text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
\subsection*{Corresponding Author}
{*}Email: lshen@bnu.edu.cn
\subsection*{Supplementary Information}
Electronic supplementary information (ESI) including performance of
LSTM networks on testing sets, details on LSTM networks for extended
coupling model and LSTM networks with bad performance is available.
\section*{Performance of LSTM networks on testing sets}
\begin{figure}
\noindent \centering{}\includegraphics[width=0.45\textwidth]{Testings}\caption{\label{fig:MSE} Comparison of LSTM predictions of electronic density
matrix with reference for testing sets: single-avoided crossing model
in the main text (a), dual-avoided crossing model in the main text
(b), extended coupling model with multiple networks in the main text
(c-f), dual-avoided crossing model with bad performance in Fig. \ref{fig:Tully2_fail}
(g), extended coupling model with bad performance in Figs. \ref{fig:Tully3a_fail}
(h) and \ref{fig:Tully3b_fail} (i), and extended coupling model with
moderate performance in Fig. \ref{fig:Tully3_plus} (j). All values
of $\rho_{00}$ are shifted by $-0.5$. }
\end{figure}
\pagebreak{}
\section*{Details on LSTM networks for extended coupling model}
\begin{figure}
\noindent \centering{}\includegraphics[width=1.05\textwidth]{Test_Tully3_Trajs_Classical}\caption{\label{fig:Tully3_plus} Electronic density matrix plotted as function
of time for representative trajectories of extended coupling model
at a low (a), medium (b) and high (c) initial momentum. LSTM network
is constructed with input features as $x$, $p$, $\frac{\left(G_{k}-G_{j}\right)\left|v\right|}{\left(E_{k}-E_{j}\right)^{2}}$
and $\rho_{00}$; all hyperparameters are listed in the main text.
Different colors represent different simulation methods (black: original
FSSH as reference; red: LSTM-FSSH).}
\end{figure}
\pagebreak{}
\begin{figure}
\noindent \centering{}\includegraphics[width=0.75\textwidth]{Tully3_01_LSTM_diagonly}\caption{\label{fig:collection_plus} Collective result of extended coupling
model obtained using LSTM in Fig. \ref{fig:Tully3_plus} in comparison
with reference.}
\end{figure}
\pagebreak{}
\begin{figure}
\noindent \centering{}\includegraphics[width=0.9\textwidth]{Cases}\caption{\label{fig:multiple} Multiple connected LSTM networks (labeled as
1 in blue, 2 in green, 3 in orange, and 4 in red) are applied and
switched during propagation on extended coupling model. Different
initial momenta or random surface hopping events lead to different
cases represented in (a-f). }
\end{figure}
\pagebreak{}
\section*{LSTM networks with bad performance}
\begin{figure}
\noindent \centering{}\includegraphics[width=1\textwidth]{Test_Tully2_Trajs_PROB}\caption{\label{fig:Tully2_fail} Electronic density matrix plotted as function
of time for representative trajectories of dual-avoided crossing model
at a low (a), medium (b) and high (c) initial momentum. LSTM is built
with the number of nodes for each layer as 32; other hyperparameters
are the same as that used in the main text. Different colors represent
different simulation methods (black: original FSSH as reference; red:
LSTM-FSSH). }
\end{figure}
\pagebreak{}
\begin{figure}
\noindent \centering{}\includegraphics[width=0.75\textwidth]{Tully2_01_LSTM_fail}\caption{\label{fig:fail2} Collective result of dual-avoided crossing model
obtained using LSTM in Fig. \ref{fig:Tully2_fail} in comparison with
reference.}
\end{figure}
\pagebreak{}
\begin{figure}
\noindent \centering{}\includegraphics[width=1\textwidth]{Test_Tully3_Trajs_PROB}\caption{\label{fig:Tully3a_fail} Electronic density matrix plotted as function
of time for representative trajectories of extended coupling model
at a low (a), medium (b) and high (c) initial momentum. LSTM is built
with the same input features as the first and second test systems;
422341 sequences in database are extracted with $M=20$ and $N=50$;
the number of nodes for each layer is 72 with a batch size of 64 and
a learning rate of 0.001. Different colors represent different simulation
methods (black: original FSSH as reference; red: LSTM-FSSH). }
\end{figure}
\pagebreak{}
\begin{figure}
\noindent \centering{}\includegraphics[width=0.75\textwidth]{Tully3_01_LSTM_fail}\caption{\label{fig:fail3a} Collective result of extended coupling model obtained
using LSTM in Fig. \ref{fig:Tully3a_fail} in comparison with reference.}
\end{figure}
\pagebreak{}
\begin{figure}
\noindent \centering{}\includegraphics[width=1.05\textwidth]{Test_Tully3_Trajs_PROB2}\caption{\label{fig:Tully3b_fail} Electronic density matrix plotted as function
of time for representative trajectories of extended coupling model
at a low (a), medium (b) and high (c) initial momentum. LSTM is built
with input features as $x$, $p$, $\frac{\left(G_{k}-G_{j}\right)\left|v\right|}{\left(E_{k}-E_{j}\right)^{2}}$,
$\rho_{00}$, $\mathrm{Re\left(\rho_{01}\right)}$ and $\mathrm{Im\left(\rho_{01}\right)}$;
417096 sequences in database are extracted with $M=20$ and $N=50$;
the number of nodes for each layer is 72 with a batch size of 32 and
a learning rate of 0.001. Different colors represent different simulation
methods (black: original FSSH as reference; red: LSTM-FSSH). }
\end{figure}
\pagebreak{}
\begin{figure}
\noindent \centering{}\includegraphics[width=0.75\textwidth]{Tully3_01_LSTM_fail2}\caption{\label{fig:fail3b} Collective result of extended coupling model obtained
using LSTM in Fig. \ref{fig:Tully3b_fail} in comparison with reference.}
\end{figure}
\pagebreak
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,148 |
ID: 2038 ~ Source: Waco Tribune-Herald, 6 April 1947, page 12. Accessed on newspapers.com.
