text:
The Keeper - to Have and to Hold at the Model Sligo
An edited version of this review appeared in the Sunday Times Culture magazine on 10 March 2019.
The Niland Collection is a monument to the will and indefatigable energy of Nora Niland – the Sligo County Librarian who started the collection 60 years ago. The Model in Sligo is celebrating the woman and her heritage with an exhibition, curated by its director Emer McGarry, that encompasses 100 works from the Niland collection together with a small and quirky selection from the collection of former director Jobst Graeve. Accompanying these are four fascinating contemporary video works that relate to the importance of collecting and what can be lost when we don't "keep", or "keep" properly.
A seminal work in the Niland Collection is Leaving the Far Point by Jack B. Yeats (see above), painted in 1946 and given to his wife Cottie as a birthday present in 1947, the year before she died. It's an imaginary scenario with Yeats, Cottie and his favourite uncle George Pollexfen taking a walk along the beach near Rosses Point – where his uncle had a house, and where the artist spent 20 happy summers. Pollexfen had died in 1910 so this much later work represents the aging Yeats looking back at an idyllic period in his life. However, the painting has a significance beyond its personal resonances for the artist. He presented it to the people of Sligo in 1954 and it was the seed from which the Niland collection emerged. Nora Niland had borrowed five other works by Yeats from the Capuchins for the inaugural Willian Butler Yeats Summer School and she decided she would like to add them to her solitary painting and start to build a Yeats collection for the county he loved so well. She raised the money by public subscription, with a little help from the Arts Council, and paid off the good friars – and thus the Niland collection was born. It now has 52 works by Jack B. Yeats – making it the most significant collection by the artist outside the National Gallery of Ireland. Niland was a determined and well-connected woman - her family owned the Niland Cash and Carry business in Galway. Money for art in the west was tight so she used her connections to approach wealthy individuals and local businesses. Arts organizations such as Friends of the National Collections were also very helpful. A major boost to the fledgling project was a bequest of 35 paintings from the Irish-American James A. Healy – a successful stockbroker. "They formed the core of the collection" according to McGarry. Another fertile source has been artists themselves to whom Niland regularly wrote asking for work. Work also arrived unbidden. As recently as last year Sean McSweeney's family donated five paintings by the popular local artist. McSweeney was an avid supporter of the Model up to his much mourned death in 2018.
The collection has expanded well beyond its initial Jack B. Yeats emphasis and it now consists of more than 300 paintings that provide a comprehensive survey of 20th Century Irish art. Emer McGarry has gone for a salon hang format to enable as much of the collection as feasible to be put on show. The exhibition is dominated numerically by the Jack B. Yeats paintings (23 of which are displayed), many of outstanding quality. There's a nice contrast between the elaborate formal and the fraught practical in his treatments of two funeral scenes: The Funeral of Harry Boland and An Island Funeral. The father, John B. Yeats, gets a look in with his famously prevaricated over self-portrait – 11 years labour and still unfinished. There's also his charming portrait of a languid William B. Yeats reading in the garden. Elsewhere an exquisite small work, Grey Pool, by Sean McSweeney catches the eye. There are strong works by Mainie Jellett (Abstract Composition) and Mary Swanzy (Abstract) and women artists generally are well represented. There's also an unusually expressive work, Bog Sun, by that purveyor of restraint and decorum Patrick Scott.
The Niland collection is accompanied by work from the Jobst Graeve Collection – on temporary loan to the Model. This featured quirkier and more idiosyncratic work – a leather jacket here, a cow's nipple shoe there, elegant craft work, and some agitprop paintings (such as Rita Duffy's striking Belfast Pieta). The benefactor himself features, naked of torso and full-length of pleated skirt, in a Mick O'Dea portrait that the charitable will assume is an essay in the mock-heroic.
The third strand of this ambitious and absorbing exhibition features four well-presented and accessible pieces of video art by four contemporary artists. Sadly one of them, Susan Miller, died between the shows's gestation and the actual opening. It is ironic indeed that her exhibit is called The Last Silent Movie. In it we hear snatches of dead and dying languages accompanied by sub-titled translations. This artist's dying word encompassing the dying words of other civilizations and tribes.
Perhaps more pertinent to the theme of collecting is Ed Atkins' Trick Brain. Atkins film takes us on a tour of André Breton's Paris apartment as it was when he died in 1966. A veritable cabinet of wonders, it was crammed with weird and wonderful artifacts with a noticeable bias towards the bizarre, the African and the surreal. Bretons's family wanted it preserved as a museum but the French government demurred and the collection was sold at auction and dispersed in 2003. Money trumps the common good in today's art world.
Turner Price winning artist Elizabeth Price's video A Restoration views with a jaundiced eye the "taxonomical recklessness" shown to artifacts recovered from Knossos on Crete by Sir Arthur Evans and his team during their excavations in the early 20th century. Collecting and preserving the past requires rigour and integrity – qualities that Evans appeared to lack.
The fourth video work by Taus Makhacheva tales us to a village in Dagestan where every resident is an expert tight-rope walker – a necessity more than a sport in a land of gorges and ravines. We see aerial maestros walk across a rope suspended over a gorge while carrying works of art. It's a metaphor with many applications: art as a precarious occupation and the difficulties of building a collection being the most obvious.
Curator of the show and Director of the Model Emer McGarry emphasizes that the collection is still a living one and acquisitions will continue where funds permit. "We definitely want to add works of museum quality". This year already it has acquired The Racecard Seller, a characterful early work by Jack B.Yeats, from the office of the Taoiseach. It's on loan for two years but history has taught us that works loaned to the Niland Collection tend to stick around – especially if they're by Yeats. And rightly so. They are at home. Yeats has said "From the beginning of my painting life every painting which I have made has somewhere in it a thought of Sligo".
www.themodel.ie
Cheltenham 2019 - Post Mortem
Cheltenham 2019 - Day 4 Thoghts
Cheltenham 2019 - Day 3 Thoughts
Last Ones Left Alive by Sarah Davis-Goff


boundary 2 (2016) 43 (1): 1-3.
Questions of value might seem beyond the pale in cases of sound and music. Both are objects of immense accumulation, appreciation, exploration, and investment—not just for the human species but also among other species, and indeed the world. Sound simply is, its existence is inexhaustible, and remarkable things happen in and through it—end of story. Why, then, the question of value? Divesting sound and music from naive notions of intrinsic value, the essays here examine heterogeneous modalities by which sound and music produce value in and as history, politics, and ontology. In turn, the very question of what sound and music are—of what constitutes them, as well as what they constitute—is precisely what is at stake.


The computer was important to shipping container design even in the 1950s at the beginning of the containerization revolution. In 1956 Matson Navigation Company, a shipper who dominated traffic between the west coast of the U.S. and Hawaii, used computers to analyze thousands of shipments. Matson concluded that the 20-25 foot container was optimal.
Another important feature of cargo container design were the heavy steel corner posts developed specifically to support stacking. Matson's freighters were specifically designed to handle six high stacks of shipping containers.
Matson turned computer power to analyzing the design of its cranes at Alameda and other ports and as a consequence improved load times to 400 tons per hour, which was 40 times the average manual load time from longshoremen. Cranes were specifically designed to meet the task of unloading standardized size containers loaded both in the holds and on the decks of Matson freighters.
The newly invented electric cranes traveled on rails placed on both sides of the ship so containers could be unloaded efficiently row by row. After the first row was removed, the practice of roll-on, roll-off occurred, with loading and unloading taking place simultaneously. Approximately every 3 minutes a crane would complete a cycle of rolling on, and rolling off containers.
Early shipping container design requirements dictated that freighters be outfitted with a structure of metal cells built to hold containers in place. They were 1 1/4 inches longer than the container, and ¾ inch wider and had cell guides that the crane operator had to ease the container in to. This was the design for the Ideal-X, the first container ship. The new design allowed for roll-on, roll-off loading and unloading, which is much more efficient than doing each in a separate process.
An important aspect of shipping container design, the locking device, greatly impacted trucks as well. The locking mechanism on the trucks used to haul containers from the Ideal-X and other container ships saved time because it meant that the truck could be loaded and leave immediately rather than taking up time and space at the port having the cargo chained down.
Ships also had to be redesigned to handle increasingly large loads of cargo. By 1969 ships specifically designed for the roll-on/roll-off cargo containers were carrying 1000 to 1200 20-foot (TEU) equivalents of containers on the North Atlantic routes and 1300 to 1600 TEU on the Asian routes. These new container ships were designed to go 50% or more faster than conventional freighters.
Shipping container design, and its impact on crane and freighter design, had come a long way by 1969 from its beginning in the mid-1950s.


text:
E-DVD WINNING CHESS THE EASY WAY - VOLUME 13 - Mastering The French - PART 3
Product Code: E-DVD0013SP
Hosted by: World Champion Grandmaster Susan Polgar
Running Time: Over 100 Minutes
On this 3 Part DVD series Susan Polgar will share with you her experiences, exciting battles, and won games from the first opening she ever learned at the early age of 4. Although the French can be complex, the main benefit is there are not many long and forceful lines compared to other openings.Susan will teach you the key to learning the French, to understand the pawn strategies, tactical motifs and basic plans.
So join Susan as well as some of the world's elite grandmasters such as Victor Korchnoi, Nigel Short and Alexander Morozevich in playing this fun and exciting opening defense.
This DVD covers:
Chapter 5: Steinitz variation 3.Nc3 Nf6 4.e5
Chapter 6: Classical variation 3.Nc3 Nf6 4.Bg5
Chapter 7: Winawer variation 3.Nc3 Bb4 sidelines on move 4
Chapter 8: 3.Nc3 Bb4 4.e5 b6
Chapter 9: 3.Nc3 Bb4 4.e5 c5 with 7.Qg4
Chapter 10: 3.Nc3 Bb4 4.e5 c5 with 7.Nf3
Chapter 11: Rubinstein variation 3.Nc3 dxe4
Chapter 12: Side Variations 2.d3, 2.b3 and 2.Qe2
Grandmaster Susan Polgar: 4-time Women's World Champion World's only Triple-Crown Winner (World Blitz, Rapid & Classical World Champion) 5-time Olympic Champion (5 Gold, 4 Silver, 1 Bronze) Currently Ranked #1 in the U.S. and the World 2003 Grandmaster of the Year and U.S. Open Blitz Champion Award Winning and Best Selling Author Founder of the Susan Polgar Foundation, a non-profit organization to promote chess for young people
In collaboration with FM Paul Truong:
11-time National Champion and Winner of over 120 tournaments in U.S., Asia and Europe Captain of the 2004 Historic U.S. Women's Olympiad Silver-Medalist Team Award Winning Chess Author and Trainer with 35 years experience
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You're reviewing: E-DVD WINNING CHESS THE EASY WAY - VOLUME 13 - Mastering The French - PART 3
GM Susan Polgar
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redpajama_set_name: RedPajamaCommonCrawl


