
\mathcal{F}^\mathrm{s}=\mathcal{E}^\mathrm{s}-\sum_lv_l^\mathrm{s}n_l^\mathrm{s}-\sum_l\Phi_l^\mathrm{s}j_l^\mathrm{s}\:,
\end{equation}
where $\mathcal{E}^\mathrm{s}$ is the total energy of the single-particle system and the following two equations are valid
\begin{equation}\label{LF4}
\begin{aligned}
v_l^\mathrm{s}=&-\frac{\partial \mathcal{F}^\mathrm{s}}{\partial n_l^\mathrm{s}}\:,\\
\Phi_l^\mathrm{s}=&-\frac{\partial \mathcal{F}^\mathrm{s}}{\partial j_l^\mathrm{s}}\:.
\end{aligned}
\end{equation}
The crucial point is that in the ground state the real and the Kohn-Sham systems share the same site occupation and paramagnetic
current, i.e. $n_l=n_l^\mathrm{s}$ and $j_l=j_l^\mathrm{s}$.

Thus one is now in the position of defining the XC energy, $\mathcal{E}^\mathrm{xc}$, as usual, i.e. as the difference between $\mathcal{F}$
for the interacting and the Kohn-Sham systems after the classical Hartree energy $\mathcal{E}^\mathrm{H}$ has also been subtracted,
\begin{equation}\label{xcene}
\mathcal{E}^\mathrm{xc}[n_l,j_l]=\mathcal{F}[n_l,j_l]-\mathcal{F}^\mathrm{s}[n_l,j_l]-\mathcal{E}^\mathrm{H}[n_l]\:.
\end{equation}
Note that for all the functionals in equation (\ref{xcene}) we took the short notation $\{n_l\}\rightarrow n_l$ and $\{j_l\}\rightarrow j_l$, i.e.
the functionals depend on all the on-site occupations and bond paramagnetic currents. The single-particle effective potentials and phases
can now be defined. In fact by taking the functional derivative of equation (\ref{xcene}) with respect to $n_l$ and $j_l$ and by using
the equations (\ref{LF3}) and (\ref{LF4}) one obtains
\begin{equation}\label{kspot}
 \begin{aligned}
  v_l^\mathrm{s}=&v_l^\mathrm{ext}+v_l^\mathrm{H}+v_l^\mathrm{xc}\:,\\
  \Phi_l^\mathrm{s}=&\Phi_l+\Phi_l^\mathrm{xc}\:,
 \end{aligned}
\end{equation}
where
\begin{equation}
 \begin{aligned}
  v_l^\mathrm{xc}=&\frac{\partial \mathcal{E}_l^\mathrm{xc}}{\partial n_l}\:,\\
  \Phi_l^\mathrm{xc}=&\frac{\partial \mathcal{E}_l^\mathrm{xc}}{\partial j_l}\:,
 \end{aligned}
\end{equation}
and $v_l^\mathrm{H}=\partial \mathcal{E}_l^\mathrm{H}/\partial n_l$ ($=Un_l/2$) is the Hartree potential.

Finally $\mathcal{E}^\mathrm{xc}$ can be re-written in terms of the expectation values of the original Hamiltonian. In fact by substituting
the functional forms of $\mathcal{F}$ and $\mathcal{F}^\mathrm{s}$ into the equation (\ref{xcene}),
\begin{equation}\label{exc2}
\mathcal{E}^\mathrm{xc}=\mathcal{E}-\mathcal{E}^\mathrm{s}+\sum_l(v_l^\mathrm{s}-v_l^\mathrm{ext})n_l+\sum_l
(\Phi_l^\mathrm{s}-\Phi_l)j_l-\mathcal{E}^\mathrm{H}[n_l]\:,
\end{equation}
by using the equations (\ref{Hint}) and (\ref{Hs}),
\begin{equation}\label{vsvl}
\sum_l(v_l^\mathrm{s}-v_l^\mathrm{ext})n_l=\mathcal{E}^\mathrm{s}-\mathcal{E}-\langle\Psi^\mathrm{s}|\hat{T}^\mathrm{s}|\Psi^\mathrm{s}
\rangle+ \langle\Psi|\hat{T}+\hat{U}|\Psi\rangle\:,
\end{equation}
and again by substituting equation (\ref{vsvl}) into equation (\ref{exc2}), one obtains a close expression for the XC energy
\begin{equation}\label{exc3}
\mathcal{E}^\mathrm{xc}=\langle\Psi|\hat{T}+\hat{U}|\Psi\rangle-\langle\Psi^\mathrm{s}|\hat{T}^\mathrm{s}|\Psi^\mathrm{s}
\rangle+\sum_l(\Phi_l^\mathrm{s}-\Phi_l)j_l-\mathcal{E}^\mathrm{H}[n_l].
\end{equation}

Once the theory is formally established the remaining task is that of finding an appropriate approximation for
$\mathcal{E}^\mathrm{xc}$. As for the case of standard LDFT \cite{Capelle1,Capelle2}, the strategy here is that of considering
the BA solution for the homogeneous limit of $\hat{H}^\Phi_\mathrm{Hubbard}$ (this is defined in equation (\ref{Hint}) by setting
$v_l=v$ and $\Phi_l=\Phi$) and then of taking its local density approximation $n\rightarrow n_l$, $\Phi\rightarrow\Phi_l$ \cite{Schenk}, i.e.
\begin{equation}
\mathcal{E}^\mathrm{xc}_\mathrm{LDA}[n_l,j_l]=\sum_le^\mathrm{xc}[n_l,j_l],
\end{equation}
where $e^\mathrm{xc}[n,j]={\mathcal{E}^\mathrm{xc}[n,j]/L}$ is the XC energy density (per site) of the homogeneous system. The first term of the
equation (\ref{exc3}) can be calculated exactly using the BA procedure \cite{Shastry}. This provides the ground state energy as a function
of $n$ and $\Phi$, so that one still needs to re-express it in terms of $n$ and $j$. However the phase variable $\Phi$ can be eliminated from
the ground state energy by using
\begin{equation}
j=\frac{\partial \mathcal{E}(n,\Phi)}{\partial \Phi}\:.
\end{equation}

Thus finally one can explicitly write $e^\mathrm{xc}(n,j)$ (the full derivation for the 1D Hubbard Hamiltonian is presented in
the Appendix)
\begin{equation}\label{exc51}
e^\mathrm{xc}(n,j)=e^\mathrm{xc}(n,0)+\frac{1}{2}\Lambda^\mathrm{xc}(n)j^2,
\end{equation}
where
\begin{equation}
\begin{aligned}
e^\mathrm{xc}(n,0)=&\frac{\mathcal{E}^\mathrm{BA}(n,0)-\mathcal{E}^0(n,0)-\mathcal{E}^\mathrm{H}(n)}{L}\:,\\
\Lambda^\mathrm{xc}(n)=&\frac{1}{2}\left [\frac{1}{D_c^0(n)}-\frac{1}{D_c^\mathrm{BA}(n)}\right ].
\end{aligned}
\end{equation}
In the equations above $\mathcal{E}^0(n,0)$ and $D_c^0(n)$ are respectively the non-interacting ground state energy and charge stiffness,
while $\mathcal{E}^\mathrm{BA}(n,0)$ and $D_c^\mathrm{BA}(n)$ are the same quantities for the interacting case as calculated from the BA.
Finally, the XC contributions to the Kohn-Sham potential can be obtained by simple functional derivative (in this case by simple derivative)
of the exchange and correlation energy density with respect to the fundamental variables $n$ and $j$, i.e.
\begin{equation}\label{vxc1}
v^\mathrm{xc}_\mathrm{BALDA}(n_l,j_l)=\left.\frac{\partial e^\mathrm{xc}(n,j)}{\partial n}\right|_{n\rightarrow n_l,j\rightarrow j_l}\:,
\end{equation}
and
\begin{equation}\label{phixc1}
\Phi^\mathrm{xc}_\mathrm{BALDA}(n_l,j_l)=\left.\frac{\partial e^\mathrm{xc}(n,j)}{\partial j}=\Lambda^\mathrm{xc}(n)j\right|_{n\rightarrow n_l,j\rightarrow j_l}\:,
\end{equation}
where BALDA, as usual, stands for Bethe Ansatz local density approximation.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.48\textwidth,angle=0.0]{./Fig1}
\end{center}
\caption {(Color online) The XC energy density (per site) for a homogeneous 1D Hubbard ring threaded by a magnetic flux as a function of the
electron density and for different values of interaction strength $U/t$: (a) $e^{xc}(n,0)$ and (b) $\Lambda^{xc}(n)$.} \label{exchange_lambda}
\end{figure}
In the two panels of figure \ref{exchange_lambda} we present $e^\mathrm{xc}(n,0)$ and $\Lambda^\mathrm{xc}(n)$ as a function of the electron
density, $n$, for different interaction strengths $U/t$. As in the case of standard LDFT also for CLDFT there is a divergence in the $n$-derivative of both
$e^\mathrm{xc}(n,0)$ and $\Lambda^\mathrm{xc}(n)$ at half-filing ($n=1$). This is in correspondence of the metal-insulator-transition present in the
1D Hubbard model for finite $U/t$. In the case of $\Lambda^\mathrm{xc}(n)$ the divergence is also in $\Lambda^\mathrm{xc}(n)$ itself.