The first print ad for Circle Lumber Company was published on April 6, 1947 in the Waco Tribune-Herald. Original owner Frank Stevens used both newspaper ads and radio spots to promote his company to McLennan County residents. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,078 |
@interface PrimeNumbersWithLoggingPerformanceTest ()
@property (nonatomic, assign) NSInteger count;
@property (nonatomic, assign) NSInteger from;
@property (nonatomic, strong) PrimeNumbersGeneratorManager *manager;
@end
@implementation PrimeNumbersWithLoggingPerformanceTest
- (instancetype)initWithIterationsCount:(NSInteger)count from:(NSInteger)from
{
self = [super init];
if (self) {
_count = count;
_from = from;
_manager = [[PrimeNumbersGeneratorManager alloc] initWithFrom:from];
}
return self;
}
- (NSString *)name
{
return [NSString stringWithFormat:@"Print %ld prime numbers starting from %ld", (long)self.count, (long)self.from];
}
- (ExecutionBlock)noGeneratorBlock
{
return ^() {
NSInteger i = 0;
NSInteger from = self.from;
while (TRUE) {
for(NSInteger n = from; ; n++) {
int j;
for(j = 2; j < n; j++)
if(n % j == 0)
break;
if(j == n) {
NSLog(@"%ld", (long)n);
if (i++ >= self.count) {
return;
}
}
}
}
};
}
- (ExecutionBlock)smGeneratorSyncBlock
{
SMGenerator *smGenerator = [self.manager smSyncGenerator];
return ^() {
NSInteger i = 0;
while (i++ < self.count) {
NSNumber *number = [smGenerator next];
NSLog(@"%@", number);
}
};
}
- (ExecutionBlock)smGeneratorAsyncBlock
{
SMGenerator *smGenerator = [self.manager smAsyncGenerator];
return ^() {
NSInteger i = 0;
while (i++ < self.count) {
NSNumber *number = [smGenerator next];
NSLog(@"%@", number);
}
};
}
- (ExecutionBlock)maGeneratorBlock
{
Generator maGenerator = [self.manager maGenerator];
return ^() {
NSInteger i = 0;
while (i++ < self.count) {
NSNumber *number = maGenerator();
NSLog(@"%@", number);
}
};
}
- (ExecutionBlock)extCoroutineBlock
{
Generator extCoroutine = [self.manager extCoroutine];
return ^() {
NSInteger i = 0;
while (i++ < self.count) {
NSNumber *number = extCoroutine();
NSLog(@"%@", number);
}
};
}
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,406 |
Orthodox theology
Theology of the Icon, and Recognizing Saints
A word from the Patriarch on unity, grace, and life after death
Life & Faith
Synaxis of the Holy Glorious Prophet, Forerunner and Baptist John
Feast of the Theophany of our Lord and Savior Jesus Christ
Serbian Bishop Antonije awarded with the Medal of St. Mark of Ephesus
14. July 2020 - 9:49
The Serbian Orthodox Bishop Antoniје of Moravica was awarded with the highest decoration of the Department of Foreign Church Affairs of the Russian Orthodox Church - the medal of St. Mark of Ephesus I degree.
On Sunday, July 12, 2020, on the feast of the Holy Apostles Peter and Paul - the church feast of the Representation of the Serbian Orthodox Church in Moscow, His Eminence Hilarion, Metropolitan of Volokolamsk, President of the Department of Foreign Church Affairs of the Patriarchate of Moscow, presented to His Grace Antonije, Bishop of Moravica and dean of the Representation of the Serbian Orthodox Church in Moscow, the highest decoration of that Department - the medal of St. Mark of Ephesus I degree.
The award ceremony was held during the celebration of St. Peter's Day, the church feast of the Church of the Holy Apostles Peter and Paul - the Representation of the Serbian Orthodox Church in Moscow.
His Eminence Hilarion, Metropolitan of Volokolamsk, addressed to His Grace Anthonije the following words:
- Your Grace, dear Bishop! I cordially congratulate you on your jubilee. A significant part of Your Grace's life has been connected with the Russian Orthodox Church, which has found in your person a worthy envoy of the Church of Saint Sava. During all these years, living with us, you have been and remain a good and sincere friend, beloved by many believers of our Church.
From the walls of the ancient monastery of the Venerable Sergius of Radonezh you have brought a deep and sincere love for the liturgical tradition of the Russian Church, the Russian language and culture. All the knowledge you acquired during your studies at the Moscow Theological Academy has helped you to fulfill the responsible duty as the dean of the reestablished Representation of the Serbian Orthodox Church in Moscow. You have managed to renew all those glorious traditional Russian-Serbian relations that were established in the time before the outbreak of the Revolution. The paternal spiritual care for the Serbian diaspora on the canonical territory of the Moscow Patriarchate, as well as the tireless efforts of Your Eminence aimed at the comprehensive development of relations between the Russian and Serbian Orthodox Churches, have written new pages in the common history of our two Orthodox peoples.
The love for the beauty of the church and "zeal for the house of the Lord" (Ps 68:10) inspired you to sacrifice your efforts in order to enhance the beauty of the church of the Holy Apostles Peter and Paul, while great pastoral qualities helped you to gather a large spiritual community.
Thanks to your translation and author's work, we have been lucky enough to get acquainted with spiritual values of the Orthodox Serbian people. On the other hand, Russian theology and the saints of our Church have become closer to the Serbian people, who - getting acquainted with the Russian spiritual culture - can feel more clearly the words of the Venerable Ava Justin, who says: "It is a huge, wonderful and infinite paradise of the Russian soul, the miraculous and infinite holiness of the glorious saints of the Russian lands" (Venerable Justin of Celije, On the Paradise of the Russian Soul). You have done a lot when it comes to preserving and improving the ancient tradition of educating Serbian students in Russian theological schools, Venerable Simeon of Dajbabe and Venerable Sebastian of Jackson, St. Nicholas of Ohrid and Zica and St. Mardarije Uskokovic, but also many other Serbian saints who were educated in Russia.