Maternal and child health is a global priority. It refers to the period in women's life that involves pregnancy; Child Birth and postnatal care. It is integrally linked to the prenatal care of children. This being the period of gestation and the month after birth. Numerous treaties, initiatives and programmes have been formulated to try and improve the health and well being of pregnant women and children. The latest effort is that of the Millennium Development Goals that aim to inspire countries to drastically reduce maternal and child mortality and address. Specific diseases and relate challenges (United National Millennium Development 2015).
Balliere's Nurse Dictionary (1995) defines pregnancy as being with child, the condition from conception to the expulsion of the foetus. The normal period is 280 days or 40 weeks. During this period expectant mother care must be more intensified to be able to carry out necessary supervision care and advice to women during pregnancy, labour and post partum – this referred to anti-natal, which should be responsibilities to conduct deliveries and care of the new born and infants. This anti-natal includes preventive measures, early detection of abnormal condition in mother and child, and an advice on execution of emergency measures in the absence of medical help.
According to World Health Organization (WHO 2011), maternal and child health has been described as one of the foremost and the most neglected health problem, and human right abuse in the world, violating the right of about 515,000 women annually (Nyles, 2001). Whatever stage of development a country is, it is essential that the health policy of the country includes activities toward the care of mothers and children, especially during pregnancy and delivery in order to reduce the rate of maternal morbidity and mortality prevalent in women aged 15-49 years and children of all ages (WHO, 2011). The International Federation of Gynecologist and Obstetrician (EGO) define maternal health as one occurring during pregnancy, labour or as a consequence of pregnancy within 42 days after delivery or abortion.
According to United Nation Fund for Population Activities (UNFPA 2010), Nigeria maternal mortality situation has been indicated as one of the highest to the world. The most recent official document indicated a figure of 630 maternal deaths, per 100,000 live birth of 116/100,000 in contrast with developed countries. The health status of mother and children, remain poor in most developing countries. The same is true for South Africa despite its middle income status, local data shows an increase in infant, less than 5 mortality and material health status is also not optimal. South Africa adopted almost all international treaties, initiatives and programs concerted effort must therefore be made to rectify and address the contributing factors to poor maternal and child health care many of these lie outside of the health sectors. The health services have a significant contribution to make and at the very least health intervention with known effectiveness must be implemented in the best possible way. All sectors need to be held accountable for their role in improving maternal and child health (WHO, 2010). In general, health is scarce commodity that everybody strives to posses, it can be influenced by several factors and some of these factors are; Cultural factors which is defined as the way people live. This way of life include arrangement and method of obtaining food from the convenient and method of adapting it. It also includes rules and regulations that cover people's behavior in a particular society. It also include beliefs, religion, moral behavior and whatever the people concerned have produced using their available resource and knowledge, culture is something that has evolved overtime from 2 people's experience. Example custom of letting a woman to go back to her paternal home for child birth and remaining there until the baby is wearned. This is common practice in many rural Nigeria (PHCFMOH, 1990). Economic factor that can influence one's health is his education which leads to enlightenments, educated people are less likely to become controlled by various cultural beliefs, practice and taboos which tends to become detrimental to health, hence the higher educated the population, the higher health status. Poverty and ignorance is a prevalent problem in Nigerian community. Because all the above factors may result to ill health and other conditions like, malnutrition and anemia.
All pregnant women are expected to attend an approve health facility because care of the children begins from the first trimester of pregnancy. Statistical data has shown the rate of poor attendance in Kano Municipal Council from 2016 – 2017 as 2,625 registered for antenatal, but only 1085 women delivered (Health Department Monitoring Evaluation Unit, Kano Municipal Council of Kano State.
Nigeria is still passing through various stages of development, many women still deliver their babies at home, without attending Antenatal Clinic, while some pregnant mothers visit the clinic only for them to have the card and for emergency reason. Some of the women after registration do not attend the clinic, do not return to post-natal care, this is according to the record of those that registered.
All the concept of health is being on preventive rather than curative, health facilities are sited within communities so proximity is not a problem as to attend, yet the utilization among pregnant mothers is not encouraging. It is important therefore to help and motivate the pregnant mothers to utilize the government health services in the maternal and child health centers, effectively.
The trend in ante-natal clinic records in Kano Municipal Council, shows that it has been found that the number of pregnant mothers that were booked in ante-natal clinic was 1,320 from July – 2016 – July 2017, 120 pregnant women booked every week, 480 pregnant mothers per month. But recently from August 2016 – July 2017 the figure has declined from 480 – 400 every month and total population of 1,200 pregnant mothers were recorded. All this could be a promotive measure towards increasing both maternal and infant's mortality and morbidity rate.
The role of health workers in the management of pregnant mothers' is very important for ensuring that clients receive appropriate care from the state of conception, birth and post partum. Unfortunately today many women see health workers role differently being hostile, in confident, unnecessary delay, aggressive and not competent enough. The challenge now is what are responsible for the sudden poor attendance of pregnant mothers in ante-natal clinics. Based on the sudden change and attitude of pregnant mothers towards attending ANC, the researcher intend to find out strategies for improvement of utilization of ante-natal services in Kano Municipal Council of Kano State.
i. Ascertain the attitude of pregnant women toward health services.
ii. Identify the factors that hinder women of child bearing age from attending the maternal and child health services.
pregnant women in Kano Municipal Council of Kano State.
This study is intended to raise the awareness of pregnant mothers towards effective utilization of the government health services. Also with hope that local government concerned will be aware of the important of motivating the bearing mother to utilize maternal and child health service and for the authority to understand the problem that hinder clinic and utilize it so that maternal death will reduce and also increase chance of having good access and good utilization.
This study will also help the health workers working in the health facility to understand and realize their weakness and the strategies in rendering services that will improve the maternal and child health services thereby improving the chances of its utilization by women.
Findings of the study will help in reducing the mortality rate among pregnant women and improve the overall well being of women in the community thereby reducing resources and manpower wastages. Also when the study is completed, factors responsible for poor attendance of pregnant mothers' in the ante-natal clinics, the result will effect positive changes especially when it involves appropriate knowledge, skills, attitude, values and code of conduct of health workers. The result will serve as a significant tool to the clinician, the pregnant mother's and the management concerned.
i. What are the attitudes of pregnant mothers towards ante-natal health services?
mothers attending ante-natal clinic in Kano Municipal Council of Kano State?
iii. What are the strategies for improving the utilization of health services by pregnant mother's in Kano Municipal Council of Kano State?
The study seek to ascertain the attitude of pregnant women toward the utilization of health services in Kano Municipal Council, through identification of strategies for improving the utilization of services by pregnant mothers in the Local Government.


I have a passion for solving problems, and am deeply gratified when our solutions improve our clients' outcomes. Through almost 15 years as a management consultant, I have been exposed to a multitude of industries and continuously learned different approaches and methods to solving my clients' greatest challenges. I joined Spraoi to bring my flexible mindset together with Spraoi's technology capabilities to more efficiently create solutions for clients with greater impact – practical, insightful, and quick.Prior to joining Spraoi, I worked as a hedge fund analyst before embarking on the journey as a consultant at PwC and EY. While at Spraoi, I continue to provide advisory services in pursuit of new opportunities to improve the insurance industry.
Why Is Data Driven ML So Amazing?


text:
\section{Introduction}
\label{sec:Introduction}

 Matrix models naturally emerge in string theories, topological field theories and Yang-Mills theories \cite{MakeenkoGaugeMethods, Marino:04:1, Eguchi:82:1}. One of the most popular models which allows one to trace various relations between matrix models, string theories and gauge theories is the two-dimensional pure Yang-Mills theory, which can be interpreted either as a string theory \cite{Gross:93:1, Gross:93:2, Vafa:04} or as a matrix model \cite{Douglas:93:1, Minahan:93:1}.

 Perhaps the most direct way to arrive at the matrix model which describes two-dimensional Yang-Mills theory on the cylinder is to impose the gauge $A_{0} = 0$ and to consider the monodromy of the gauge field around the compactified spatial dimension \cite{Minahan:93:1}:
\begin{eqnarray}
\label{UnitaryMatrixFromYangMills}
W(t) = \mathcal{P} \exp{\left( i g_{YM}^{\:} \int \limits_{0}^{L} dx A_{1}(x,t) \right) }
\end{eqnarray}
where $L$ is the circumference of the compactified spatial dimension and $g_{YM}^{\:}$ is the coupling constant of the Yang-Mills theory. The Yang-Mills lagrangian can be then expressed in terms of $W(t)$ as \cite{Minahan:93:1}:
\begin{eqnarray}
\label{2DYMSphereMMLagrangian}
\mathcal{L} = \frac{1}{2} \int \limits_{0}^{L} dx  {\rm Tr} \:  F_{01}^{2} = - \frac{1}{2 g^{2}_{YM} L} \:  {\rm Tr} \:  \left( W^{-1} \dot{W} \right)^{2}
\end{eqnarray}
which is the lagrangian for the one-dimensional $c=1$ matrix model \cite{Douglas:93:1, Minahan:93:1}. In addition, (\ref{UnitaryMatrixFromYangMills}) implies the following constraints \cite{Minahan:93:1}:
\begin{eqnarray}
\label{2DYMTorusMMConstraint}
\left[W, \dot{W} \right] = 0
\end{eqnarray}
If the boundaries of the cylinder are situated at $t = t_{1}$ and $t = t_{2}$, the definition (\ref{UnitaryMatrixFromYangMills}) implies that $W(t_{1})$ and $W(t_{2})$ are the holonomies of the gauge field around these boundaries.