The solution of the Kohn-Sham problem proceeds as follows. First an initial guess for the site occupations is used to construct the initial local
paramagnetic current density. Then, the functional derivatives of equations (\ref{vxc1}) and (\ref{phixc1}) are evaluated at these given $n$ and
$j$ so that the Kohn-Sham potential is constructed. The Kohn-Sham equations are then solved to obtain the new set of Kohn-Sham orbitals
from which the new orbital occupations and  bond paramagnetic currents are calculated [by using equation (\ref{occup})]. The procedure is then
repeated untill self-consistency is reached, i.e. until the potentials (or the densities) at two consecutive iterations vary below a certain threshold.
After convergence is achieved the total energy for the interacting system is calculated from
\begin{equation}\label{totalenergy2}
 \mathcal{E}=\sum_\alpha f_\alpha\epsilon_\alpha+\mathcal{E}^\mathrm{xc}[n_l,j_l]-\mathcal{E}^\mathrm{H}[n_l]-\sum_lv_l^\mathrm{xc}n_l,
\end{equation}
where the first term is the sum of single-particle energies and the other terms are the so-called \textit{double counting} corrections.

\section{Results and Discussion}

We now discuss how CLDFT performs in describing both the energetics and the transport properties of 1D Hubbard rings in presence of a magnetic
flux. For small rings our results will be compared with those obtained by diagonalizing exactly the Hamiltonian of equation (\ref{Hint}), while
CLDFT for large rings will be compared with the BA solution. First we will consider homogeneous rings and then we will explore the single impurity
problem.

\subsection{Homogeneous rings: general properties}

In this section we focus our attention on discussing the general features of CLDFT applied to homogeneous Hubbard rings threatened by
a magnetic flux, i.e. on the performance of CLDFT in describing the Ahanorov-Bohm effect. We start our analysis by comparing the CLDFT
results with those obtained by ED. Since ED is numerically intensive such a comparison is limited to small systems.

In figure \ref{12_6low_lying_stateU0_U2_U4_U6} we present the first low-lying energy levels, $\mathcal{E}$, calculated by ED as a function
of the magnetic flux, $\Phi$, for a small 12-site ring at quarter filling ($n=1/2$). In particular we present results for the non-interacting case
[panel (a)] and for the interacting one at three different interaction strengths: (b) $U/t=2$, (c) $U/t=4$ and (d) $U/t=6$. Exact results (ED) are
in black, while those obtained with CLDFT in red. In general the ground state energy is mimimized at $\Phi=0$ when the number of electrons
is $N=4m+2$ and at $\Phi=\pi$ for $N=4m$, with $m$ being an integer \cite{Nakano}. Here we consider the case $N=4m+2$ where the ground
state is a singlet \cite{Stafford}.

For non-interacting electrons, $U/t=0$, the total energy of the singlet ground state is a parabolic function of $\Phi$. Also the various
excited states have a parabolic dependence on $\Phi$ and simply correspond to single-particle levels with different wave-vectors.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.48\textwidth,angle=0.0]{./Fig2}
\end{center}
\caption {(Color online) The low lying energy spectrum, $\mathcal{E}$, of a 12-site ring at quarter filling ($n=1/2$) as a function of the magnetic
flux, $\Phi$, and calculated for different interaction strengths $U/t$. The black dotted lines represent ED results while the dashed red ones are
for CLDFT. Note that for the non interacting case, $U/t=0$, in panel (a) there is no difference between CLDFT and ED. Panels (b)-(d) are for
the interacting case at different interaction strengths: (b) $U/t=2$, (c) $U/t=4$ and (d) $U/t=6$. In panel (b) the blue arrows indicate the region
where the triplet state becomes the ground state.} \label{12_6low_lying_stateU0_U2_U4_U6}
\end{figure}
As the electron-electron interaction is turned on the non-interacting spectrum gets modified in two ways. Firstly there is a second branch
in the ground state energy as a function of $\Phi$ appearing at around $\Phi=\pm\pi$ (see the blue arrows in panel (b) of
Fig.~\ref{12_6low_lying_stateU0_U2_U4_U6}). This originates from the degeneracy lifting between the single and the triplet solution at
$\Phi=\pm\pi$, with the triplet being pushed down in energy and becoming the ground state. The $\Phi$ region where the ground state
is a triplet widens as the interaction strengths increases. The second effect is the expected reduction of the ground state total energy
as a function of $U/t$.

Since CLDFT is a ground state theory, it provides access only to the ground state energy, $\mathcal{E}$. This is calculated next and plotted
in figure \ref{12_6low_lying_stateU0_U2_U4_U6} in the interval $-\pi\le\Phi\le\pi$ for different $U/t$. As one can clearly see from the figure
the performance of CLDFT is rather remarkable, to a point that the CLDFT energy is practically identical to that calculated with ED. However
CLDFT completely misses the cusps in the $\mathcal{E}(\Phi)$ profile arising from the crossover between the singlet and the triplet state.
Level crossing invalidates the BA approximation leading to the interacting XC energy [see equation (\ref{fluxdependence3}) in the appendix]
and so failures are expected \cite{Romer}. This observation is in agreement with earlier studies \cite{Viefers} in which the inability of CDFT
to reproduce level crossing was already noted. Nevertheless, as long as the singlet remains the ground state, the agreement between
CLDFT and ED results is remarkable, even if this small ring is rather far from being a good approximation of the thermodynamic limit (the BA
solution) upon which the functional has been constructed.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.43\textwidth,angle=0.0]{./Fig3}
\end{center}
\caption {(Color online) Persistent current profile, $j$, for a 12-site ring at quarter filling ($n=1/2$) obtained with both ED and CLDFT for
different $U/t$. The full lines are the $j$ calculated with ED while the dashed ones are for CLDFT.} \label{12_6persistentU0_U2_U4_U6}
\end{figure}
Having calculated the total energies with both ED and CLDFT, the corresponding persistent currents, $j$, can be obtained by taking the
numerical derivative of $\mathcal{E}(\Phi)$ with respect to $\Phi$. In figure \ref{12_6persistentU0_U2_U4_U6} we show results for the
12 site ring at quarter filling ($n=1/2$), whose total energy was presented in figure \ref{12_6low_lying_stateU0_U2_U4_U6}. In particular we plot
$j$ only over the period $-\pi<\Phi<\pi$, since all the quantities are 2$\pi$ periodic. The figure confirms the linearity of the persistent
currents with the magnetic flux for all the interaction strengths considered. The same is also true for other fillings for the 12 site ring (not
presented here) away from half-filling. We also observe that the magnitude of persistent currents reduces with increasing $U/t$ for both ED
and CLDFT and that the precise dependence of $j$ on $U/t$ is different for different fillings. This is in good agreement with previous
calculations based on the BA technique \cite{BoBo}.