Your Grace, on the day of your 50th anniversary, I wish you good health and the abundant help of God in your ascetic, archpastoral and church-diplomatic service. In recognition of all your successes, I consider you worthy to present you with this high award of the Department of Foreign Church Affairs of the Moscow Patriarchate - the medal of St. Mark of Ephesus of the First Degree. For many and fruitful years, beloved Bishop!"
(translated by R.Rakic)
Orthodox Churches
Theophany celebrated in Djurdjevi Stupovi
The Feast of Theophany in the Cathedral church in Novi Sad
Metropolitan Porfirije: There will be challenges, but we will never lose faith that God is with us
Bishop of Pozega and Bishop of Slavonia visited the Diocese of Gornji Karlovac
Bishop Irinej receives new Ambassador of Serbia to USA, Marko Djuric
Feast of the Baptism of the Lord celebrated in Jerusalem
The Epiphany is celebrated at the Russian Orthodox Church Representation in Damascus
The Feast of the Circumcision of the Lord and the Commemoration of Saint Basil in Jerusalem
First Maasai priest in Tanzania
Saint Stephen's feast in Jerusalem
Christians invited to join virtually in prayer for 54th Week of Prayer for Christian Unity
Pope Francis and the Pope emeritus receive Covid-19 vaccine
Christmas Visit of President Vucic to Chilandar Monastery
Pakistan's Christians and other faiths hold Christmas event
"Christians in Nigeria are Slaughtered Like Animals"
Copyright © 1999-2021 by The Information Service of the Serbian Orthodox Church
11000 Belgrade, Kralja Petra no.5 | +381.11.3025.112 | info@spc.rs | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,760 |
"Finally! A book about consumerism that goes to the very heart of the matter—that it corrodes our precious human capacities to know truth, see beauty, and feel love. These seventeen highly intelligent, compassionate, and lucid Buddhist teachers each give a unique understanding of what gnaws at most of us about our consumer habits. They each show how Buddhist thought can help clear our minds and settle us down. _Hooked!_ is also just an exceptional Buddhist primer for Westerners no matter what their consumer habits. I highly recommend these essays to everyone."
—Vicki Robin, coauthor of _Your Money or Your Life_ and founder of Conservation Cafes
"Stephanie Kaza is gently and winningly shrewd; Buddhism is the faith practice that has looked most clearly at desire and what it means. This volume, therefore, is extremely readable and extremely useful to those of us from other faith traditions trying to come to grips with the modern plague of consumption."
—Bill McKibben, author of _Enough: Staying Human in an Engineered Age_
ABOUT THE BOOK
At one time or another, most of us have experienced an all-consuming desire for a material object, a desire so strong that it seems like we couldn't possibly be happy without buying this thing. Yet, when we give in to this impulse, we often find ourselves feeling frustrated and empty. Advertisers, of course, aim to hook us in this way, and, from a global perspective, our tendency to get hooked fuels the rampant over-consumption that is having a devastating impact on the world's stability and on the environment.
According to the contributors to this unique anthology, Buddhism can shed valuable light on our compulsions to consume. Craving and attachment—how they arise and how to free ourselves of them—are central themes of Buddhist thought. The writings in this volume, most of which have never been previously published, offer fresh perspectives and much-needed correctives to our society's tendency to believe that having more will make us happier.
_Hooked!_ includes a range of writings on how to apply Buddhist thought and ethics to understand and combat the problem of over-consumption as individuals and collectively. Contributors include popular Western teachers, Asian masters, scholars, and practitioners such as:
* Pema Chödrön—on what is actually happening at the moment we're "hooked," and how to get beyond that.
* Joseph Goldstein—on how mindfulness training can help us stop "wanting to want."
* Bhikshuni Thubten Chödrön—on how consumer mentality influences spiritual practice.
* Judith Simmer-Brown—on how cultivating spiritually based activism and compassionate action can help us address the negative effects of consumerism.
* Rita Gross—on how understanding moderation can curb overconsumption.
* Santikaro Bhikkhu—on practicing generosity in a consumer world.
STEPHANIE KAZA, Ph.D., teaches environmental ethics, the radical environmental movement, and ecophilosophy at the University of Vermont and the Institute for Deep Ecology.
Sign up to learn more about our books and receive special offers from Shambhala Publications.
Or visit us online to sign up at shambhala.com/eshambhala.
Hooked!
Buddhist Writings on Greed, Desire,
and the Urge to Consume
EDITED BY
Stephanie Kaza
FOREWORD BY
PAUL HAWKEN
Shambhala
Boston & London 2011
Shambhala Publications, Inc.
Horticultural Hall
300 Massachusetts Avenue
Boston, Massachusetts 02115
www.shambhala.com
© 2005 by Stephanie Kaza
"How We Get Hooked, How We Get Unhooked," copyright Pema Chödrön. Reprinted from _Shambhala Sun_ (March 2003) by permission from Pema Chödrön. Portions of "You Are What You Download" appeared originally in _Inquiring Mind_ (Fall 2002). "Consuming Time," copyright David Loy and Linda Goodhew. Printed by permission from David Loy and Linda Goodhew. "Wash Your Bowls," copyright Norman Fischer. Printed by permission from Norman Fischer.
All rights reserved. No part of this book may be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher.
Library of Congress Cataloging-in-Publication Data
Hooked!: Buddhist writings on greed, desire, and the urge to consume/edited by Stephanie Kaza.—1st ed.
p. cm.