The constraints (\ref{2DYMTorusMMConstraint}) are first-class constraints for the lagrangian (\ref{2DYMSphereMMLagrangian}), therefore one can apply the usual quantization methods developed for systems with first-class constraints \cite{HenneauxQuantGauge}, such as implementing reduced phase space variables, introducing new second-class constraints or imposing BRST symmetry on the extended phase space complemented with ghost variables \cite{HenneauxQuantGauge}. The approach of  \cite{Douglas:93:1, Minahan:93:1} is exactly the reduced phase space approach. Fortunately, for the constraints (\ref{2DYMTorusMMConstraint}) the reduced phase space variables are simply the eigenvalues of the matrix $W$ and the reduced hamiltonian is explicitly known - the model is equivalent to $N$ free nonrelativistic fermions \cite{Douglas:93:1, Minahan:93:1} and can be investigated using the methods of conformal field theory.

 However, very often it is quite difficult to find the full set of reduced phase space variables. For instance, in the case of models with several matrix-valued variables it is impossible to transform all matrices to diagonal form simultaneously, and the methods developed in \cite{Douglas:93:1, Minahan:93:1} are not applicable. Furthermore, it is often desirable to preserve the covariance of the theory in terms of the original variables. For example, in the context of correspondence between string theories and matrix models, or for two-dimensional Yang-Mills theory, it could make the identification of stringy degrees of freedom easier \cite{Marino:04:1, MakeenkoGaugeMethods}. Preserving the group structure can be also advantageous if one wants to use finite-dimensional Lie groups as regularizations of infinite-dimensional groups such as the group of area-preserving diffeomorphisms $SDiff(\mathcal{M})$ arising in the description of relativistic membranes in the light-cone gauge \cite{Pope:90:1, Hoppe:88}. In these cases BRST quantization is more suitable.

The aim of this paper is to perform BRST quantization of the matrix model (\ref{2DYMSphereMMLagrangian}) with the constraints (\ref{2DYMTorusMMConstraint}). In order to make the analysis as general as possible the gauge group will not be specified and the coordinates on the group manifold will not be fixed. Only local features of the group geometry will be considered. Hopefully such general analysis can be extended to the models with several matrix-valued variables and to infinite-dimensional groups relevant in string theories.

The structure of this paper is the following: in the section \ref{sec:Geometry} the basic concepts of classical and quantum mechanics on the group manifold are reviewed and the constraints (\ref{2DYMTorusMMConstraint}) are shown to be first-class and reducible. Hamiltonian formalism is used, as the BRST construction is inherent to canonical quantization \cite{HenneauxQuantGauge}. Classical and quantum BRST generators for the constraints (\ref{2DYMTorusMMConstraint}) and BRST-invariant hamiltonians are constructed in the sections \ref{sec:ClassicalBRST} and \ref{sec:QuantumBRST} respectively. BRST path integral for the lagrangian (\ref{2DYMSphereMMLagrangian}) is considered in the section \ref{sec:PathInt}. Some technical details such as explicit expressions for the geometric constructions used throughout the paper are relegated to the appendices.

\section{Classical and quantum mechanics on the group manifold}
\label{sec:Geometry}

 In this section classical and quantum mechanics on the group manifold are briefly reviewed. Group generators in the fundamental representation are denoted as $T_{a}$. The structure constants $C^{c}_{ab}$ and the metrics $c_{a b}$ of the Lie algebra are fixed by the relations:
\begin{eqnarray}
\label{LieAlgebraProperties}
 {\rm Tr} \:  \left( T_{a} T_{b} \right) = c_{a b}, \quad
[T_{a}, T_{b}] = i C^{c}_{ab} T_{c}
\end{eqnarray}

  Suppose that group elements are parametrized by some coordinates $x^{\alpha}$. From now on latin indices $a, b, c, \ldots$ will be used to denote the elements of the Lie algebra and the first greek indices $\alpha, \beta, \ldots$ for tensors on the group manifold. Left and right actions of the group generators $T_{a}$ define the left- and right-invariant vector fields $L^{\alpha}_{a}(x)$ and $R^{\alpha}_{a}(x)$ \cite{DeWittGroupsAndFields}:
\begin{eqnarray}
\label{LeftRightVectorFields}
L^{\alpha}_{a} \partial_{\alpha} W(x) = i T_{a} W(x), \quad  R^{\alpha}_{a} \partial_{\alpha} W(x) = i W(x) T_{a}
\end{eqnarray}
where $W(x)$ are the matrices of the fundamental representation of the group. The difference of the vector fields $L^{\alpha}_{a}$ and $R^{\alpha}_{a}$, which will be denoted as $Q^{\alpha}_{a} = L^{\alpha}_{a} - R^{\alpha}_{a}$, generates shifts within group classes:
\begin{eqnarray}
\label{ClassVectorFields}
Q^{\alpha}_{a} \partial_{\alpha} W(x) = i \left[ T_{a}, W(x) \right]
\end{eqnarray}
It is important to note that while the vector fields $L_{a}^{\alpha}$ and $R_{a}^{\alpha}$ build complete bases in each point, the vector fields $Q^{\alpha}_{a}$ are not all independent locally, but build an overfull basis in the tangent space to the group classes, which means that there exist such functions $u^{a}_{k}$ that $u^{a}_{k} Q_{a}^{\alpha} = 0$. One can show that this condition is equivalent to the orthogonality of the vector fields $u_{k}^{\alpha} = u^{a}_{k} L_{a}^{\alpha}$ and $Q^{\alpha}_{a}$: $g_{\alpha \beta} Q_{a}^{\alpha} u^{\beta}_{k} = 0$. It will be assumed that $u_{k}^{a}$ are linearly independent reducibility conditions, therefore vector fields $u_{k}^{\alpha}$ and $Q_{a}^{\alpha}$ together build an overfull basis in the tangent space at each point of the group manifold.

It is also convenient to introduce the left- and right- invariant 1-forms $L_{\alpha}^{a}$ and $R_{\alpha}^{a}$, defined as inverse to the vector fields $L^{\alpha}_{a}$ and $R^{\alpha}_{a}$ respectively:
\begin{eqnarray}
\label{LRFormsDef}
L_{\alpha}^{a} L^{\beta}_{a} = \delta_{\alpha}^{\beta}, \quad R_{\alpha}^{a} R^{\beta}_{a} = \delta_{\alpha}^{\beta}
\end{eqnarray}
These 1-forms take especially simple form in matrix notation:
\begin{eqnarray}
\label{LRFormsMatrix}
L_{\alpha} = L_{\alpha}^{a} T_{a} =  - i \partial_{\alpha} W W^{-1}, \nonumber \\
R_{\alpha} = R_{\alpha}^{a} T_{a} = - i W^{-1} \partial_{\alpha} W
\end{eqnarray}

The lagrangian (\ref{2DYMSphereMMLagrangian}) can now be rewritten in terms of the group metric (Killing form) $g_{\alpha \beta} = c_{ab} L^{a}_{\alpha} L^{b}_{\beta} = c_{ab} R^{a}_{\alpha} R^{b}_{\beta} =  {\rm Tr} \:  \left( L_{\alpha} L_{\beta} \right) =  {\rm Tr} \:  \left( R_{\alpha} R_{\beta} \right)$ as:
\begin{eqnarray}
\label{2DYMSphereMMLagrangianGeo}
\mathcal{L} = \frac{1}{2 g^{2}_{YM} L} \: g_{\alpha \beta} \dot{x}^{\alpha} \dot{x}^{\beta}
\end{eqnarray}
while the constraints (\ref{2DYMTorusMMConstraint}) can be written as $Q^{a}_{\alpha} \dot{x}^{\alpha} = 0$.

In hamiltonian formalism the transformations (\ref{LeftRightVectorFields}) and (\ref{ClassVectorFields}) are generated by the functions $L_{a} = L_{a}^{\alpha} p_{\alpha}$, $R_{a} = R_{a}^{\alpha} p_{\alpha}$ and $Q_{a} = L_{a} - R_{a}$, where $p_{\alpha}$ are the momenta canonically conjugate to $x^{\alpha}$: $\{ x^{\alpha}, p_{\beta}  \} = \delta^{\alpha}_{\beta}$. The algebra of these functions is the Lie algebra of the group:
\begin{eqnarray}
\label{CommutationRelationsClassic}
\{ L_{a}, L_{b} \} = - C^{c}_{a b} L_{c}, \quad \{ R_{a}, R_{b} \} = C^{c}_{a b} R_{c}  \nonumber \\
\{ L_{a}, R_{b} \} = 0, \quad \{ Q_{a}, Q_{b} \} = - C^{c}_{a b} Q_{c}
\end{eqnarray}

The hamiltonian corresponding to (\ref{2DYMSphereMMLagrangian}) and (\ref{2DYMSphereMMLagrangianGeo}) is:
\begin{eqnarray}
\label{InvariantHamiltonianClassic}
H_{0} = \frac{g^{2}_{YM} L}{2} \: c^{ab} L_{a} L_{b} = \nonumber \\ =
 \frac{g^{2}_{YM} L}{2} \: c^{ab} R_{a} R_{b} = \frac{g^{2}_{YM} L}{2} \: g^{\alpha \beta} p_{\alpha} p_{\beta}
\end{eqnarray}
while the constraints (\ref{2DYMTorusMMConstraint}) are simply $Q_{a} = 0$. As $Q_{a}$ are the integrals of motion for the hamiltonian (\ref{InvariantHamiltonianClassic}) and build the closed algebra (\ref{CommutationRelationsClassic}), the constraints (\ref{2DYMTorusMMConstraint}) are indeed first-class.