ED is computationally demanding and cannot be performed beyond a certain system size. For this reason, in order to benchmark CLDFT for
larger rings, we have calculated the ground state energy with the BA method. An example of these calculations is presented in figure
\ref{20_sites_2_6_10_14}, where once again we show $\mathcal{E}(\Phi)$ for $L=20$, $U/t=4$ and different numbers of electrons. Also
in this case the agreement between the BA results and those obtained with CLDFT is remarkably good as long as the ground state is a
singlet. Interestingly we note that the agreement is better for low filling but it deteriorates as one approaches the half-filling case ($N=20$
in this case). This is somehow expected given the discontinuity of $\Lambda^\mathrm{xc}$ and of the derivative of $e^\mathrm{xc}$ at $n=1$
(see figure~\ref{exchange_lambda}), leading to the Mott transition. The presence of these discontinuities, although qualitatively correct, poses
numerical problems and losses in accuracy.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.48\textwidth,angle=0.0]{./Fig4}
\end{center}
\caption {(Color online) Ground state energy, $\mathcal{E}(\Phi)$, as a function of the magnetic flux, $\Phi$, calculated with both the
BA technique (dotted black line) and CLDFT (dashed red line). Calculations are carried out for $L=20$, $U/t=4$ and different numbers of
electrons: (a) $N=2$ ($n=1/10$), (b) $N=6$ ($n=0.3$), (c) $N=10$ ($n=1/2$) and (d) $N=14$ ($n=0.7$).} \label{20_sites_2_6_10_14}
\end{figure}

The final quantity we wish to consider is the charge stiffness or Drude weight, $D_\mathrm{c}$, defined as
\begin{equation}\label{chargestiff}
D_\mathrm{c}=\frac{L}{2}\frac{\partial^2\mathcal{E}(n,\Phi)}{\partial\Phi^2}|_{\Phi=0}\:.
\end{equation}
This is essentially the slope of the persistent current as a function of $\Phi$ calculated at $\Phi=0$ and defines the magnitude of the real part of the
optical conductivity in the long wave-length limit (see appendix for more details). $D_\mathrm{c}$ determines both qualitatively and quantitatively
the transport properties of the ring. Importantly in the limit of large rings it exponentially vanishes for insulators, while it saturates to a finite value
for metals. Many studies have been devolved to calculating $D_\mathrm{c}$ for interacting systems. R\"{o}mer and Punnoose have studied
$D_\mathrm{c}$ for finite Hubbard rings using an iterative BA technique \cite{Romer}. Eckern \textit{et. al.} explored the relation between
$D_\mathrm{c}$ and the so-called phase sensitivity, $\Delta\mathcal{E}$,  for spinless fermions. $\Delta\mathcal{E}$ is the difference in the total
energy calculated at $\Phi=0$ (periodic ground state) and that at $\Phi=\pi$ (antiperiodic ground state) \cite{Schenk1, Schmitteckert}.
Recently a density matrix renormalization group algorithm has been developed to deal with complex Hamiltonian matrices and used to calculate
$D_\mathrm{c}$ for spinless fermions \cite{Dias}.

Since the agreement between CLDFT and ED is proved for small rings (the slopes of the persistent currents as a function of $\Phi$ calculated
with CLDFT and ED are essentially identical in figure \ref{12_6persistentU0_U2_U4_U6}) we concentrate here on a larger system, namely a
homogeneous 60 site ring at quarter filling. Our results for  the Drude weight as a function of $U/t$ are presented in figure \ref{Dc_scheme}.
Again the CLDFT data are compared with those calculated with the BA in the thermodynamic limit ($L\rightarrow\infty$) and the agreement
is rather satisfactory. We note that, as for the ground state energy, also for the Drude weight the CLDFT seems to perform less well as $U/t$
increases, i.e. as the interaction strength becomes large.
\begin{figure}
\begin{center}
\includegraphics[width=0.40\textwidth,angle=0.0]{./Fig5}
\end{center}
\caption {(Color online) Drude coefficient $D_\mathrm{c}$ as a function of the interaction strength $U/t$ (top panel) and of the number of sites in the
ring, $L$ (bottom panel). All the calculations are for quarter filling and the results in the top panel are for a 60-site ring. In the figure we compare
CLDFT results (dotted black lines) with those obtained by the BA technique in the thermodynamic limit (dashed red lines). Calculations in the
lower panel are for $U/t=2$.}
\label{Dc_scheme}
\end{figure}
Then in the lower panel of figure \ref{Dc_scheme} we illustrate the scaling properties of $D_\mathrm{c}$ as a function of the number of sites
in the ring, $L$ (we consider quarter filling and $U/t=2$). Clearly $D_\mathrm{c}$ does not vanish at any lengths demonstrating that the system
remains metallic. Furthermore it approaches a constant value already for $L>40$. In the picture we also report the asymptotic value predicted
by the BA in the thermodynamic limit $L\rightarrow\infty$ for this set of parameters. We find that the calculated CLDFT value is only 0.06\% larger
than the BA one, i.e. it is in quite remarkable good agreement.

\subsection{Scaling properties}

Next we take a more careful look at the scaling properties of the persistent currents and the Drude weights as a function of both the ring
size and the interaction strength. It is well known that $j$ is strongly size dependent, since it originates from electron coherence across
the entire ring \cite{Dias}. For a perfect metal one expect $j$ to scale as $1/L$ \cite{Bouzerar}. In Figure \ref{different_sizes_U4} the
value of the persistent currents as a function of the ring size are presented for different electron fillings and for the two representative
interaction strengths of $U/t=2$ (a) and $U/t=4$ (b). Calculations are performed with both the exact BA and CLDFT. As a matter
of convention we calculate the persistent currents at $\Phi=\pi/2$.

In general we find a monotonic reduction of the persistent current with $L$ and an overall excellent agreement between the BA and the
CLDFT results over the entire range of lengths, occupations and interaction strengths investigated.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.48\textwidth,angle=0.0]{./Fig6}
\end{center}
\caption {(Color online) Persistent current, $j$, as a function of the number of site in the ring, $L$, and for different electron occupations, $n$:
(a) $U/t=2$, (b) $U/t=4$. Results are obtained with both the exact BA technique and CLDFT. In the figure the persistent currents are
calculated at $\Phi=\pi/2$, i.e. $j=j(\pi/2)$} \label{different_sizes_U4}
\end{figure}
A non-linear fit of all the curves of figure~\ref{different_sizes_U4} returns us an almost perfect $1/L$ dependence of $j$ with no
appreciable deviations at any $n$ or $U/t$. This indicates a full metallic response of the rings in the region of parameters investigated,
thus confirming previous results obtained with the BA approach \cite{BoBo}.

Then we look at the dependance of $j$ and $D_\mathrm{c}$ on the interaction strength. In this case we consider a 60 site ring and
three different different electron fillings. In general for small fluxes one expects $j=2D_\mathrm{c}\Phi$ and our numerical results of
Fig.~\ref{PCandDW} demonstrates that this is approximately correct also for our definition of persistent currents [$j=j(\Phi=\pi/2)$]
over the entire $U/t$ range investigated.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.5\textwidth,angle=0.0]{./Fig7}
\end{center}
\caption {(Color online) Persistent current, $j$, and Drude weight, $D_\mathrm{c}$ as a function of interaction strength $U/t$ for a
60 site ring at different fillings. Results are obtained with both the exact BA technique and CLDFT.} \label{PCandDW}
\end{figure}
We find that both $j$ and $D_\mathrm{c}$ monotonically decrease as a function of the interaction strength, essentially meaning that
the predicted long-wavelength optical conductivity is reduced as the electron repulsion gets larger.