Includes bibliographical references.
eISBN 978-0-8348-2238-2
ISBN 1-59030-172-2
1. Desire—Religious aspects—Buddhism. 2. Buddhism—Doctrines. I. Kaza, Stephanie.
BQ4430.D47H66 2005
294.3′444—DC22
2004016053
Contents
Foreword
PAUL HAWKEN
Introduction
STEPHANIE KAZA
PART ONE
Getting Hooked: Desire and Attachment
1. Desire, Delusion, and DVDs
JOSEPH GOLDSTEIN
2. How We Get Hooked, How We Get Unhooked
PEMA CHÖDRÖN
3. The Inner Pursuit of Happiness
RUBEN L. F. HABITO
4. Young Buddhists in Shopping Shangri-la
SUMI LOUNDON
5. Marketing the Dharma
THUBTEN CHÖDRÖN
6. You Are What You Download
DIANA WINSTON
PART TWO
_Practicing with Desire: Using Buddhist Tools_
7. Cultivating the Wisdom Gaze
JUDITH SIMMER-BROWN
8. No River Bigger than _Tanha_
PRACHA HUTANUWATR AND JANE RASBASH
9. Taming the "I Want" Mind
SUNYANA GRAEF
10. Penetrating the Tangle
STEPHANIE KAZA
11. Form and Elegance with Just Enough
RITA M. GROSS
12. Consuming Time
DAVID LOY AND LINDA GOODHEW
PART THREE
_Buddhist Ethics of Consumption_
13. Three Robes Is Enough
AJAHN AMARO
14. Practicing Generosity in a Consumer World
SANTIKARO
15. Wash Your Bowls
NORMAN FISCHER
16. Green Power in Contemporary Japan
DUNCAN RYUKEN WILLIAMS
17. Mutual Correction
DAVID W. CHAPPELL
_Notes_
_Contributors_
_E-mail Sign-Up_
Foreword
FOR PART OF MY CHILDHOOD, I was raised on a farm belonging to my Swedish grandmother and Scottish grandfather. Nothing was thrown away. Every other plate was chipped, but the china never left the dinner table with food on it. Gravy and juices were mopped up by homemade bread, vegetable peelings went to the chickens, the eggs were eaten at breakfast, the eggshells were put into the coffee grounds, the coffee grounds were placed into the compost, the compost was tilled into the garden, the beans and corn from the garden were canned into glass jars that joined the jams and jellies lining cool, dark basement walls. Paper lunch bags were brought back from school and neatly folded for the next day. Our idea of play included capturing horned toads and pretending they were dinosaurs or lying face up in the irrigation ditch, the tiny fry tickling our toes, and imagining we were floating down a great Amazonian river. Our only toy was a tire swing. Had my grandparents been from Chile, Korea, or Kerala, it essentially would have been the same. Nothing would have been wasted.
Until recently, most cultures and religions honored frugality and cautioned against excess. No longer. Western consumer society, the de facto global culture, is unique in all of history because underlying it is the highly developed consumption-based "science" called economics. It could even be called a science of voraciousness because at its roots is the belief that in order for nations to prosper, our desires must expand without limit. And grown they have. In the U.S. there are 45,000 shopping malls employing 10.7 million people. The average American family of four metabolizes four million pounds of material every year to support their lifestyle. That's 11,000 lbs. a day, 7.5 lbs. a minute. This keeps us busy, yet we are heedless because we don't see most of that consumption. It is offshore, and in mines, stockyards, slag heaps, landfills, and wastewater treatment plants. Billowing gases migrate to the stratosphere and double glaze the planet on behalf of us all. This constant expansion of desire and material goods forms our current definition of a healthy economy. Economists who take seriously the idea of steady-state production and consumption are marginalized or ignored by their peers although the deleterious effects of unquenchable desires are omnipresent. The consequences are studied by police, psychiatrists, physicians, sociologists, environmentalists, and biologists. But not economists.
In the Buddhist canon, there are six mind-states or realms, one of which is called the hungry ghost, depicted as a craven figure with a protuberant stomach and long pencil neck, a maundering wraith unable to satisfy its insatiable desires. In this realm, attempts to avoid pain by seeking satisfaction cause more pain for oneself and others. It is a useful metaphor reminding us of the compulsive shopper, the sports addict, the speculator, the megalithic global corporation hooking poor children around the world on fast food and hip-hop. In medieval times, the specter of the hungry ghost was a repugnant reminder of greed. Today the hungry ghost stars in movies and is the host on shopping channels. The women are svelte, tucked, and toothy; the men have private jets and new designer wives. At a private high school near my home, eighteen-year-olds hunger for today's car du jour, a Porsche Cayenne SUV.
It is tempting to see the problem of consumption as something other people do. People with SUVs should cut back and buy smaller cars, get more exercise, and use a bicycle. But this wonderfully edited volume shows us that it is more relevant and poignant to look at our own lives. A Buddhist perspective on consumption offers understanding of oneself. The quotidian ways in which we rob the earth are pathways to genuine insight. And in the awareness of self arises compassion for others, especially those who are weighed down so heavily by material desire. It is fair to say that people are overwhelmed by this world we share and live in. Alleviating people's sense of isolation and fear can do more than any recycling program. As Buddhist teachers so aptly point out, we can reduce our and others' desires by being generous and kind. It is hard to be grasping when we are reaching out.
Of course, we need to do everything in our power to lessen the harm to nature caused by this blowout sale of the earth's resources. More importantly, we must attend to the suffering this destruction visits upon people, rich and poor, everywhere. To live in this time and to attend to the suffering of others are gifts that we have received. All wars are wars of consumption, and every war starts with self. If we are borrowing resources from our grandchildren, which is an unpayable debt, we can also write checks of restoration to them. We can honor our veterans by not making more of them. We can honor an overpopulated world by welcoming and caring for every new child. We can honor resources by caring for everything that has already been made. We can begin to examine, mindfully and patiently, our every act and object, one by one, in order to understand how our lives affect others. We can use consumption, as is done in this book, as a means to know who and where we are. We can create lovely practices that remind us of the fragility of this earth and the joy of being able to reside here.