In quantum mechanics the counterparts of the classical functions $L_{a}$, $R_{a}$ and $Q_{a}$ are the differential operators $\hat{L}_{a} = - i L_{a}^{\alpha} \partial_{\alpha}$, $\hat{R}_{a} =  - i R_{a}^{\alpha} \partial_{\alpha}$ and $\hat{Q}_{a} = \hat{L}_{a} - \hat{R}_{a}$, which also build a representation of the Lie algebra (\ref{LieAlgebraProperties}):
\begin{eqnarray}
\label{CommutationRelationsQuantum}
\left[ \hat{L}_{a}, \hat{L}_{b} \right] = - i C^{c}_{a b} \hat{L}_{c}, \quad \left[ \hat{R}_{a}, \hat{R}_{b} \right] = i C^{c}_{a b} \hat{R}_{c} \nonumber \\
\left[ \hat{L}_{a}, \hat{R}_{b} \right] = 0, \quad \left[ \hat{Q}_{a}, \hat{Q}_{b} \right] = - i C^{c}_{a b} \hat{Q}_{c}
\end{eqnarray}

Quantum counterpart of $H_{0}$ is proportional to the Laplace operator on the group, or the second-order Casimir operator on the space of differentiable functions on the group manifold:
\begin{eqnarray}
\label{InvariantHamiltonianQuantum}
\hat{H}_{0} = \frac{g^{2}_{YM} L}{2}  \hat{L}_{a} \hat{L}_{a} = \nonumber \\ =
- \frac{g^{2}_{YM} L}{2} \:  \sqrt{g^{-1}} \partial_{\alpha} \left( \sqrt{g} g^{\alpha \beta} \partial_{\beta} \right) \quad
\end{eqnarray}
where $g = {\rm det} \: (g_{\alpha \beta})$. In the case of compact groups eigenvalues of $\hat{H}_{0}$ are proportional to the eigenvalues of quadratic Casimir operators of irreducible unitary representations of the group and the corresponding eigenfunctions are the matrices of these representations \cite{HoweTanNonAbelianHarmonicAnalysis}. For the sake of brevity from now the factor $\frac{g^{2}_{YM} L}{2}$ in front of the hamiltonian will be omitted.

\section{Classical BRST generator and BRST-invariant hamiltonian}
\label{sec:ClassicalBRST}

The constraints $Q_{a} = 0$ on the original phase space can be replaced by the requirement of invariance under BRST transformation generated by the BRST generator $\Omega$ on the extended phase space complemented with ghost variables \cite{HenneauxQuantGauge}. In order to do this, two generations of ghosts should be introduced: fermionic ghosts $X^{a}$ and the conjugate ghost momenta $\Pi_{a}$ which correspond to the constraints $Q_{a} = 0$, and bosonic "ghosts of ghosts" $\chi^{k}$ and the conjugate momenta $\pi_{k}$ which are associated with the  reducibility conditions $u^{a}_{k} Q_{a} = 0$ \cite{Henneaux:93, HenneauxQuantGauge}. Ghost numbers of these variables are \cite{HenneauxQuantGauge}:
\begin{eqnarray}
\label{GhostNumbers}
 {\rm gh} \:  X^{a} = 1, \: \:  {\rm gh} \:  \Pi_{a} = -1, \: \:   {\rm gh} \:  \chi^{k} = 2, \: \:  {\rm gh} \:  \pi_{k} = - 2
\end{eqnarray}

Any BRST generator should be nilpotent, i.e. $\{ \Omega, \Omega \} = 0$, and be of ghost number one. In order to define a proper BRST cohomology, BRST generator should have the form $\Omega = X^{a} Q_{a} + \chi^{k} u_{k}^{a} \Pi_{a} + \: (more)$, where $(more)$ contains higher-order ghost terms \cite{HenneauxQuantGauge}. The first guess is to combine this expression with the simplest possible expression for reducible first-class constraints which build a closed algebra \cite{HenneauxQuantGauge, Henneaux:93}:
\begin{eqnarray}
\label{BRSTChargeClassic}
\Omega = X^{a} Q_{a} + \chi^{k} u_{k}^{a} \Pi_{a} - 1/2 \: C^{c}_{a b} X^{a} X^{b} \Pi_{c}
\end{eqnarray}
The nilpotency condition reads explicitly:
\begin{eqnarray}
\label{Nilpotency}
1/2 \{ \Omega, \Omega \} = \frac{\partial \Omega}{\partial x^{\alpha}} \: \frac{\partial \Omega}{\partial p_{\alpha}} +
\frac{\partial \Omega}{\partial \chi^{k}} \: \frac{\partial \Omega}{\partial \pi_{k}} -
\frac{\partial^{L} \Omega}{\partial X^{a}} \: \frac{\partial^{L} \Omega}{\partial \Pi_{a}} = \nonumber \\ =
\chi^{k} \Pi_{a} X^{b} \left( \{u^{a}_{k}, Q_{b} \} - C^{a}_{f b} u^{f}_{k} \right) = 0 \quad
\end{eqnarray}
Thus the BRST generator of the form (\ref{BRSTChargeClassic}) is nilpotent iff $\{u^{a}_{k}, Q_{b} \} - C^{a}_{f b} u^{f}_{k} = 0$. This equation can be formulated as the commutativity of the vector fields $u_{k} = u^{a}_{k} L_{a}$ and $Q_{a}$:
\begin{eqnarray}
\label{NilpotencyCondition}
\{Q_{a}, u_{k} \} = 0
\end{eqnarray}

It follows from (\ref{Nilpotency}) that $u^{a}_{k}$ span the Cartan subspace of the Lie algebra (however, different Cartan subspace in each point), since $u^{a}_{k} u^{b}_{l} C_{a b}^{c} = 0$. The vector fields $u^{\alpha}_{k}$ which satisfy the commutation relations (\ref{NilpotencyCondition}) are explicitly constructed for $SU(N)$ group in Appendix \ref{sec:SUNPolar}. This construction can be easily generalized for an arbitrary Lie group.

A function $F$ on the extended phase space is called BRST-closed if $\{ \Omega, F \} = 0$ and BRST-exact if it is equal to the Poisson brackets of some other function with $\Omega$: $F = \{ \Omega, G \}$. Nilpotent BRST generator defines the BRST cohomology on the space of functions on the extended phase space, with cohomological classes consisting of BRST-closed functions modulo BRST-exact functions \cite{HenneauxQuantGauge}. A proper BRST-generator is defined in such a way that the only nontrivial cohomological class contains gauge-invariant functions. The hamiltonian $H_{0}$ is a gauge-invariant function on the original phase space, but not necessarily on the extended phase space, as in general $\{\Omega, H_{0} \} \neq 0$. In order to construct an invariant hamiltonian on the extended phase space, one should add to $H_{0}$ some terms which contain ghost variables. A proper BRST-invariant extension $H$ of the hamiltonian $H_{0}$ should have ghost number zero and even grassman parity, be BRST-closed and be equal to $H_{0}$ if all ghost variables are set to zero. The ghost number zero  and grassman parity conditions are restrictive enough to eliminate many possible ghost terms. The first nontrivial extension of $H_{0}$ with the maximal antighost number $2$ is:
\begin{eqnarray}
\label{BRSTHamiltonianClassic}
H = H_{0} + \chi^{k} h^{a b}_{k} \Pi_{a} \Pi_{b}
\end{eqnarray}
where $h^{a b}_{k}$ is antisymmetric in $a$ and $b$ and depends only on $x^{\alpha}$. Poisson brackets of the hamiltonian $H$ and the BRST generator (\ref{BRSTChargeClassic}) are:
\begin{eqnarray}
\label{OmegaHPoissonBrackets}
\{ \Omega, H \} =
\{\Omega, H  \}_{pq} + \{ \Omega, H \}_{\pi \chi} - \nonumber \\
 - \frac{\partial^{L} H}{\partial \Pi_{a}} \: \frac{\partial^{L} \Omega}{\partial X^{a}}
 - \frac{\partial^{L} H}{\partial X^{a}} \: \frac{\partial^{L} \Omega}{\partial \Pi_{a}} = \nonumber \\ =
\chi^{k} \Pi_{a} \left( \{ u^{a}_{k},H_{0} \} - 2 h^{b a}_{k} Q_{b} \right) + \nonumber \\ +
\chi^{k} \Pi_{a} \Pi_{b} X^{c} \left( \{Q_{c}, h^{a b}_{k}\} - 2 h^{d a}_{k} C^{b}_{d c}  \right)
\end{eqnarray}
where $\{ \Omega , H \}_{pq}$ and $\{ \Omega , H \}_{\pi \chi}$ are Poisson brackets w.r.t. the variables $\left( x^{\alpha}, \: p_{\alpha} \right)$ and $\left( \chi^{k}, \: \pi_{k} \right)$. Thus the hamiltonian $H$ is BRST closed iff the following equations hold:
\begin{eqnarray}
\label{ClosednessCondition}
\{u^{a}_{k}, H_{0} \} + 2 h^{a b}_{k} Q_{b} = 0 \nonumber \\
\{Q_{c}, h^{a b}_{k} \} - h^{d [ a}_{k} C^{b ]}_{d c} = 0
\end{eqnarray}

These equations are solved in Appendix \ref{sec:ClosednessSolution}. It turns out that the solution is most conveniently represented in terms of the 2-form $h_{k \: \alpha \beta} = h^{a b}_{k} Q_{a \: \alpha} Q_{b \: \beta}$:
\begin{equation}
\label{ClosednessSolution}
h_{k} = -1/2 \: u^{a}_{k} \: d Q_{a}, \: \:
h_{k \: \alpha \beta} = - i  {\rm Tr} \:  \left( u_{k} \left[ L_{\alpha}, L_{\beta} \right] \right)
\end{equation}
where $d Q_{a}$ is the external derivative of the 1-form $Q_{a \: \alpha} = g_{\alpha \beta} Q^{\beta}_{a}$ and $u_{k} = u^{a}_{k} T_{a}$. If $S^{b \: \beta}$ are such vector fields that $Q_{a \: \alpha} S^{b \: \alpha} = P^{a}_{b}$, where $P^{a}_{b}$ is the projective operator which projects on the subspace in Lie algebra spanned on $Q_{a}^{\alpha}$, than $h_{k}^{a b}$ can be obtained as:
\begin{eqnarray}
\label{ClosednessSolution1}
h_{k}^{a b} = h_{k \: \alpha \beta} S^{a \: \alpha} S^{b \: \beta}
\end{eqnarray}
The vector fields $S^{a \: \alpha}$ are explicitly constructed for $SU(N)$ group in the Appendix \ref{sec:SUNPolar}. Thus the BRST-invariant extension of the hamiltonian $H_{0}$ has been constructed.

It is also interesting to note that the first equation in (\ref{ClosednessCondition}) implies the commutativity of the vector fields $u^{\alpha}_{k}$:
\begin{equation}
\label{uCommutation}
\{u_{k}, u_{l} \} = 0
\end{equation}

The BRST-invariant hamiltonian (\ref{BRSTHamiltonianClassic}) is still quadratic in the momenta and thus can be thought of as a free hamiltonian on a supermanifold with coordinates $x^{\alpha}, X^{a}, \chi^{k}$.