Also in this case the agreement between the BA and the CLDFT results is substantially good, although significant deviations appear
in the limit of large $U/t$ and electron filling approaching half-filling. This again corresponds to a region of the parameter space where
the XC potential approaches the derivative discontinuity.

It was numerically demonstrated in the past \cite{BoBo} that the persistent current (and so the Drude weight) at half-filling follows the scaling
relation $j\sim\mathrm{e}^{-U^2/\xi}$, with $\xi\sim1$. However, to the best of our knowledge, no scaling relation was ever provided in the
metallic case. We have then carried out a fitting analysis (the fit is limited to values of $j$ and $D_\mathrm{c}$ for $U/t>2$) and found that our
data can be well represented by the scaling lows
\begin{equation}\label{esl}
j=j_0(U/t)^{-\beta},\;\;\;\;\;\;\;D_\mathrm{c}=D_0(U/t)^{-\gamma}\:.
\end{equation}
In general and as expected we find $\beta=\gamma$ and a quite significant dependence of the exponents on the filling. In particular
table~\ref{thetable} summarizes our results and demonstrates that the decay rate of both the persistent currents and the Drude weights
increases as the filling approaches half-filling. Furthermore the table also quantifies the differences between the BA and the CLDFT
solutions, whose exponents increasingly differ from each other as the electron filling gets closer to $n=1$ (for $n=0.7$ we find
$\beta^\mathrm{BA}\sim2\beta^\mathrm{CLDFT}$).
 \begin{table}[h]
\begin{tabular}{ccc} \hline\hline
$n$ & $\beta^\mathrm{CLDFT}$ & $\beta^\mathrm{BA}$ \\ \hline
0.3 & 0.036 & 0.036  \\
0.5 & 0.085 & 0.104  \\
0.7 & 0.151 & 0.246  \\ \hline\hline
\end{tabular}\caption{\label{thetable} Exponents for the empirical scaling laws of equation (\ref{esl}) as fitted from the data of figure
\ref{PCandDW}.}
\end{table}

Finally, by combining all the results of this section we can propose a scaling law for both the persistent currents and the
Drude weights, valid in the metallic limit of the Hubbard model, i.e. away from half-filling. This reads
\begin{equation}
j=\frac{j_0(n)}{L}\left(\frac{U}{t}\right)^{-\beta(n)}\:,
\end{equation}
where both the constant $j_0$ and the exponent $\beta$ are function of the electron filling $n$. Note that an identical equation
holds for $D_\mathrm{c}$.

\subsection{Scattering to a single impurity}

Having established the success of the BALDA to CLDFT for the homogeneous case we now move to a more stringent test for the theory, namely
the case of a ring penetrated by a magnetic flux in the presence of a single impurity. Such a problem has already received considerable
attention in the past \cite{Viefer2, Koskinen, Cheung}. Note that, as in {\it ab initio} DFT, this is a situation different from the reference system used
to construct the BALDA (since it deals with a non homogeneous system) and therefore one might expect a more pronounced disagreement with
exact results. As the BA equations are integrable only for the homogeneous case we now benchmark our CLDFT results with those obtained by
ED. This however limits our analysis to small rings.

The single impurity in the ring is described by simply adding to the Hamiltonian of equation (\ref{Hint}) the term
\begin{equation}\label{impurity_ham}
\begin{aligned}
\hat{H}_\mathrm{imp}=&\varepsilon_\mathrm{imp}\hat{n}_{i}\:,
\end{aligned}
\end{equation}
where $\varepsilon_\mathrm{imp}$ is the modification to the on-site energy at the impurity site $i$. The inclusion of an impurity produces in general
electron backscattering so that we expect the persistent currents to get reduced. In figure \ref{53_26_persistent_vs_e1} we present the general
transport features for this inhomogeneous system. Calculations have been carried out with CLDFT for a ring comprising 53 sites and $N=26$,
$U/t=4$. Again the persistent currents are calculated at $\Phi=\pi/2$.

\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.48\textwidth,angle=0.0]{./Fig8}
\end{center}
\caption {(a) Persistent current, $j$, as a function of single impurity strength, $\varepsilon_\mathrm{imp}$, obtained from the CLDFT for $L=53$, $N=26$,
$U/t=4$ and $\Phi=\frac{\pi}{2}$. In (b) we show a typical site density profile for a positive single impurity site potential.} \label{53_26_persistent_vs_e1}
\end{figure}
Panel (a) shows $j$ as a function of the impurity on-site energy. As expected from standard scattering theory the current is reduced as
$\varepsilon_\mathrm{imp}$ increases, thus creating a potential barrier. The electron density profile for this situation is presented in panel (b), where
one can clearly observe an electron depletion at the impurity site and Friedel's oscillations around it.

A quantitative assessment of our CLDFT results is provided in Fig.~\ref{BAvsCLDFT} where they are compared with those obtained by exact
diagonalization for a 13 site ring close to quarter filling ($N=6$). In particular we present $j$ as a function of the impurity potential,
$\varepsilon_\mathrm{imp}$, for both $U/t=2$ and $U/t=4$. In general we find a rather satisfactory agreement between CLDFT and the
exact results in particular for small $\varepsilon_\mathrm{imp}$ and $U/t$. As the electron scattering becomes more significant deviations
appear and the quantitative agreement is less good. Importantly we notice that the ED results systematically provide a persistent current
lower than that calculated with CLDFT, at least for the values of electron filling investigated here. This seems to be a consistent trend also present
for the homogeneous case (see figure~\ref{PCandDW}), although the deviations in that case are less pronounced (for the same electron filling and
interaction strength). Therefore we tentatively conclude that most of the errors in the impurity problem have to be attributed to the errors already
present in the homogeneous case. We then expect that CLDFT provides a good platform for investigating scattering problems at only minor
computational costs. As such CLDFT appears as the ideal tool for investigating the interplay between electron-electron interaction and
disorder in low dimensional structures.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.48\textwidth,angle=0.0]{./Fig9}
\end{center}
\caption {(Color on line) Comparison between the persistent currents calculated with CLDFT (black symbols and dotted line) and by ED
(red symbols and dashed line) for a 13 site ring and $N=6$. The $j$'s are obtained at $\Phi=\pi/2$ for two different values of the interaction
strength, namely $U/t=2$ (a) and $U/t=4$ (b).} \label{BAvsCLDFT}
\end{figure}

\section{Conclusion}
In this work we have presented an extension of the BALDA for the one-dimensional Hubbard problem on a ring to CLDFT. We have then investigated
the response of interacting rings to an external flux both in the homogeneous and inhomogeneous case, and we have compared our results with
those obtained by numerically exact techniques. Our analysis has been confined to the metallic limit, i.e. away from half-filling, where the Hubbard model has
a metal to insulator transition. In general we have found that CLDFT performs rather well in calculating both the persistent currents and the
Drude weights in the homogeneous case. Furthermore a similar level of accuracy is transferred to the impurity problem. With these results in hands
we propose to use CLDFT in the study of AB rings where the combined effect of electron-electron interaction and disorder can be addressed
for large rings, so that a numerical evaluation of the various scaling laws proposed in the past can be accurately carried out.

\section{Acknowledgements}
We thank N. Baadji, I. Rungger and V. L. Campo for useful discussions. This work is supported by Science Foundation of Ireland under the
grant SFI05/RFP/PHY0062 and 07/IN.1/I945. Computational resources have been provided by the HEA IITAC project managed by the Trinity
Center for High Performance Computing and by ICHEC.