I have a friend who has, count them, six hundred objects in his home. That includes everything, even teaspoons. At one time he was officer of one of the world's largest banks. When he wants to buy something, or receives a gift, he selects something to give away. This is not a zero sum game. As the years have gone by, his home has become more nuanced and lovely. Every object has meaning; nothing is retained unnecessarily. His home is like a small temple. He needs very little money to live on, which means he spends most of this time helping others. He is utterly alive, elfish, bright-eyed and present.
We are human. We will always consume. The big question is how.
—Paul Hawken
Introduction
Stephanie Kaza
IN 1997 the film _Affluenza_ premiered to audiences around the United States, offering a diagnosis for what ails the planet. It spoke to people of all political persuasions, receiving high ratings in both conservative and liberal cities. The virus at loose seemed to be infecting every member of society and, as the film's producer, John de Graaf, said, "threatening our wallets, our friendships, our families, our communities, and our environment." In coining the term, he defined affluenza as "a painful, contagious, socially transmitted condition of overload, debt, anxiety, and waste resulting from the dogged pursuit of more."
The film received tremendous response. Finally someone was making an effort to confront the high-impact habits of the consumer society. How was it possible that Americans spend more for trash bags than 90 of the world's 210 countries spend for everything? Could it really be true that we have twice as many shopping malls as high schools? That we consume our average body weight—120 pounds—every day in extracted and processed materials? That humans take 40 percent of the earth's entire plant productivity for themselves?
These dramatic figures caught my attention. As a professor and student of environmental studies, I have been following the accelerating decline of the earth's resources for thirty years. For the most part, it is very discouraging. To engage this information with students is often heartbreaking work. Species extinction, dying lakes, contaminated oceans, nuclear accidents, oil spills—the degradation of virtually every aspect of life is hard news to swallow. Even harder is the realization that human actions are responsible for much of the decline. The film _Affluenza_ pointed out the obvious: the current rates of consumption are not sustainable. Life-support systems are giving out.
To deal with my own despair around these issues, I developed a course called "Unlearning Consumerism." Each week the students undertook a lab exercise to evaluate some aspect of their consumption habits. One of our first exercises was "the property list." The students had to make a list of _all_ of their belongings, from underwear to electric guitars. The group also took up analyses of energy use, transportation habits, and food consumed. Students assessed their diets not in calories but in estimated energy expense to the planet. To break the grip of everyday consumption, I assigned a three-day technology fast. The students had to give up the Internet, the car, the television, or another technology of their choice and then evaluate the impact it carried in their lives.
This class and the students' enthusiastic response got me started in pursuing the links between consumption and environmental degradation. For too long economic development has focused mostly on technological improvement and population issues in Third World countries. Examining our own levels of consumption has been virtually off the table. "The American way of life is not up for negotiation," said President George H. W. Bush at the 1992 Earth Summit in Brazil. Fortunately this cloak of silence has been lifted by excellent research. In 1999 the Union for Concerned Scientists analyzed in detail the impact of U.S. energy use, transportation, food production, and housing on ecosystem health. They sorted through consumer dilemmas such as paper versus plastic bags and concluded it was the bigticket items—housing and vehicle use—that need our greatest attention. In 2004 the Worldwatch Institute focused its entire _State of the World_ report on the consumer society, presenting current figures on global rates of resource use and generation of waste. The authors argued that it is not only possible but essential to move toward a less consumptive society.
But there are other reasons to study this topic. Philosopher David Loy shows how "the Market" has become a world religion, replacing traditional religions in determining our reigning worldview and values. The two unshakable and unchallengeable statements of faith in this religion are (1) that growth and enhanced world trade will benefit everyone, and (2) that growth will not be constrained by the inherent limits of a finite planet. From a religious perspective, the power of this worldview lies in its extremely effective conversion techniques. The seductive appeal of product after product captures the masses, replacing other approaches to meaning and satisfaction. Loy points out that a significant flaw of economic religion is that it depletes "moral capital." Though the market requires character traits such as trust in order to be efficient, it simultaneously tends to erode personal responsibility for other people. Just as the market depends on the biosphere to regenerate natural capital, it also depends on the human community to regenerate moral capital. To confront the impact of consumerism is to confront this moral deterioration.
My own concern is that consumer identity is crowding out or displacing ecological identity. Our sense of place, ecological concerns, and environmental values (such as respect, compassion, and reverence for life) make up our ecological identity. These all influence how we relate to the earth and to what degree we make environmentally conscious choices. Consumer identity, in contrast, is based on brand-name preferences, material possessions, class status, social group, and market desires. Just as ecological identity is tied to environmental behavior, consumer identity is tied to purchasing behavior. When more time is taken up in consumer activities, the consumer identity flourishes, and less time is available for cultivating our ecological identity.
But the greatest motivator for studying consumption and consumerism may in the end be self-preservation. All signs point to increasing difficulty in sustaining ecological life-support systems and thus the human populations dependent on them. Pollution, depletion, and resource damage continue to worsen, taking an enormous toll on ecosystems and human health. As developing countries increase their rates of consumption, the rate of environmental impact increases even faster. Multiply this by the growing world population and an aspiring global consumer class and the result is only more alarming. While predictions indicate population levels may eventually stabilize, rates of consumption seem only to be growing.
Before proceeding much further, let me clarify some of these terms and provide a little historical context for this current wave of consumerism. Neva Goodwin, director of the Tufts Global Development and Environmental Institute, defines the consumer society as characterized by its use of leisure time for spending money and for its belief that owning things is the primary means to happiness, the assumed primary goal in life. In a consumption-oriented society, your identity is tied more to what you consume than to what you produce. "Consumerism" as a belief system accepts consumption "as the way to self-development, self-realization, and self-fulfillment." At its 1997 international meeting in Japan, the Buddhist Think Sangha defined consumerism further as
the dominant culture of a modernizing invasive industrialism which stimulates—yet can never satisfy—the urge for a strong sense of self to overlay the angst and sense of lack in the human condition. As a result, goods, services, and experiences are consumed beyond any reasonable need. This undermines the ecosystem, the quality of life, and particularly traditional cultures and communities and the possibility of spiritual liberation.