\section{Quantum BRST generator and BRST-invariant hamiltonian}
\label{sec:QuantumBRST}

There are several methods to quantize theories with first-class constraints: quantization on the reduced phase space, Dirac quantization and BRST quantization. Reduced phase space quantization amounts to eliminating all nondynamical coordinates and dealing only with dynamical ones. For the matrix model (\ref{2DYMSphereMMLagrangian}) with the constraints (\ref{2DYMTorusMMConstraint}) the reduced Hilbert space is equivalent to the Hilbert space of $N$ nonrelativistic free fermions \cite{Minahan:93:1, Douglas:93:1}. In the Dirac quantization method the constraints are imposed on the states of the Hilbert space of the unconstrained system:
\begin{eqnarray}
\label{ConstraintQuantum}
\hat{Q}_{a} | \phi \rangle = 0
\end{eqnarray}
The constraints (\ref{ConstraintQuantum}) are also first-class quantum-mechanically, as $[\hat{Q}_{a}, \hat{H}_{0}] = 0$ and $\hat{Q}_{a}$ build the algebra (\ref{CommutationRelationsQuantum}).

The Hilbert space of the unconstrained system (\ref{2DYMSphereMMLagrangian}) is the space of functions on the group manifold. In this paper wave functions in the Schr\"{o}dinger representation are assumed to be scalar functions (not 1/2-densities, as was suggested in the work \cite{Henneaux:93} and also implicitly assumed in the works \cite{Minahan:93:1, Douglas:93:1}). When the group is simple and the equation (\ref{NilpotencyCondition}) holds for the constraints and reducibility conditions, scalar wave functions differ from those of \cite{Henneaux:93} just by the factor $\sqrt{g}$. In the case of compact groups the matrices of irreducible unitary representations build an orthonormal basis in the space of functions on the group manifold \cite{HoweTanNonAbelianHarmonicAnalysis}. The constraints $\hat{Q}_{a} | \phi \rangle = 0$ select the subspace of functions on the group classes. Group characters build an orthonormal basis in this subspace \cite{HoweTanNonAbelianHarmonicAnalysis}.

In the BRST quantization method the constraints $\hat{Q}_{a} | \phi \rangle = 0$ are replaced by a single constraint $\hat{\Omega} | \Phi \rangle = 0$ on the extended Hilbert space complemented with ghost states, where $\hat{\Omega}$ is the quantum counterpart of the classical BRST generator \cite{HenneauxQuantGauge, Henneaux:93, Henneaux:94}. In this paper the Schr\"{o}dinger representation will be used, where wave functions depend on the original variables $x^{\alpha}$ as well as on the ghost variables $\chi^{k}$ and $X^{a}$. The ghost momenta operators are $\hat{\Pi}_{a} = -i \frac{\partial^{L}}{\partial X^{a}}$ and $\hat{\pi}_{k} = - i \frac{\partial}{\partial \chi^{k}}$. Any quantum BRST generator $\hat{\Omega}$ should be nilpotent, self-conjugate and of ghost number one. As $\hat{\Omega}$ is nilpotent, one can define the quantum BRST cohomology as the quotient space of BRST-closed states modulo BRST-exact states. For a properly constructed BRST generator the only nontrivial cohomological class contains physical states. The results of \cite{HenneauxQuantGauge, Henneaux:93, Henneaux:94} imply that for the hamiltonian (\ref{InvariantHamiltonianQuantum}) the proper quantum BRST generator for the constraints (\ref{ConstraintQuantum}) and the corresponding BRST-invariant hamiltonian can be directly obtained from the classical expressions (\ref{BRSTChargeClassic}) and (\ref{BRSTHamiltonianClassic}):
\begin{eqnarray}
\label{BRSTChargeQuantum}
\hat{\Omega} = \hat{X}^{a} \hat{Q}_{a} + \hat{\chi}^{k} u_{k}^{a} \hat{\Pi}_{a} - 1/2 \: C^{c}_{a b} \hat{X}^{a} \hat{X}^{b} \hat{\Pi}_{c}
\end{eqnarray}
\begin{eqnarray}
\label{BRSTHamiltonianQuantum}
\hat{H} = \hat{H}_{0} + \hat{\chi}^{k} h^{a b}_{k} \hat{\Pi}_{a} \hat{\Pi}_{b}
\end{eqnarray}
No operator-ordering ambiguities arise for such BRST generator and BRST-invariant hamiltonian in the case of simple groups.

\section{BRST path integral}
\label{sec:PathInt}

In this section the BRST path integral representation for the evolution operator of the model (\ref{2DYMSphereMMLagrangian}) with the constraint (\ref{2DYMTorusMMConstraint}) will be constructed. In terms of two-dimensional Yang-Mills theory on the cylinder this evolution operator is the Wick-rotated partition function.

In the Dirac quantization method the constraints (\ref{ConstraintQuantum}) select the subspace of singlet states. Therefore the kernel of the evolution operator of the constrained matrix model (\ref{2DYMSphereMMLagrangian}) can be written as (the factor $\left( 2 g^{2}_{YM} L \right)$ in front of the hamiltonian is again omitted for the sake of brevity) \cite{Minahan:93:1, Douglas:93:1}:
\begin{eqnarray}
\label{EvolutionOperator}
U \left( W(t_{1}), W(t_{2}) \right) = \nonumber \\ =
\sum \limits_{R} \bar{\chi}_{R} \left(W(t_{2}) \right) \chi_{R} \left(W(t_{1}) \right)
\exp{\left( - i (t_{2} - t_{1}) C_{2 \: R} \right)} = \nonumber \\ =
\langle W(t_{2}) | \hat{P}_{s} \exp{\left( - i \hat{H}_{0} (t_{2} - t_{1}) \right)} \hat{P}_{s} | W(t_{1})  \rangle \quad
\end{eqnarray}
where $\chi_{R}$ and $C_{2 \: R}$ are the group characters and the second-order Casimir in the representation $R$ and the operator $\hat{P}_{s}$ projects on the subspace of functions on the group classes. The same kernel can be written as the so-called projected kernel in the Dirac quantization procedure \cite{HenneauxQuantGauge}, which is obtained by inserting the operator version of the gauge-fixing conditions between bras and kets of the initial and final physical states \cite{HenneauxQuantGauge}. In the Schr\"{o}dinger representation this amounts to eliminating the volume of the gauge orbits from the integrals over configuration space of the system. However, in order to recover the partition function (\ref{EvolutionOperator}) from the projected kernel one should use the scalar product in the Hilbert space of the unconstrained system, i.e. $\langle \phi_{1} | \phi_{2} \rangle = \int d^{n} x \sqrt{g} \: \bar{\phi}_{1} \phi_{2}$, where $d^{n} x \sqrt{g}$  is the invariant measure on the group manifold and $n$ is the dimensionality of the group. Group characters are orthonormal w.r.t. this scalar product, and therefore all the states will be counted with the same weight and the expression (\ref{EvolutionOperator}) will be reproduced.

In order to establish a mathematically precise connection between the projected kernel and the kernel of the BRST-invariant extension of the operator, the phase space should be further enlarged by the variables of the so-called nonminimal sector \cite{HenneauxQuantGauge, Henneaux:93, Henneaux:94}. These variables are the lagrange multipliers $\lambda^{s \: a_{s}}_{k}$ and the conjugate momenta $b^{k}_{s \: a_{s}}$ as well as the ghosts $C^{s}_{k \: a _{s}}$ and ghost momenta $\rho^{k \: a_{s}}_{s}$ which correspond to the first-class constraints $b^{k}_{s \: a_{s}} = 0$, where $0 \le k \le 1$, $k \le s \le 1$ \cite{Henneaux:94}. The indices $a_{0}, \: b_{0}, \: c_{0}, \: \ldots$ with subscript zero are equivalent to the latin indices $a,\: b,\: c$ and the indices $a_{1}, \: b_{1}, \: c_{1}$ are equivalent to the indices $k, \: l, \: m, \: \ldots$ labelling reducibility conditions. Poisson brackets of the variables of the nonminimal sector are \cite{Henneaux:94}:
\begin{eqnarray}
\label{NonminimalCommutators}
\{ b^{k'}_{s' \: b_{s'}}, \lambda^{s \: a_{s}}_{k}  \} = \{ \rho^{k' \: a_{s}}_{s}, C^{s'}_{k \: b_{s'}} \} = - \delta^{k'}_{k} \delta^{s}_{s'} \delta^{a_{s}}_{b_{s'}}
\end{eqnarray}
Grassman parities and ghost numbers of the variables of the nonminimal sector are \cite{Henneaux:94}:
\begin{eqnarray}
\label{NonminimalGhostNumbers}
\e{b^{k}_{s \: a_{s}}} = \e{\lambda^{s \: a_{s}}_{k}} = s - k \mod 2 \nonumber \\
\e{\rho^{k \: a_{s}}_{s}} = \e{C^{s}_{k \: a_{s}}} = s - k + 1 \mod 2 \nonumber \\
 {\rm gh} \:  b^{k}_{s \: a_{s}} = -  {\rm gh} \:  \lambda^{s \: a_{s}}_{k} = k - s \nonumber \\
 {\rm gh} \:  \rho^{k \: a_{s}}_{s} = -  {\rm gh} \:  C^{s}_{k \: a_{s}} = s - k + 1
\end{eqnarray}
The variables of the nonminimal sector should be also included in the quantum and classical BRST generators (\ref{BRSTChargeQuantum}) and (\ref{BRSTChargeClassic}). Additional terms which should be added to (\ref{BRSTChargeQuantum}) and (\ref{BRSTChargeClassic}) have the following form \cite{Henneaux:94}:
\begin{eqnarray}
\label{BRSTChargeNonminimal}
\hat{\Omega}_{nonmin} = \sum \limits_{k = 0}^{1} \sum \limits_{s = k}^{1} \hat{b}^{k}_{s \: a_{s}} \hat{\rho}^{k \: a_{s}}_{s}
\end{eqnarray}