\section{APPENDIX: Local Density Approximation for the CLDFT}
We use the BA solution for the homogeneous part of the $\hat{H}_U^\Phi$ [equation~(\ref{Hint})] to estimate the XC energy. Then the local
approximation is taken,
\begin{equation}
\mathcal{E}^\mathrm{xc}_\mathrm{LDA}[n_l,j_l]=\sum_le^\mathrm{xc}[n_l,j_l]\:.
\end{equation}
Here $e^\mathrm{xc}(=\frac{\mathcal{E}^\mathrm{xc}[n,j]}{L})$ is the XC energy per site for the homogeneous system, which is provided
in equation (\ref{exc3}). The first term of the equation (\ref{exc3}) can be calculated exactly using the BA procedures \cite{Shastry} to obtain
the ground state energy as a function of $n$ and $\Phi$. Then the phase variable $\Phi$ can be eliminated from the ground state energy
to contain the current via
\begin{equation}
j=\frac{\partial \mathcal{E}(n,\Phi)}{\partial \Phi}\:.
\end{equation}

The complete flux dependence of the ground state energy for the Mott insulator phase ($n=1$) in the thermodynamic limit has been shown
to be \cite{Stafford}
\begin{equation}
\mathcal{E}(n,\Phi)-\mathcal{E}(n,0)=\frac{2D_c(n)}{L}(1-\cos\Phi)\:,
\end{equation}
while away from half filling and $L\rightarrow\infty$ this is
\begin{equation}\label{fluxdependence2}
\mathcal{E}(n,\Phi)-\mathcal{E}(n,0)=\frac{D_\mathrm{c}(n)}{L}\Phi^2\:.
\end{equation}
Here $D_\mathrm{c}(n)$ is the charge stiffness (Drude weight) defined as
\begin{equation}\label{chargestiff}
D_\mathrm{c}=\left.\frac{L}{2}\frac{\partial^2\mathcal{E}(n,\Phi)}{\partial\Phi^2}\right|_{\Phi=0}.
\end{equation}
In physical terms the Drude weight $D_\mathrm{c}$ is the real part of the optical conductivity $\sigma_1(w)$ in the long wavelength
limit \cite{Stafford},
\begin{equation}
 \sigma_1(w)=2\pi D_\mathrm{c}\delta (w)+\sigma_1^{\text{reg}}(w)\:,
\end{equation}
where we took $\hbar=e=c=1$. If we denote $\mathcal{E}^\mathrm{BA}(n_\mathrm{BA},\Phi_\mathrm{BA})$ and $\mathcal{E}^0(n_{0},\Phi_{0})$
respectively as the ground state energy for the interacting system [first term in equation (\ref{exc3})] and for the non-interacting one [second term
in equation (\ref{exc3})], away from half-filling we will write
\begin{equation}\label{fluxdependence3}
\begin{aligned}
\mathcal{E}^\mathrm{BA}(n_\mathrm{BA},\Phi_\mathrm{BA})=&\mathcal{E}^\mathrm{BA}(n_\mathrm{BA},0)+\frac{D_\mathrm{c}^\mathrm{BA}(n_\mathrm{BA})}{L}\Phi^{2}_\mathrm{BA}\:,\\
\mathcal{E}^0(n_{0},\Phi_{0})=&\mathcal{E}^0(n_{0},0)+\frac{D_c^0(n_{0})}{L}\Phi^{2}_0\:,
\end{aligned}
\end{equation}
and
\begin{equation}\label{jdependence3}
\begin{aligned}
j^\mathrm{BA}(n_\mathrm{BA},\Phi_\mathrm{BA})=&2\frac{D_\mathrm{c}^\mathrm{BA}(n_\mathrm{BA})}{L}\Phi_\mathrm{BA}\:,\\
j^0(n_{0},\Phi_{0})=&2\frac{D_c^0(n_{0})}{L}\Phi_0\:.
\end{aligned}
\end{equation}
The fundamental requirement of the KS mapping is that $n_\mathrm{BA}=n_{0}=n$ and $j^\mathrm{BA}=j^{0}=j$ while we note that
$\Phi_\mathrm{BA}=\Phi$ and $\Phi_{0}=\Phi^s$ in equation (\ref{exc3}). By substituting equation (\ref{fluxdependence3}) and
the expressions for $\Phi^s$ and $\Phi$ obtained from equation (\ref{jdependence3}) into equation (\ref{exc3}) one obtains
\begin{equation}\label{exc4}
\mathcal{E}^\mathrm{xc}(n,j)=\mathcal{E}^\mathrm{BA}(n,0)-\mathcal{E}^0(n,0)-\mathcal{E}^\mathrm{H}(n)+\frac{L}{2}\Lambda^\mathrm{xc}(n)j^2,
\end{equation}
where
\begin{equation}\label{lambda}
\Lambda^\mathrm{xc}(n)=\frac{1}{2}\left [\frac{1}{D_\mathrm{c}^0(n)}-\frac{1}{D_\mathrm{c}^\mathrm{BA}(n)}\right ].
\end{equation}
Here $D_\mathrm{c}^0(n)$ is the non-interacting charge stiffness defined as
\begin{equation}
 D_\mathrm{c}^0(n)=\frac{2t}{\pi}\sin\left (\frac{n\pi}{2}\right )
\end{equation}
for $L\rightarrow\infty$. $D_\mathrm{c}^\mathrm{BA}(n)$ can then be obtained in the thermodynamic limit by using \cite{Kawakami}
\begin{equation}\label{Dccalc}
 D_\mathrm{c}^\mathrm{BA}(n)=\frac{1}{2\pi}[\xi_\mathrm{c}(Q)]^2v_\mathrm{c}
\end{equation}
where $\xi_\mathrm{c}$ is an element of the dressed charge matrix, which is used to describe the scattering between the quasi-particles and
$v_\mathrm{c}$ is velocity of the charge excitation. Therefore one finally obtains
\begin{equation}\label{exc5}
e^\mathrm{xc}(n,j)=e^\mathrm{xc}(n,0)+\frac{1}{2}\Lambda^\mathrm{xc}(n)j^2,
\end{equation}
so that
\begin{equation}\label{vxc}
v^\mathrm{xc}_\mathrm{BALDA}(n_l,j_l)=\left.\frac{\partial e^\mathrm{xc}(n,j)}{\partial n}\right|_{n\rightarrow n_l,j\rightarrow j_l},
\end{equation}
and
\begin{equation}\label{phixc}
\Phi^\mathrm{xc}_\mathrm{BALDA}(n_l,j_l)=\left.\frac{\partial e^\mathrm{xc}(n,j)}{\partial j}=\Lambda^\mathrm{xc}(n)j\right|_{n\rightarrow n_l,j\rightarrow j_l}.
\end{equation}