British cultural theorists Yiannis Gabriel and Tim Lang identify five understandings of "consumerism," which reveal its complexity in sociocultural discourse. It can be seen as (1) a moral doctrine for developed countries—the vehicle to freedom and power as well as happiness; (2) a social ideology for establishing class distinctions; (3) an economic ideology for global development (in contrast to the austerity of communism); (4) a political ideology, with the modern state protecting transnational corporations; and (5) a social movement promoting the rights of consumers.
Consumption per se is not inherently problematic. Everyone must consume to survive. But when it becomes an end in itself or the primary measure of economic success, then it overruns other social goals of well-being. Looking back to some of the origins of today's consumerism, historian Peter Stearns describes the consumer society of mid-nineteenth-century Europe, where the commercial economy was developing rapidly. Trade with global colonies sparked interest in cotton from India and porcelain from China. Small shops and markets took up the practice of advertising to promote a range of personal products from perfume to parasols. With increased prosperity from expanded trade, especially the slave trade, more goods were sold for profit. The rationalist philosophy of the time reinforced secular values, undercutting the importance of traditional religious values of restraint and frugality.
In the early years of the United States, consumerism was slow to take off because of the financial struggle for independence and the strong Puritan values. But once the country stabilized and manufacturing expanded, an explosion of consumer goods entered the marketplace. The first department stores with their wide array of products and changing fashions were all the rage. Agencies dedicated specifically to advertising developed persuasive techniques to help producers compete effectively. With the invention of radio, and later television, advertisers spread their gospel far and wide.
The consumer society we know today took shape in the 1920s with the emergence of brand names and packaged, processed foods for a growing urban culture. Economists deemed mass consumption beyond basic needs as key to U.S. economic and political success. Supporting the economy was (and still is) touted as a patriotic duty. Though consumption slowed temporarily during the Great Depression and World War II, after the war the boom was on. Inspired by the stunning success of wartime production, government leaders expanded their vision of the United States as a major world economic leader. President Dwight Eisenhower's chief economic advisor proclaimed that the ultimate purpose of the American economy was "to produce more consumer goods."
Since the 1950s, a significant factor driving consumption has been the steady commercialization of the household economy. In earlier times, people managed their own cooking, gardening, food storage, laundry, and clothes making. As women shifted into the labor market, these functions shifted into the money economy. Business soared in fast food, household appliances, and ready-made clothing. With the advent of efficient shipping and globalized trade, consumerism spread beyond the borders of the industrialized countries. Coca-Cola products are now found in more than 170 countries; McDonald's opens two thousand new restaurants each day somewhere in the world. As the values and structures of this wave of consumerism have spread around the globe, they have been met with both fascination and resistance. People in Japan took rapid adoption of Western goods as a sign of modernization, releasing them from two hundred years of isolation. People in the Middle East, in contrast, targeted consumerism as a threat to Islamic moral and social principles.
What makes the current wave of consumerism distinct from previous eras is that it encompasses the entire world community and gravely threatens the future health of the planet. The ecological consequences of manufacturing, waste, and global trade now affect every region and country. Environmental or social impacts in one region multiply in cascading complexity as products travel around the world to expanding markets. The pace of economic globalization over the last decade has accelerated so rapidly it is impossible even to keep track of all the changes. It seems that affluenza has penetrated every reach of the globe.
SCOPE OF IMPACT
What exactly does this global consumption look like on the ground? Let's take an example that illustrates the far-reaching impacts of North American consumption—our beloved coffee. Say the average person drinks two cups a day. A year's worth of coffee is about eighteen pounds of beans per year, which requires twelve coffee trees along with eleven pounds of fertilizer and pesticides. In the processing, forty pounds of coffee pulp are released into rivers, consuming life-supporting oxygen as they decompose. The beans travel to the United States and are roasted using natural gas. After being packed in multilayer bags, they are shipped by trucks (getting six miles to the gallon) to a regional warehouse. Coffee is the second-leading export crop in the world after oil and is the second-largest source of foreign income for developing nations. In the cool highlands of Costa Rica, Brazil, and Colombia, thousands of acres of biologically rich tropical forest have been cleared to support the North American boom in espresso shops.
What about the other items on our breakfast table? Orange juice from Brazil, grapes from Chile, apples from New Zealand, cocoa from Malaysia, bananas from Costa Rica—all of these appear at the supermarket with production and shipping costs virtually invisible. An average bite of American food travels more than twelve hundred miles from field to fork. Food processing, packaging, distribution, and storage in the United States use 17 percent of all energy consumption, and food packaging makes up 20 percent of municipal solid waste. More than 6.5 million tons of food travel around the earth each year, with global markets competing for consumers' dollars. This unfortunately leads producers to cut costs, raising the hazards of food-borne disease. The global consumer class eats the lion's share of the world's meat and consumes in one form or another 40 percent of the world's grain.
Indicators show that the consumer class is responsible for most of the environmental impact on the planet. Industrial nations use 62 percent of the world's oil, with the United States' oil use alone increasing over the last ten years by 2.7 million barrels a day. Though Americans comprise less than 5 percent of the earth's people, they produce 25 percent of greenhouse gas emissions. The global consumer class is responsible for 90 percent of the chlorofluorocarbons destroying the ozone layer and 96 percent of the world's radioactive waste. Per capita fossil fuel use is conspicuously highest for people in the United States. The total number of cars in the world has gone from 50 million in 1950 to 500 million in 1990 and is projected to double again by 2015.