It was proven in \cite{Henneaux:94, HenneauxQuantGauge} that the projected kernel of a gauge-invariant operator on the Hilbert space of the unconstrained system is equal to the kernel of the BRST-invariant extension of this operator with suitable ghost states and a suitable gauge-fixing fermion $\hat{K}$. As the evolution operator is a gauge-invariant operator, the projected kernel $U \left( W(t_{1}), W(t_{2}) \right)$ can be expressed in terms of the BRST-invariant extension (\ref{BRSTHamiltonianQuantum}) of the hamiltonian $\hat{H}_{0}$:
\begin{widetext}
\begin{eqnarray}
\label{ProjectedKernelAndBRST}
U \left( W(t_{1}), W(t_{2}) \right) =
 \langle W(t_{2}) | \hat{P}_{s}
 \exp{\left( - i \hat{H}_{0} (t_{2} - t_{1}) \right)}
 \hat{P}_{s} | W(t_{1}) \rangle
 = \nonumber \\ =
\langle W(t_{2}) | \langle ghosts | \hat{P}_{s}
 \exp{\left( - i \left( \hat{H} - [\hat{K}, \hat{\Omega}] \right) (t_{2} - t_{1}) \right)}
 \hat{P}_{s} | W(t_{1}) \rangle | ghosts \rangle
\end{eqnarray}
\end{widetext}
The states $| W \rangle$ are the eigenstates of the coordinate operator and are normalized to the delta-function on the group manifold. In order to get rid of the projection operators $\hat{P}_{s}$ one should consider the states $| \tilde{W} \rangle = \int dV \: | V W V^{-1} \rangle $ smeared over the gauge orbits, i.e. over the group classes. Ghost states, denoted as $|ghosts \rangle$ in (\ref{ProjectedKernelAndBRST}), are the eigenstates of ghost variables with zero eigenvalues \cite{HenneauxQuantGauge, Henneaux:94}:
\begin{eqnarray}
\label{GhostBoundaryConditions}
\hat{X}^{a} | ghosts \rangle = 0, \quad \hat{\chi}^{k} | ghosts \rangle = 0 \nonumber \\
\hat{b}^{k}_{s \: a_{s}} | ghosts \rangle = 0, \quad \hat{C}^{s}_{k \: a_{s}} | ghosts \rangle = 0, \: k \: even \nonumber \\
\hat{\lambda}^{s \: a_{s}}_{k} | ghosts \rangle = 0, \quad \hat{\rho}^{k \: a_{s}}_{s} | ghosts \rangle = 0, \: k \: odd
\end{eqnarray}

The gauge-fixing  fermion $\hat{K}$ in (\ref{ProjectedKernelAndBRST}) regularizes the products of physical states and mixes the variables of the minimal and nonminimal sectors, the former property being important for the existence of BRST cohomology at ghost number zero. A careful examination of the proof of the theorem 14.9 in \cite{HenneauxQuantGauge} leads to the conclusion that the additional terms to be included in BRST extensions of the kernels of gauge-invariant operators are:
\begin{eqnarray}
\label{GFFermion}
\exp{\left( i\left[ \hat{K}, \hat{\Omega} \right] \right)} = \exp{ \left( i \hat{\lambda}^{0 a}_{0} \hat{Q}_{a} + i \hat{\Pi}_{a} \hat{\rho}^{0 a}_{0}  - i \hat{\pi}_{k} \hat{\rho}^{0 k}_{1} \right) }
\end{eqnarray}

Following the proof of the theorem 3 in \cite{Henneaux:94} and using the standard time slicing procedure one can express the projected kernel of the evolution operator (\ref{EvolutionOperator}) in terms of the path integral:
\begin{widetext}
\begin{eqnarray}
\label{EvolutionOperatorPathIntBRST}
U( W(t_{1}), W(t_{2}) ) = \int \limits_{W(t_{1})}^{W(t_{2})} \mathcal{D} x^{A} \mathcal{D} p_{A}
\: \exp{ \left( i \int \limits_{t_{1}}^{t_{2}} d t \left( p_{A} \dot{x}^{A}  - H  +  \lambda^{0 a}_{0} Q_{a} + \Pi_{a} \rho^{0 a}_{0}  - \pi_{k} \rho^{0 k}_{1} \right)
\right)}
\end{eqnarray}
\end{widetext}
where $x^{A}$ denotes all coordinates, including ghosts and the nonminimal sector, and $p_{A}$ all conjugate momenta. Boundary conditions for the ghost variables and for the variables of the nonminmal sector are given by (\ref{GhostBoundaryConditions}).

The momenta variables can be integrated out in order to see how the lagrangian (\ref{2DYMSphereMMLagrangian}) is modified, however, after that the explicit BRST symmetry is lost. It is also more convenient to integrate out the ghost variables $X^{a}$ and to keep the ghost momenta $\Pi_{a}$, which yields:
\begin{widetext}
\begin{eqnarray}
\label{EvolutionOperatorPathIntBRST1}
U( W(t_{1}), W(t_{2}) ) = \int \limits_{W(t_{1})}^{W(t_{2})}
\mathcal{D} W(t) \: \mathcal{D} \Pi(t) \: \mathcal{D} \chi(t) \: \mathcal{D} (nonminimal) \: \nonumber \\
\delta \left(\dot{\Pi} \right) \delta \left(\dot{\lambda}^{0 a}_{0} \right)
\delta \left(\dot{\chi}^{k} - \rho^{0 k}_{1} \right) \delta \left(\dot{\rho}^{0 a}_{0} \right)
\delta \left(\dot{\rho}^{0 k}_{1} \right)
\nonumber \\
\exp{ \left( -i \int \limits_{t_{1}}^{t_{2}} d t \left( \frac{1}{2 g^{2}_{YM} L} \:
 {\rm Tr} \:  \left(W^{-1} \dot{W} + \lambda \right)^{2} + \frac{g^{2}_{YM} L}{2} \: \chi^{k} h_{k}^{a b} \Pi_{a} \Pi_{b} -  \frac{g^{2}_{YM} L}{2} \: \Pi_{a} \rho^{0 a}_{0}
\right)
\right)}
\end{eqnarray}
\end{widetext}
where $\lambda = \lambda^{0 a}_{0} Q_{a}^{\alpha} L_{\alpha}$ is the matrix-valued lagrange multiplier and the factors $\frac{g^{2}_{YM} L}{2}$ were restored again. The constraints $\dot{\Pi}=0$, $\dot{\lambda}^{0 a}_{0}=0$, $\dot{\chi}^{k} = \rho^{0 k}_{1}$, $\dot{\rho}^{0 a}_{0}=0$, $\dot{\rho}^{0 k}_{1}=0$ imply that the only variable which depends on time is $W(t)$, while for all other variables the path integral reduces to the ordinary one.

\section{Conclusions}

 In this paper BRST quantization of the one-dimensional matrix model (\ref{2DYMSphereMMLagrangian}) with the constraints (\ref{2DYMTorusMMConstraint}) was performed. The problem was reformulated in terms of classical and quantum mechanics on the group manifold, and BRST invariance requirement was imposed in the hamiltonian formalism. Classical and quantum BRST-invariant hamiltonians (\ref{BRSTHamiltonianClassic}) and (\ref{BRSTHamiltonianQuantum}) were constructed. The kernel of the evolution operator between physical states was expressed in terms of BRST path integral (\ref{EvolutionOperatorPathIntBRST}) and (\ref{EvolutionOperatorPathIntBRST1}).

In order to carry out similar analysis directly in the lagrangian formalism, one can use the antifield formalism developed by Batalin, Fradkin and Vilkovisky \cite{Batalin:83:1} (also known as the lagrangian BRST quantization) which is equivalent to BRST quantization \cite{HenneauxQuantGauge}. As in the antifield formalism one needs exactly as many auxiliary variables as in the BRST formalism \cite{HenneauxQuantGauge, Batalin:83:1}, the complexity of the problem is the same for both methods. Antifield formalism can be also suitable for zero-dimensional matrix models which are of special interest in quantum gravity and string theories \cite{Marino:04:1, MakeenkoGaugeMethods}.

It is important to note that as the gauge group was not specified explicitly, one can apply the above analysis to such non-simple gauge groups as $\left(SU(N) \right)^{M}$, i.e. to the models with several matrix-valued variables, where the reduced phase space can not be constructed by diagonalization as in \cite{Minahan:93:1, Douglas:93:1}. It seems that infinite-dimensional groups such as $SDiff(\mathcal{M})$ could also be considered \cite{Hoppe:88, Pope:90:1}, which could be interesting in the context of correspondence between large $N$ two-dimensional Yang-Mills theories and string theories \cite{Gross:93:1, Gross:93:2, Vafa:04},  however, this possibility requires more detailed investigation of topological features of these groups.

\begin{acknowledgments}
I would like to thank Dr. Hossein Sadeghpour for his kind hospitality at ITAMP (Harvard University). I am also grateful to the members of the ITEP lattice group (ITEP, Moscow), especially to Dr. M. I. Polikarpov and E. Luschevskaya, for their hospitality, support and stimulating discussions. This work was partially supported by the U.S. National Science Foundation through a grant for the Institute for Theoretical Atomic, Molecular and Optical Physics at Harvard University and Smithsonian Astrophysical Observatory.
\end{acknowledgments}