redpajama_set_name: RedPajamaArXiv


text:
Diversity of phytoplasmas identified in the polyphagous leafhopper Euscelis incisus (Cicadellidae, Deltocephalinae) in Serbia: pathogen inventory, epidemiological significance and vectoring potential
Jakovljević, Miljana
Jović, Jelena
Krstić, Oliver
Mitrović, Milana
Marinković, Slavica
Toševski, Ivo
Cvrković, Tatjana
Euscelis incisus is polyphagous leafhopper that is widely distributed and abundant in diverse agroecosystems. Two generations per year allows this species to come into contact with a plethora of different phytoplasmas. We first investigated the interactions of E. incisus with phytoplasmas in different ecosystems as a bioindicator of phytoplasma diversity. Among the 510 analyzed E. incisus specimens collected from eight localities in Serbia, 53 (10%) tested positive for diverse 'Ca. Phytoplasma' taxa. Restriction fragment length polymorphism (RFLP) analysis and sequence comparison based on the F2nR2 fragment of the 16S rRNA gene revealed the presence of six 16S phytoplasma ribosomal groups and eight subgroups in E. incisus (16SrI-R, 16SrI-F, 16SrII-E, 16SrIII-B, 16SrIX-C, 16SrIX-E, 16SrXI-G and 16SrXII-A). The most prevalent was the 16SrXII-A phytoplasma group, represented by two multilocus stolbur phytoplasma genotypes: STOLg and Rqg31g. While the 16SrXII-A phytoplasmas were identical ...to the previously recorded isolates from Serbia, the 16SrI-F and 16SrI-R subgroups closely related to the previously documented 16SrI-B and 16SrI-C subgroups were recorded for the first time in Serbia. In addition, records of the 16SrIX and 16SrXI groups represent the first findings of these phytoplasma groups in Serbia. Transmission trials of 'Ca. P. solani' were performed with naturally infected E. incisus adults. The leafhoppers successfully transmitted stolbur phytoplasma to exposed Catharanthus roseus plants, indicating their role as a natural vector.
Euscelis incisus / Epidemiology / 'Candidatus Phytoplasma' species / Multilocus (MLST) genotypes / Vectoring potential
European Journal of Plant Pathology, 2020, 156, 201-221
SCOPES program of the Swiss National Science Foundation (IZ73Z0_152414)
Agrobiodiversity and land-use change in Serbia: an integrated biodiversity assessment of key functional groups of arthropods and plant pathogens (RS-43001)
DOI: 10.1007/s10658-019-01878-w
AU  - Jakovljević, Miljana
AU  - Jović, Jelena
AU  - Krstić, Oliver
AU  - Mitrović, Milana
AU  - Marinković, Slavica
AU  - Toševski, Ivo
AU  - Cvrković, Tatjana
AB  - Euscelis incisus is polyphagous leafhopper that is widely distributed and abundant in diverse agroecosystems. Two generations per year allows this species to come into contact with a plethora of different phytoplasmas. We first investigated the interactions of E. incisus with phytoplasmas in different ecosystems as a bioindicator of phytoplasma diversity. Among the 510 analyzed E. incisus specimens collected from eight localities in Serbia, 53 (10%) tested positive for diverse 'Ca. Phytoplasma' taxa. Restriction fragment length polymorphism (RFLP) analysis and sequence comparison based on the F2nR2 fragment of the 16S rRNA gene revealed the presence of six 16S phytoplasma ribosomal groups and eight subgroups in E. incisus (16SrI-R, 16SrI-F, 16SrII-E, 16SrIII-B, 16SrIX-C, 16SrIX-E, 16SrXI-G and 16SrXII-A). The most prevalent was the 16SrXII-A phytoplasma group, represented by two multilocus stolbur phytoplasma genotypes: STOLg and Rqg31g. While the 16SrXII-A phytoplasmas were identical to the previously recorded isolates from Serbia, the 16SrI-F and 16SrI-R subgroups closely related to the previously documented 16SrI-B and 16SrI-C subgroups were recorded for the first time in Serbia. In addition, records of the 16SrIX and 16SrXI groups represent the first findings of these phytoplasma groups in Serbia. Transmission trials of 'Ca. P. solani' were performed with naturally infected E. incisus adults. The leafhoppers successfully transmitted stolbur phytoplasma to exposed Catharanthus roseus plants, indicating their role as a natural vector.
PB  - Springer Nature
T2  - European Journal of Plant Pathology
T1  - Diversity of phytoplasmas identified in the polyphagous leafhopper Euscelis incisus (Cicadellidae, Deltocephalinae) in Serbia: pathogen inventory, epidemiological significance and vectoring potential
author = "Jakovljević, Miljana and Jović, Jelena and Krstić, Oliver and Mitrović, Milana and Marinković, Slavica and Toševski, Ivo and Cvrković, Tatjana",
abstract = "Euscelis incisus is polyphagous leafhopper that is widely distributed and abundant in diverse agroecosystems. Two generations per year allows this species to come into contact with a plethora of different phytoplasmas. We first investigated the interactions of E. incisus with phytoplasmas in different ecosystems as a bioindicator of phytoplasma diversity. Among the 510 analyzed E. incisus specimens collected from eight localities in Serbia, 53 (10%) tested positive for diverse 'Ca. Phytoplasma' taxa. Restriction fragment length polymorphism (RFLP) analysis and sequence comparison based on the F2nR2 fragment of the 16S rRNA gene revealed the presence of six 16S phytoplasma ribosomal groups and eight subgroups in E. incisus (16SrI-R, 16SrI-F, 16SrII-E, 16SrIII-B, 16SrIX-C, 16SrIX-E, 16SrXI-G and 16SrXII-A). The most prevalent was the 16SrXII-A phytoplasma group, represented by two multilocus stolbur phytoplasma genotypes: STOLg and Rqg31g. While the 16SrXII-A phytoplasmas were identical to the previously recorded isolates from Serbia, the 16SrI-F and 16SrI-R subgroups closely related to the previously documented 16SrI-B and 16SrI-C subgroups were recorded for the first time in Serbia. In addition, records of the 16SrIX and 16SrXI groups represent the first findings of these phytoplasma groups in Serbia. Transmission trials of 'Ca. P. solani' were performed with naturally infected E. incisus adults. The leafhoppers successfully transmitted stolbur phytoplasma to exposed Catharanthus roseus plants, indicating their role as a natural vector.",
publisher = "Springer Nature",
journal = "European Journal of Plant Pathology",
title = "Diversity of phytoplasmas identified in the polyphagous leafhopper Euscelis incisus (Cicadellidae, Deltocephalinae) in Serbia: pathogen inventory, epidemiological significance and vectoring potential",
doi = "10.1007/s10658-019-01878-w"
Jakovljević, M., Jović, J., Krstić, O., Mitrović, M., Marinković, S., Toševski, I.,& Cvrković, T.. (2020). Diversity of phytoplasmas identified in the polyphagous leafhopper Euscelis incisus (Cicadellidae, Deltocephalinae) in Serbia: pathogen inventory, epidemiological significance and vectoring potential. in European Journal of Plant Pathology
Springer Nature., 156, 201-221.
Jakovljević M, Jović J, Krstić O, Mitrović M, Marinković S, Toševski I, Cvrković T. Diversity of phytoplasmas identified in the polyphagous leafhopper Euscelis incisus (Cicadellidae, Deltocephalinae) in Serbia: pathogen inventory, epidemiological significance and vectoring potential. in European Journal of Plant Pathology. 2020;156:201-221.
doi:10.1007/s10658-019-01878-w .
Jakovljević, Miljana, Jović, Jelena, Krstić, Oliver, Mitrović, Milana, Marinković, Slavica, Toševski, Ivo, Cvrković, Tatjana, "Diversity of phytoplasmas identified in the polyphagous leafhopper Euscelis incisus (Cicadellidae, Deltocephalinae) in Serbia: pathogen inventory, epidemiological significance and vectoring potential" in European Journal of Plant Pathology, 156 (2020):201-221,
https://doi.org/10.1007/s10658-019-01878-w . .


You have been on my mind recently, and no more than last night when I was riding a bike.
Now, mind you, it was just a bike, but it was no normal ride. Not a fantastic or out of the ordinary ride, but one that took me back to the Summer of Love, late nights, early mornings, battles with Mr. Wind, pre-ordered ambulances, and the deadly sand traps of Provincetown.
I was wearing a pair of crazy multi-colored shorts and a shirt and was heading from my house with a friend to Marlborough Street to watch the fireworks. He had his bike. I didn't. Need I say more? I took off my shirt and said get on the seat, I'll pump. He said, "You can't do that, I'm too heavy." And I said, "Get on the seat and watch me."
Though only a short distance up Columbus Avenue with a turn onto Dartmouth and then a swing left onto Marlborough, it was a wonderful trip. I stood upright and pedaled strongly and smoothly with nary a wobble. Through the light, around cars, missing pedestrians, applying brakes accordingly so as not to stop, coasting down hill, and knowingly lacing my way to the destination. Just like you never forget how to ride a bike, you never forget how to ride a bike at night, with a passenger, in shorts and no shirt, only your good eye working, and a big smile on your face.
As my friend complimented me on my biking skills, I said, "You're looking at 50, and that's what 50 does."