Today the picture is changing dramatically as more and more of the world joins the consumer class. Of the estimated 1.7 billion members of the consumer class, nearly half are now in the developing world. China, for example, added eleven thousand more cars to its streets every day in 2003. In India the film and electronics industries are growing rapidly, supplying economic support for a consumer lifestyle. Together China and India's consumer class is 20 percent of the world total, larger than the entire consumer class of western Europe. If the average Chinese consumer increased his or her energy budget to American levels, China would need 90 million barrels of oil each day—11 million more than were even produced each day in 2001 for all the world's consumers.
As the global consumer class grows, so does consumer waste. Americans remain the waste champions, producing 51 percent more waste per person than any other industrialized nation. Certain product waste streams are growing at an astonishing rate, especially electronic waste. By 2005 the global collection of used cell phones may top 500 million, most destined for landfills. Obsolete computers are an even greater challenge, with more than half a billion sold in 2002. Electronic waste is the source of 70 percent of the heavy metals found in U.S. landfills. Many computers are recycled to China as part of the toxics trade flow, with workers picking through parts by hand for anything of value.
Environmental impacts alone are reason enough to challenge the explosion of global consumerism. But social, psychological, and human health are also strongly affected by consumer values and priorities. Mass-marketing techniques perfected in the United States are now employed on every continent, impacting local values and eroding cultural self-esteem. Helena Norberg-Hodge has documented the rapid erosion of local values in Ladakh and Bhutan. Contact with goods from outside the culture has dramatically increased the desire to buy them. In a very short time, local people have come to see their internal standards of value as secondary to the high status represented by American goods. Industrial-scale, chemically dependent cash-cropping systems have replaced locally adapted agricultural practices in order to supply consumer goods. For Norberg-Hodge, economic globalization is establishing a social monoculture, destroying cultural as well as ecological diversity in its wake.
Psychological effects may be harder to measure, but David Loy and others suggest that the drive to consume has displaced the psychic space once filled by religion, family, and community. More time spent on personal lifestyle pleasures tends to mean less time spent in civic engagement and public life. Kalle Lasn, author of _Culture Jam_ , speaks of "microjolts of commercial pollution" that flood our brains—about three thousand marketing messages per day. "Every day, an estimated 12 billion display ads, 3 million radio commercials, and more than 200,000 TV commercials are dumped into North Americans' collective unconscious." Around the world, dollars spent on advertising reached $446 billion in 2002. Advertisers will now go everywhere and anywhere to sell their products, even printing logos on hot dogs and eggs! With competition so fierce for the consumer dollar, people are barraged by sales pitches on subways, at cash registers, in airports, and on ski lifts. Even if they forget the ad, they entrain the message: There is a product to solve life's every problem.
Advertising deliberately promotes a climate of self-centeredness revolving around material desires, setting up stereotypes that foster greed, status envy, hyperstimulation, and at root, a sense of psychological dissatisfaction and inadequacy. Children are particularly vulnerable to commercial brainwashing, easily replacing their authentic needs and wants with what they've been told to want. It is not uncommon for people to turn to shopping to alleviate their suffering. If this becomes a deeply entrenched habit, they become "shopaholics," caught in a cycle of desire and dissatisfaction.
Author Bill McKibben once did the experiment of watching every minute of television that was aired on a single day by the largest cable system at the time. He concluded that the central theme, repeated on ad after ad, was this: "You are the most important thing on earth." Can this really be the primary orientation of our times? In place of caring for others, look out for yourself. Instead of communing with God or nature, surf the shopping channel. McKibben calls this "I-dolatry," the extreme self-referencing fostered by the profiteers of consumerism.
Understandably, psychic numbing and depression are not uncommon among those afflicted with affluenza. Physical as well as mental diseases of consumption are on the rise. Being a member of an affluent society is correlated with high rates of heart disease, cancer, and diabetes. More than a billion people worldwide are now overweight or obese. Though consumerism offers many attractive opportunities for pleasure and comfort, its hidden shadow is now becoming alarmingly visible.
ROLE FOR RELIGION
What is the role for religion in responding to this state of affairs? How should religious leaders and institutions engage the moral dimensions of consumerism? For some denominations, the environmental crisis has served as a wake-up call, inspiring study groups and greening projects. Others raise issues of global inequity, the condition of the poor, the driving presence of greed in the world economy. Religions have historically played an important role in raising fundamental questions about the quality and meaning of life. Over the last decade there has been increasing scholarly attention as well as activism addressing environmental issues from a religious perspective. The Center for a New American Dream, among others, has developed specific projects addressing the moral concerns related to consumerism.
Gary Gardner, Worldwatch Institute researcher, points to five significant assets religions can contribute to the global dialogue on environment (and consumerism). For one, religions wield considerable moral authority, both in their own pulpits and in some political arenas. They have, as a body, a very large membership base and extensive material resources (both financial and real estate) that can be engaged to raise awareness. They are also a strong influence in shaping worldviews and would be supportive in questioning consumerist ideology from more deeply rooted values. Perhaps their greatest asset is the religious capacity for building community and social capital. Some of the most intractable aspects of consumerism will be dislodged only through creating better infrastructures for well-being. Religiously based communities hold great potential for leading the way.
Consumer resistance movements have almost always been morally driven. Gandhi promoted the values of frugality and local production, urging his followers to boycott British goods. The Japanese consumer co-op movement resisted the government's plan to import U.S. rice, defending the values of self-sufficiency. When Ralph Nader took on the automobile industry, he challenged the collusion and secrecy behind commercial interests. Recent resistance movements have taken up ethical issues related to environmental protection and fair trade. First World consumers have found ways to join in solidarity with Third World producers, offering moral alternatives to sweatshop clothing and unfair trade pressures. Activist campaigns questioning bioengineered crops have catalyzed a storm of global doubt, slowing consumer acceptance of genetically engineered products. By engaging the moral issues involved in these concerns, religious institutions could expand citizen participation considerably, advancing both knowledge and moral integrity.