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Traveling with Peace of Mind and Self Respect
Did you know that Dallas has one of the few remaining "Green Book" landmarks that provided a safe haven for African-American travelers, by automobile, in Dallas during segregation? That place is the old Moorland Branch YMCA which is now the home of the Black Dallas Dance Theater right in the middle of Dallas' Arts District; 2700 Ann Williams Way, Dallas, TX 75201. This building has a state historical marker indicating its legacy.
What is this green book? Many people young and old do not know the history of this book because it is not needed today. But that was not the case during the era of segregation. According the Jacinda Townsend, the author of the article "How the Green Book Helped African-American Tourists Navigate a Segregated Nation", "Traveling by car in the era of segregation, the open road presented serious dangers. Driving interstate distances to unfamiliar locales, black motorists ran into institutionalized racism in a number of pernicious forms, from hotels and restaurants that refused to accommodate them to hostile "sundown towns," where posted signs might warn people of color that they were banned after nightfall."
Getting gas or using the restroom could lead to a life or death situation. "It didn't matter if you were Lena Horne or Duke Ellington or Ralph Bunche traveling state to state, if the road was not friendly or obliging," according to playwright Calvin Alexander Ramsey, you could be in trouble.
Thus the green book. The visionary entrepreneur and creator Victor H. Green, a 44-year-old black postal carrier in Harlem, relied on his own experiences and on recommendations from black members of his postal service union for the inaugural guide bearing his name, The Negro Motorist Green-Book, in 1937.
The green book listed hotels, restaurants and other businesses open to African-Americans, providing a safety net to guide them during their travel, by car, during the Jim-Crow era.
"Not only was the green book beneficial to African-American automobile travelers, they were also indispensable to African-American businesses.", according to Smithsonian curator Joanne Hyppolite.
"There will be a day sometime in the future when this guide will not have to be published," Green wrote in the introduction to multiple editions. "That is when we as a race will have equal opportunities and privileges in the United States. It will be a great day for us to suspend this publication, because then we can go wherever we please, and without embarrassment. But until that time comes we shall continue to publish this information for your convenience each year."
The Green-Book final edition, in 1966-67, filled 99 pages and embraced the entire nation and even some international cities. This was after the passage of the Civil Rights Act of 1964.
This historical building housing the Black Dallas Dance Theater was also the political headquarters for civil rights planning meetings and a cultural and social center for the black community.
Thank you Dallas for keeping African American history alive.
Read more: https://www.smithsonianmag.com/smithsonian-institution/history-green-book-african-american-travelers-180958506/#SffJMZl8ZJERjuTd.99 ;
https://www.sevendaysvt.com/vermont/before-the-civil-rights-act-tourist-homes-welcomed-black-travelers/Content?oid=4164681
#hiddenhistorydfw #greenbook #greenbookmag #dallasblackhistory #civilrights #texastourism #visit_dallas #tourist #tourists #dallas #dallasevents #dallasobserver #newindallas #dallasnewintown #history #black #blackowned #blackpower #blackhistory #africanamercianhistory
The Disappearance of the Hall of Negro Life
JUNETEENTH: AMERICA'S OTHER INDEPENDENCE DAY & GENERAL ORDER NO. 3
Hidden History DFW
info@hiddenhistorydfw.com
©2021 by Hidden History DFW. Proudly created with Wix.com


text:
Football & Mental Health
info@swaggarlicious.com | | |
Raising the bar: Discussing Mental Health in football | Kickitout.org
madmin
From the cheers and splendour of winning, to the frustration and anger of losing, football is a sport that brings out the extremes of emotions.
These emotions are shared by everyone involved in football regardless of level, and can in instances lead to a greater impact away from the field of play.
Mental health has been an issue which the sport has begun to recognise in recent years and Michael Bennett, Head of Player Welfare at the Professional Footballers Association (PFA), knows too well the consequences of not dealing with any potential problems.
Michael had played for England at youth level before a serious knee injury curtailed his promising career, eventually having to hang up his boots at the age of 29. Reflecting on the time of his injury, Michael admits the lack of understanding around mental health prevented him from speaking out.
"I sustained a really bad injury in 1991 and there was concerns about whether I would play again.
"I suddenly had all these questions and fears going through my mind and I didn't have anyone in the game to speak to about it. I wish I had someone from a footballing background to discuss the issues I was having.
"Looking back, I feel as though my career didn't reach the heights it should have reached because I didn't feel mentally right; I was concerned with getting injured. After my career ended I wanted to come back into football and offer a service which could help players like me."
The issues of mental health are not only prevalent in the professional levels of the sport.
The grassroots level of the game provides a platform for people to engage in an activity away from their daily lives. According to Manisha Tailor MBE, the lack of resources within the amateur ranks are preventing people from exploring opportunities to develop their mental health.
"From my experience at grassroots and community level, there is a real lack of provision for adults with mental health to participate and engage in sport as a coping mechanism and recovery tool.
"It is extremely difficult for service providers to seek provision for those that they work with given financial constraints and low budget.
COPYRIGHT 2016. SWAGGARLICIOUS LTD. ANOTHER WeAreTheCity DESIGNS WEBSITE


"Stratigraphy, Depositional Environments and Basin Structure of the Had" by Jonathan G. Wynn, Diana C. Roman et al.
Sediments exposed in the Dikika Research Project area form a nearly continuous sequence spanning the period from older than 3.8 Ma to younger than 0.15 Ma. By developing a stratigraphic framework of sedimentary basins, we are able to reconstruct a regional geological history that illuminates environmental changes resulting from tectonic events in the Afar triple junction region. The sequence begins with the Basal Member of the Hadar Formation, which was deposited on a dissected and deeply weathered surface of the uppermost flow of Dahla Series Basalt (8–4 Ma). This contact signals an increase in sediment accumulation rate due to active extension along faults parallel to the Red Sea Rift system. Sediments of the Hadar Formation indicate the progressive infilling of the Hadar Basin and migration of the shoreline northward or northeastward toward the axial depocenter, with several brief transgressions southward. After 2.9 Ma, the Dikika Research Project area was uplifted, and the Hadar Formation was faulted and eroded on an angular unconformity. Subsequent to 2.7 Ma, sedimentation returned, although the character and position of the newly developed Busidima half-graben had changed. This basin was formed by the rotation of an asymmetric marginal half-graben around a border fault that paralleled the western escarpment of the Ethiopian Rift. The Busidima Formation deposited in this basin records the migration of the paleo–Awash River across its floodplain in response to a changing tectonic setting. These local paleoenvironmental changes are primarily the response to regional tectonics and are superimposed on the global and regional records of climate change.
Wynn, Jonathan G.; Roman, Diana C.; Alemseged, Zeresenay; Reed, Denné; Geraads, Denis; and Munro, Stephen, "Stratigraphy, Depositional Environments and Basin Structure of the Hadar and Busidima Formations at Dikika, Ethiopia" (2008). School of Geosciences Faculty and Staff Publications. 242.


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text:
The Measured Energy Savings from Two Lighting Control Strategies
Francis M Rubinstein, Mahmut Karayel
LBL-14651
The energy-saving benefits of two lighting control strategies — scheduling and daylighting — were investigated at demonstration sites in two large commercial buildings. A continuously-dimmable lighting control system was installed at the Pacific, Gas & Electric Co. building in San Francisco and an on/off switching system was installed at the World Trade Center building in New York City. By automatically scheduling the operation of the lighting systems to conform with occupancy patterns, lighting energy consumption was reduced 10 to 40%. Several scheduling techniques were investigated and the influence of switching zone size on energy savings was examined. Using photo-electrically controlled lighting systems which switch or dim lighting in accordance with available daylight, the energy consumed for lighting in daylit areas was reduced 25 to 35%. The influence of clear and overcast conditions on the energy savings associated with daylight-linked controls is discussed.
IEEE-IAS Transactions
EEB-L-82-08, L-67
Building Technologies Department, Building Technology and Urban Systems Division, Electronics, Lighting and Networks
BTUS Lighting and Electronics


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text:
Q: How to identify which lines/polygons intersect when using raster data in R We would like to merge vector and raster data to a common spatial grid. For example, suppose we have a vector file of roads; we'd like to know which roads intersect which cells in the grid. The image below provides a toy example, as well as the data we'd like to recover. The numbers on the top left corner of each cell is the cell ID, and the different colors represent the different roads that were rasterized. The yellow-orange represents road 2 (vertical line) and green represents road 1 (diagonal line).

While it's easy to solve this toy problem, we're working with global data and constructing a high resolution grid (~1km at equator). Given this scope and resolution, we need a computationally efficient solution. (Converting the grid to a shapefile, for example, using a spatial merge is not an attractive solution.)
Our initial approach to merging vector data to our spatial grid involved rasterizing the shapefile using common extents and resolution. Using the gdal_rasterize function, we could burn into the raster cells the feature identifiers associated with feature (e.g., each road in our data). However, in instances where two features fall within the same raster cell, only one feature ID is retained.
From the toy example above, in the cell containing both roads, we would only retain one of the road IDs after rasterizing instead of both the roads as shown in Table A. However, we want to retain all the roads and retrieve Table B. This way the table will let us know that there were two unique roads intersecting in this particular cell. Note: What we are currently getting is Table A, but we want to get something like Table B, which was manually created for demonstration. The column "val" indicates the road ID. For instance row 2 of Table B would represent road 2 in cell 2. Row 3 of Table B would represent road 1 in cell 2. Hence, the repetition in cell 2.
We've included a small but reproducible example here:
Note

*

*You will need to create a directory called temp in your desktop.

*We want to use our own rasterize function using gdal_rasterize shown in the code as we will be working with larger data sets and it is faster than using the raster package.
   ###################
   ## Load packages ##
   ###################
   pkgs <- c("rgdal", "rgeos", "raster", "data.table", "dplyr")
   sapply(pkgs, require, character.only = TRUE)

   #####################
   ## Create toy data ##
   #####################
   df <- rbind(c(1,1), c(4,4),c(3,1), c(3,4))

   coord_1 <- Line(rbind(c(1,1), c(4,4)))
   coord_2 <- Line(rbind(c(3,1), c(3,4)))

   l1 <- Lines(list(coord_1), ID = "road1")
   l2 <- Lines(list(coord_2), ID = "road2")

   Sl <- SpatialLines(list(l1, l2))

   df <- data.frame(len = sapply(1:length(Sl), function(i) gLength(Sl[i, ])))
   rownames(df) <- sapply(1:length(Sl), function(i) Sl@lines[[i]]@ID)

   toy.lines <- SpatialLinesDataFrame(Sl, data = df)
   toy.lines@data$polygon_id <- 1:nrow(toy.lines@data)

   # output shapefile
   setwd("~/Desktop/temp")
   writeOGR(toy.lines, ".", "toylines", driver="ESRI Shapefile")

   ####################
   ## gdal_rasterize ##
   ####################
   # rasterize function using gdal_rasterize
   Rasterize <- function(shp_dir, shp_fname, burn, output_wd,
                  gdal_cmd = "/Library/Frameworks/GDAL.framework/Versions/Current/Programs/gdal_rasterize",
                  config = "--config GDAL_CACHEMAX 2000",
                  compress = "-co compress=LZW",
                  extents = "-te 1 1 4 4",
                  resolution = "-tr 2 -2 -tap",
                  datatype = "-ot Int16") {

   new_fname <- gsub("shp$", "tif", shp_fname)

   shp_file <- paste0(shp_dir, "/", shp_fname)
   dest_file <- paste0(output_wd, "/", new_fname)

   cmd <- paste(gdal_cmd, config, burn, extents,
           resolution, datatype, compress,
           shp_file, dest_file)