text:
'use strict';
require('app-templates');

var App = function($urlRouterProvider) {
    $urlRouterProvider.otherwise('/');
};

App.$inject = ['$urlRouterProvider'];

var trafficOps = angular.module('trafficOps', [
        'config',
        'ngAnimate',
        'ngResource',
        'ngSanitize',
        'ngRoute',
        'ngMap',
        'ui.router',
        'ui.bootstrap',
        'restangular',
        'app.templates',
        'angular-jwt',
        'angular-loading-bar',

        // public modules
        require('./modules/public').name,
        require('./modules/public/login').name,

        // private modules
        require('./modules/private').name,

        // current user
        require('./modules/private/user').name,
        require('./modules/private/user/edit').name,

        // admin
        require('./modules/private/admin').name,
        require('./modules/private/admin/asns').name,
        require('./modules/private/admin/asns/edit').name,
        require('./modules/private/admin/asns/list').name,
        require('./modules/private/admin/asns/new').name,
        require('./modules/private/admin/cdns').name,
        require('./modules/private/admin/cdns/deliveryServices').name,
        require('./modules/private/admin/cdns/edit').name,
        require('./modules/private/admin/cdns/list').name,
        require('./modules/private/admin/cdns/new').name,
        require('./modules/private/admin/cdns/profiles').name,
        require('./modules/private/admin/cdns/servers').name,
        require('./modules/private/admin/changeLogs').name,
        require('./modules/private/admin/changeLogs/list').name,
        require('./modules/private/admin/divisions').name,
        require('./modules/private/admin/divisions/edit').name,
        require('./modules/private/admin/divisions/list').name,
        require('./modules/private/admin/divisions/new').name,
        require('./modules/private/admin/divisions/regions').name,
        require('./modules/private/admin/jobs').name,
        require('./modules/private/admin/jobs/list').name,
        require('./modules/private/admin/jobs/new').name,
        require('./modules/private/admin/physLocations').name,
        require('./modules/private/admin/physLocations/edit').name,
        require('./modules/private/admin/physLocations/list').name,
        require('./modules/private/admin/physLocations/new').name,
        require('./modules/private/admin/physLocations/servers').name,
        require('./modules/private/admin/parameters').name,
        require('./modules/private/admin/parameters/cacheGroups').name,
        require('./modules/private/admin/parameters/edit').name,
        require('./modules/private/admin/parameters/list').name,
        require('./modules/private/admin/parameters/new').name,
        require('./modules/private/admin/parameters/profiles').name,
        require('./modules/private/admin/profiles').name,
        require('./modules/private/admin/profiles/deliveryServices').name,
        require('./modules/private/admin/profiles/edit').name,
        require('./modules/private/admin/profiles/list').name,
        require('./modules/private/admin/profiles/new').name,
        require('./modules/private/admin/profiles/parameters').name,
        require('./modules/private/admin/profiles/servers').name,
        require('./modules/private/admin/regions').name,
        require('./modules/private/admin/regions/edit').name,
        require('./modules/private/admin/regions/list').name,
        require('./modules/private/admin/regions/physLocations').name,
        require('./modules/private/admin/regions/new').name,
        require('./modules/private/admin/statuses').name,
        require('./modules/private/admin/statuses/edit').name,
        require('./modules/private/admin/statuses/list').name,
        require('./modules/private/admin/statuses/new').name,
        require('./modules/private/admin/statuses/servers').name,
        require('./modules/private/admin/tenants').name,
        require('./modules/private/admin/tenants/edit').name,
        require('./modules/private/admin/tenants/list').name,
        require('./modules/private/admin/tenants/new').name,
        require('./modules/private/admin/types').name,
        require('./modules/private/admin/types/edit').name,
        require('./modules/private/admin/types/list').name,
        require('./modules/private/admin/types/new').name,
        require('./modules/private/admin/types/servers').name,
        require('./modules/private/admin/types/cacheGroups').name,
        require('./modules/private/admin/types/deliveryServices').name,
        require('./modules/private/admin/types/staticDnsEntries').name,
        require('./modules/private/admin/users').name,
        require('./modules/private/admin/users/deliveryServices').name,
        require('./modules/private/admin/users/edit').name,
        require('./modules/private/admin/users/list').name,
        require('./modules/private/admin/users/new').name,

        // configure
        require('./modules/private/configure').name,
        require('./modules/private/configure/cacheGroups').name,
        require('./modules/private/configure/cacheGroups/edit').name,
        require('./modules/private/configure/cacheGroups/list').name,
        require('./modules/private/configure/cacheGroups/new').name,
        require('./modules/private/configure/cacheGroups/asns').name,
        require('./modules/private/configure/cacheGroups/parameters').name,
        require('./modules/private/configure/cacheGroups/servers').name,
        require('./modules/private/configure/cacheGroups/staticDnsEntries').name,
        require('./modules/private/configure/deliveryServices').name,
        require('./modules/private/configure/deliveryServices/edit').name,
        require('./modules/private/configure/deliveryServices/list').name,
        require('./modules/private/configure/deliveryServices/new').name,
        require('./modules/private/configure/deliveryServices/jobs').name,
        require('./modules/private/configure/deliveryServices/jobs/list').name,
        require('./modules/private/configure/deliveryServices/jobs/new').name,
        require('./modules/private/configure/deliveryServices/regexes').name,
        require('./modules/private/configure/deliveryServices/regexes/edit').name,
        require('./modules/private/configure/deliveryServices/regexes/list').name,
        require('./modules/private/configure/deliveryServices/regexes/new').name,
        require('./modules/private/configure/deliveryServices/servers').name,
        require('./modules/private/configure/deliveryServices/staticDnsEntries').name,
        require('./modules/private/configure/deliveryServices/users').name,
        require('./modules/private/configure/servers').name,
        require('./modules/private/configure/servers/deliveryServices').name,
        require('./modules/private/configure/servers/edit').name,
        require('./modules/private/configure/servers/new').name,
        require('./modules/private/configure/servers/list').name,

        // monitor
        require('./modules/private/monitor').name,

        // dashboards
        require('./modules/private/monitor/dashboards').name,
        require('./modules/private/monitor/dashboards/one').name,
        require('./modules/private/monitor/dashboards/two').name,
        require('./modules/private/monitor/dashboards/three').name,

        // common modules
        require('./common/modules/dialog/confirm').name,
        require('./common/modules/dialog/delete').name,
        require('./common/modules/dialog/reset').name,
        require('./common/modules/dialog/select').name,
        require('./common/modules/header').name,
        require('./common/modules/message').name,
        require('./common/modules/navigation').name,
        require('./common/modules/release').name,

        // forms
        require('./common/modules/form/cacheGroup').name,
        require('./common/modules/form/cacheGroup/edit').name,
        require('./common/modules/form/cacheGroup/new').name,
        require('./common/modules/form/asn').name,
        require('./common/modules/form/asn/edit').name,
        require('./common/modules/form/asn/new').name,
        require('./common/modules/form/cdn').name,
        require('./common/modules/form/cdn/edit').name,
        require('./common/modules/form/cdn/new').name,
        require('./common/modules/form/deliveryService').name,
        require('./common/modules/form/deliveryService/edit').name,
        require('./common/modules/form/deliveryService/new').name,
        require('./common/modules/form/deliveryServiceRegex').name,
        require('./common/modules/form/deliveryServiceRegex/edit').name,
        require('./common/modules/form/deliveryServiceRegex/new').name,
        require('./common/modules/form/deliveryServiceJob').name,
        require('./common/modules/form/deliveryServiceJob/new').name,
        require('./common/modules/form/division').name,
        require('./common/modules/form/division/edit').name,
        require('./common/modules/form/division/new').name,
        require('./common/modules/form/job').name,
        require('./common/modules/form/job/new').name,
        require('./common/modules/form/physLocation').name,
        require('./common/modules/form/physLocation/edit').name,
        require('./common/modules/form/physLocation/new').name,
        require('./common/modules/form/parameter').name,
        require('./common/modules/form/parameter/edit').name,
        require('./common/modules/form/parameter/new').name,
        require('./common/modules/form/profile').name,
        require('./common/modules/form/profile/edit').name,
        require('./common/modules/form/profile/new').name,
        require('./common/modules/form/region').name,
        require('./common/modules/form/region/edit').name,
        require('./common/modules/form/region/new').name,
        require('./common/modules/form/server').name,
        require('./common/modules/form/server/edit').name,
        require('./common/modules/form/server/new').name,
        require('./common/modules/form/status').name,
        require('./common/modules/form/status/edit').name,
        require('./common/modules/form/status/new').name,
        require('./common/modules/form/tenant').name,
        require('./common/modules/form/tenant/edit').name,
        require('./common/modules/form/tenant/new').name,
        require('./common/modules/form/type').name,
        require('./common/modules/form/type/edit').name,
        require('./common/modules/form/type/new').name,
        require('./common/modules/form/user').name,
        require('./common/modules/form/user/edit').name,
        require('./common/modules/form/user/new').name,

        // tables
        require('./common/modules/table/cacheGroups').name,
        require('./common/modules/table/cacheGroupAsns').name,
        require('./common/modules/table/cacheGroupParameters').name,
        require('./common/modules/table/cacheGroupServers').name,
        require('./common/modules/table/cacheGroupStaticDnsEntries').name,
        require('./common/modules/table/changeLogs').name,
        require('./common/modules/table/asns').name,
        require('./common/modules/table/cdns').name,
        require('./common/modules/table/cdnDeliveryServices').name,
        require('./common/modules/table/cdnProfiles').name,
        require('./common/modules/table/cdnServers').name,
        require('./common/modules/table/deliveryServices').name,
        require('./common/modules/table/deliveryServiceJobs').name,
        require('./common/modules/table/deliveryServiceRegexes').name,
        require('./common/modules/table/deliveryServiceServers').name,
        require('./common/modules/table/deliveryServiceStaticDnsEntries').name,
        require('./common/modules/table/deliveryServiceUsers').name,
        require('./common/modules/table/divisions').name,
        require('./common/modules/table/divisionRegions').name,
        require('./common/modules/table/jobs').name,
        require('./common/modules/table/physLocations').name,
        require('./common/modules/table/physLocationServers').name,
        require('./common/modules/table/parameters').name,
        require('./common/modules/table/parameterCacheGroups').name,
        require('./common/modules/table/parameterProfiles').name,
        require('./common/modules/table/profileDeliveryServices').name,
        require('./common/modules/table/profileParameters').name,
        require('./common/modules/table/profileServers').name,
        require('./common/modules/table/profiles').name,
        require('./common/modules/table/regions').name,
        require('./common/modules/table/regionPhysLocations').name,
        require('./common/modules/table/servers').name,
        require('./common/modules/table/serverDeliveryServices').name,
        require('./common/modules/table/statuses').name,
        require('./common/modules/table/statusServers').name,
        require('./common/modules/table/tenants').name,
        require('./common/modules/table/types').name,
        require('./common/modules/table/typeCacheGroups').name,
        require('./common/modules/table/typeDeliveryServices').name,
        require('./common/modules/table/typeServers').name,
        require('./common/modules/table/typeStaticDnsEntries').name,
        require('./common/modules/table/users').name,
        require('./common/modules/table/userDeliveryServices').name,

        // models
        require('./common/models').name,
        require('./common/api').name,

        // directives
        require('./common/directives/match').name,

        // services
        require('./common/service/application').name,
        require('./common/service/utils').name,

        // filters
        require('./common/filters').name

    ], App)

        .config(function($stateProvider, $logProvider, $controllerProvider, RestangularProvider, ENV) {

            RestangularProvider.setBaseUrl(ENV.api['root']);

            RestangularProvider.setResponseInterceptor(function(data, operation, what) {

                if (angular.isDefined(data.response)) { // todo: this should not be needed. need better solution.
                    if (operation == 'getList') {
                        return data.response;
                    }
                    return data.response[0];
                } else {
                    return data;
                }
            });

            $controllerProvider.allowGlobals();
            $logProvider.debugEnabled(true);
            $stateProvider
                .state('trafficOps', {
                    url: '/',
                    abstract: true,
                    templateUrl: 'common/templates/master.tpl.html'
                });
        })

        .run(function($log, applicationService) {
            $log.debug("Application run...");
            applicationService.startup();
        })
    ;

trafficOps.factory('authInterceptor', function ($q, $window, $location, $timeout, messageModel, userModel) {
    return {
        responseError: function (rejection) {
            var url = $location.url(),
                alerts = [];

            try { alerts = rejection.data.alerts; }
            catch(e) {}

            // 401, 403, 404 and 5xx errors handled globally; all others handled in fault handler
            if (rejection.status === 401) {
                userModel.resetUser();
                if (url == '/' || $location.search().redirect) {
                    messageModel.setMessages(alerts, false);
                } else {
                    $timeout(function () {
                        messageModel.setMessages(alerts, true);
                        // forward the to the login page with ?redirect=page/they/were/trying/to/reach
                        $location.url('/').search({ redirect: encodeURIComponent(url) });
                    }, 200);
                }
            } else if (rejection.status === 403 || rejection.status === 404) {
                $timeout(function () {
                    messageModel.setMessages(alerts, false);
                }, 200);
            } else if (rejection.status.toString().match(/^5\d[01356789]$/)) {
                // matches 5xx EXCEPT for 502's and 504's which indicate a timeout and will be handled by each service call accordingly
                $timeout(function () {
                    messageModel.setMessages([ { level: 'error', text: rejection.status.toString() + ': ' + rejection.statusText } ], false);
                }, 200);
            }

            return $q.reject(rejection);
        }
    };
});

trafficOps.config(function ($httpProvider) {
    $httpProvider.interceptors.push('authInterceptor');
});

redpajama_set_name: RedPajamaGithub


Ontario is supporting 45 art and cultural events that celebrate the province's rich culture and heritage, attract visitors and grow local economies.
Eleanor McMahon, Minister of Tourism, Culture and Sport, made the announcement today at Ryerson University's Ryerson Image Centre, which will host exhibits for the Scotiabank CONTACT Photography Festival--the world's largest photography event. With support from the province, this year's festival will feature Canadian photography at over 200 exhibitions across the Greater Toronto Area and is expected to attract over one million visitors.
Franco-Fête 2017, a festival that celebrates Ontario's francophone culture with performances in the Ottawa region.
The Confederation Plays, in Toronto, which explore the history of confederation through four key figures: John A. Macdonald, Louis Riel, Wilfred Laurier and Chief Big Bear.
A Taste of Greece, a cultural event in London that features traditional Greek dancing and music, including several traditional dance troupes from communities across the province.
The Stars and Thunder International Fireworks and Music Festival in Timmins. The eight-day event will include daily musical performances by Indigenous, French and English artists. An international fireworks competition will wrap up the festivities each night.
The Fund helps strengthen cultural tourism, which boosts local economies, creates jobs and draws visitors to communities across the province. This year's recipients also feature initiatives that commemorate Ontario's 150th anniversary and are expected to attract an attendance of approximately four million people.
Supporting local economies through cultural tourism is part of the government's plan to create jobs, grow the economy and help people in their everyday lives.
Ontario is providing over $2.8 million to 45 arts and culture organizations this spring and summer, to market and promote their unique events and exhibits and bring visitors to communities across the province.
The Scotiabank CONTACT Photography Festival received a $180,000 investment from the OCAF fund and $235,000 from Ontario's Celebrate Program.
Since 2013, the government has invested nearly $7.8 million through OCAF, which has resulted in over $15 million in support to cultural tourism in Ontario.
Culture is one of Ontario's fastest growing sectors. Culture contributes more than $25 billion to Ontario's economy and supports almost 280,000 jobs.