   # Reporting results:
   cat("Saved", dest_file, "\n")

   return(system(cmd))
   }

   ####################
   ## table function ##
   ####################

   RasterToDT <- function(raster_file){
   values <- getValues(raster_file)
   data.table(cell = 1:length(values), val = values)
   }

   ############################
   ## Rasterize our toy data ##
   ############################
   Rasterize(
   shp_dir = "~/Desktop/temp",
   shp_fname = "toylines.shp",
   burn = "-a polygon_id -init -1", #encode -1 for cell with no element
   output_wd = "~/Desktop/temp")

   # Output table
   r <- raster("~/Desktop/temp/toylines.tif")
   dt_toylines <- RasterToDT(r)

   dt_toylines

A: I made an answer with your toy lines but not with gdal (easy enough to change if you like). I decided to make a blank raster, presumably of which you know the extent? and then populate the table using extract:
# make the blank raster, the extents and resolution of which are up to you.
# the cells are numbered 1 to ncell (starting in the top left in R)
r <- raster(xmn=0,xmx=4,ymn=0,ymx=4,res=c(2,2))
r[] <- 1:ncell(r)

# make your toy.lines as above, except i've thrown in a 3rd to be daring
# why do you have length?
df <- rbind(c(1,1), c(4,4),c(3,1), c(3,4))

coord_1 <- Line(rbind(c(1,1), c(4,4)))
coord_2 <- Line(rbind(c(3,1), c(3,4)))
coord_3 <- Line(rbind(c(0,1), c(4,1)))

l1 <- Lines(list(coord_1), ID = "road1")
l2 <- Lines(list(coord_2), ID = "road2")
l3 <- Lines(list(coord_3), ID = "road3")

Sl <- SpatialLines(list(l1, l2, l3))

df <- data.frame(len = sapply(1:length(Sl), function(i) gLength(Sl[i, ])))
rownames(df) <- sapply(1:length(Sl), function(i) Sl@lines[[i]]@ID)

toy.lines <- SpatialLinesDataFrame(Sl, data = df)
toy.lines@data$polygon_id <- 1:nrow(toy.lines@data)

# use the extract function which will return a list, one element for every spatial line,
# saying which cells it passes through. Named elements by id.
l <- extract(r,toy.lines)
names(l) <- toy.lines@data$polygon_id

# make a data table of cell ID and what line it touches, unlisting the list elements
# and turning them into a long vector (and inserting that as a column)
cells.df <- data.table(cell=unlist(l),lineid=rep(as.numeric(names(l)),lapply(l, function(x) length(x))))
setkey(cells.df,cell)

# make a simple data table of all cell numbers (will enable us to keep NA cells)
all.cells <- data.table(cell=1:ncell(r))
setkey(all.cells,cell)

# merge by key. Data table orders by key and autopopulates NAs
final.df <- cells.df[all.cells]

That produces table B anyway. Unsure as to why it believes line 1 to pass through cell 4, but there you go.

redpajama_set_name: RedPajamaStackExchange


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Suitable for use in a range of presentations.
this is really great web site! very entertaining at the same time useful..
Very interesting and useful. But I digged too much for my project presentation template and i found only one anyway thanks.


text:
Sports Medicine Oregon Performs First Meniscus Replacements in Oregon with NUsurface® Implant
PORTLAND, Ore.–(BUSINESS WIRE)–Sports Medicine Oregon, a comprehensive orthopaedic clinic treating a wide variety of injuries and illnesses, and Active Implants, a company that develops orthopedic implant solutions, today announced that the first meniscus replacement procedures in Oregon have been performed by orthopaedic surgeons Drs. Richard Edelson and Jonathan Greenleaf. Sports Medicine Oregon and its affiliate Oregon Outpatient Surgery Center is the only site in Oregon – and one of just 10 sites nationwide – enrolling patients with persistent knee pain caused by injured or deteriorating meniscus cartilage in the SUN (Safety Using NUsurface®) clinical trial, which is designed to assess the safety and effectiveness of the NUsurface® Meniscus Implant (pronounced "new surface") in restoring function similar to that of a natural, healthy meniscus.
The first patient to receive the implant in Oregon was 59-year-old Philomath resident Don Bennett. Bennett grew up playing basketball and initially tore his meniscus in his left knee while playing basketball 30 years ago, only to suffer another tear eight years later. He underwent two meniscectomy surgeries to treat the meniscus tears, but the pain in his knee gradually returned and increased in severity. Over the past five years, the physical demands of his daily job function as a water system maintenance specialist and even daily walking activity aggravated his knee to the point of constant pain.
"There are limited options for patients like Don, who experience persistent knee pain following meniscus injury and surgery," Dr. Edelson said. "He had exhausted his non-surgical options. Even though his pain had increased in severity over the last five years, he was not a candidate for total knee replacement."
"Meniscus injuries can be a very painful and debilitating problem, even leading to potential joint replacement at a young age," Dr. Greenleaf said. "It is our belief that the NUsurface implant may allow patients to delay or avoid knee replacement and return to an improved level of activity without pain."
It has been nearly two months since Bennett received the implant on July 13 through a small incision in his knee and completed a six-week rehabilitation program, and he has returned to his daily leisure and sports activities. With only a month left until his retirement from a 35-year career working for the city of Corvallis, he is most looking forward to salmon fishing, spending more time going on walks with his wife, attending his daughter's Pac 12 volleyball games and coaching his son ahead of his basketball games.
"Prior to receiving the implant, I was living with constant pain and the fear that a total knee replacement was my only option," Bennett said. "The NUsurface Meniscus Implant is giving me back my mobility. I'm looking forward to supporting my kids' athletic endeavors, taking hikes with my wife and walking painlessly."
About Sports Medicine Oregon
The goal of Sports Medicine Oregon is the restoration of active lifestyles to injured athletes of all ages. The team of specialty-trained physicians takes pride in providing the community with the highest quality orthopedic care. Whether it is the professional athlete or the weekend warrior, it strives to provide timely and comprehensive care at the state-of-the-art facility which includes full service X-ray, outpatient physical therapy, and the adjoining surgery center. For more information, please visit http://sportsmedicineoregon.com/.
About Oregon Outpatient Surgery Center
Oregon Outpatient Surgery Center is a multispecialty surgical center, which includes joint replacements. Oregon Outpatient Surgery Center provides caring, friendly, highly-skilled and trained professional staff, delivering the personal attention every patient deserves in a comfortable, professional atmosphere, a cost effect alternative to traditional surgical care.
Active Implants, LLC develops orthopedic implant solutions that complement the natural biomechanics of the musculoskeletal system, allowing patients to maintain or return to an active lifestyle. Active Implants is privately held with headquarters in Memphis, Tennessee. European offices are in Driebergen, The Netherlands, with R&D facilities in Netanya, Israel. For more information, visit www.activeimplants.com.
Active Implants' NUsurface Offers Novel Menis…
A New Technique in Knee Surgery — the 'Artifi…


text:
UBS allows most employees to permanently mix work at home and in the office
UBS plans to allow up to two-thirds of its employees to work together at home and in the office for a long time, betting that this method will give the Swiss bank an advantage over Wall Street banks when it comes to hiring.
According to people familiar with the matter, the move to adopt a hybrid work model was led by CEO Ralph Hamers and his senior management, which highlights the fact that it is incompatible with the tougher approach taken by many U.S. banks. The gap is getting bigger and bigger.
UBS has decided that only employees who are required to hold positions in the office due to regulatory rules or to perform specific tasks, such as traders and branch employees, have little or no flexibility in their work practices.
According to people familiar with the matter, internal analysis of its 72,000 global employees shows that approximately two-thirds of the positions allow for mixed work.
UBS's position echoes those of its European counterparts such as France Societe Generale, But in sharp contrast with the approach taken by several U.S. banks such as JPMorgan Chase, Goldman Sachs and Morgan Stanley, which have ordered their employees in New York to resume work.
After most bankers have worked in home offices, spare rooms, and kitchen tables for more than a year, UBS's decision suggests that a legacy of the pandemic may be a fundamental divergence in work practices between European and American banks.
The UK-based bank HSBC and Standard Chartered Bank Plans have been announced to allow employees to work from home or "near home" to reduce office space and avoid urban commuting.
In an internal message to employees released last week, UBS stated, "We are committed to providing you with the flexibility of mixed work (a mix of office and work from home), where roles, tasks and locations allow."
However, even employees who offer mixed jobs still need to participate in certain activities in a manner agreed by their manager.
The Zurich-based bank has not yet determined when it will require employees to return to the office. UBS declined to comment.
In contrast, Goldman Sachs employees have been ordered to return to the bank's New York headquarters, while JPMorgan Chase's US employees are expected to resume normal work from July 6.
Morgan Stanley CEO James Gorman (James Gorman) The harshest Call on employees to return to the office. He said at a recent company event: "If you can enter a restaurant in New York City, you can enter the office, and we hope you are in the office."
Citigroup is one of the few large US banks that have introduced a mixed work model so far, and employees can work from home for up to two days a week.
Although it only moved into Broadgate 5, one of the largest buildings in the City of London five years ago, UBS has long been looking for ways to get more employees to work from home.
Last year, it tried to issue to traders in London Augmented reality headset, Allowing them to reproduce the experience of working on a crowded trading floor without leaving home.
The worst month since Chinese tech stocks suffered the global financial crisis
China stock market dynamics Sign up for myFT …
Taliban accused of killing relatives of journalists
Japan declares a state of emergency for the Tokyo Olympics
Japan will declare a Covid-19 emergency in Tokyo …


text:
CATFORD GYRATIONS
Catford Gyrations is the musical alias of Andy Jones, a London based musician who creates instrumental music that absorbs a broad range of influences, and often seeks inspiration from his surrounding local environment.
Prior to Catford Gyrations, Andy had previously been involved in indie pop outfit Kicker, who released a series of singles and LPs between 1999 and 2005. After the band split up, Andy set about finding a new means of creating music at home, and spent much of the following decade getting to grips with the technical know-how required to put his ideas into action.
In 2016, he started work on his debut eponymous LP. The album's development is being documented on this website, as an ongoing work in progress.
In addition to the continuing work on the LP, Andy contributed to the Linear Obsessional compilation A View from a Hill in December 2017 with the track Bandstand. He also released his debut EP, A205, in January 2020.
Looping the loop December 22, 2021
Eros October 25, 2021
Winslade July 25, 2021
Precinct March 3, 2021
I'm Going Outside July 17, 2020