Given these possibilities, is there a particular role for Buddhism to play? To date, Buddhist initiatives in this conversation have been modest. Several books have popularized Buddhist values of simplicity and restraint, most notably E. F. Schumacher's _Small Is Beautiful_ and Gary Snyder's _The Practice of the Wild_. Some Western Buddhist teachers have taken up particular themes relating to consumption—Philip Kapleau on vegetarianism and Robert Aitken on reducing wants and needs. Thich Nhat Hanh has expanded the fifth precept (no abuse of delusion-producing substances) to include junk television, advertising, magazines, and candy. Among scholars, Rita Gross has explored Buddhist positions regarding population, consumption, and the environment. Leading Thai intellectual Phra Payutto has written on Buddhist economics; activist Sulak Sivaraksa has advocated Buddhist principles of compassion and skillful means in economic development. Philosopher David Loy has addressed poverty, greed, and the driving psychology of "lack" as it plays out in consumerism.
As I have worked with authors on the chapters in this book, it has become more and more clear that Buddhism offers many useful and compelling paths for unlearning consumerism. Buddhist philosophy begins with the deep grasp of suffering as the fundamental ground of existence. This opens the way for examining the wide scope of suffering related to consumerism—for people certainly, but also for plants and animals, mountains and rivers. Suffering or fear of suffering (economically or politically) can also be seen as driving the actions and policies of nation-states. The suffering takes countless forms at many levels, from individual to structural systems. Because consumerism is a completely human phenomenon, every aspect of it reflects human fallibility and suffering.
Looking to the causes of suffering, the Buddhist approach focuses on desire or craving: "Desires are endless, I vow to put an end to them." This line in a Zen chant indicates the comprehensive scope of desire—for things, states of mind, preferences, and above all, the desire for relief from suffering. This is the condition of life, a driving force of our basic animal existence. We may think that consumerism is to blame for making our lives miserable, but actually our lives are already filled with suffering. Consumerism only magnifies this condition by multiplying desire.
Perhaps the most useful of the Buddhist teachings is the insight into the emptiness of the ego self. This view holds the key to releasing attachment to the constant self-inflating messages of consumerism. From a Buddhist perspective, what we perceive as the individual self is actually a fleeting aggregation of form and energy, shaped by countless causes and conditions. Believing in an autonomous independent self is a serious delusion in this view. Buddhist practice helps in breaking through the multiple reinforcing beliefs and activities that reify the false self. Many time-proven techniques have been developed to work with the persistent habits of mind that protect this self. Koans, meditation, visualizations, monastic training all provide opportunities for unraveling these false views. With hooks at every turn, consumerism presents a remarkably rich field for practice.
Seeing this teaching of emptiness from the other side, we find another useful Buddhist perspective—the law of interdependence. If all existence is shaped by causes and conditions, we can study the nature of those conditions and see how they interrelate. The Buddhist view shifts emphasis from objects or beings to the relationships that form them. A relational worldview is not unique to Buddhism, but coupled with emptiness, it becomes a powerful tool for dismantling the structures of consumerism. The many examples in this book show how this relational understanding can support ethical restraint and fruitful inquiry. It can also point the way to creating alternatives to consumerism, making new links of codependence that support well-being over material wealth.
It would be misleading to imply that Buddhism has all the answers. It certainly doesn't. Many have criticized Buddhism for being weak on structural analysis of social systems (such as consumerism) and equally weak on activist strategies for social change. Buddhism does not carry the great charge for social justice, for example, that the Abrahamic traditions hold. It is an open question whether Buddhism can be a force for social change regarding consumerism. It may be that the greatest Buddhist contribution to this arena will be at the individual level, helping people evaluate lifestyle and consumer choices. But there are some fledgling examples in Japan and Thailand that show what is possible when Buddhist leadership and teaching are engaged.
This book arose out of my own concern that accelerating levels of consumption have gone way beyond any intelligent limits of sustainability. No one is steering the planetary ship; instead all parties seem bent on pursuing their own short-term individual goals. How to work with such a planet-sized koan? I knew I could not penetrate the puzzle on my own enough to make a difference. But I thought Buddhism might offer some handholds, some time-tested teachings to temper the raging appetites around the globe.
The work in this book builds on several earlier collections of readings on Buddhism and ecology. The most recent of these, _Dharma Rain_ , laid out a broad range of published texts, commentaries, and personal explorations that frame an introduction to Buddhist sources of environmentalism. I wanted to follow up on this with some fresh thinking, what might be called "constructive theology" in Christian terms. What new light could experienced Buddhist thinkers bring to the rascally problems of consumerism? I looked for Buddhist teachers, scholars, and practitioners who shared some of my concern for the environment and who were interested in bringing their bright minds to this arena of environmental thought. I asked them each to follow their own strongest leads, drawing on the teachings they knew best. It was important to me that this book reflect Theravada, Zen, Tibetan, and Pure Land views to show how each tradition might work with consumerism.
I felt a Buddhist nonjudgmental perspective could be very helpful in looking deeply at the complex conundrum of consumerism. Evangelical anticonsumerism messages tend to be simplistic and often don't advance the conversation much at all. I really wanted to know in the biggest sense: What is going on here? How deeply can we look, accepting fully that we are all in the soup together? As I worked with the authors, we taught each other in the editing process, refining insights and clarifying the specific elements of Buddhist thought that offer skillful means for understanding. Though many topics have been addressed here, we sense we have just scratched the surface of this Big Conversation.
The book is organized into three sections, with five or six essays in each section. The first section, "Getting Hooked: Desire and Attachment," contains pieces that describe in Buddhist terms what is actually going on in the process of consumption. The authors look at greed, delusion, and attachment, showing how the common phenomenon of "being hooked" illuminates ego clinging. The second section, "Practicing with Desire: Using Buddhist Tools," contains essays that explain Buddhist methods for working with desire or craving and the urge to consume. This includes the Four Noble Truths, the Three Refuges, the Twelve Links of Codependent Origination, causal analysis, the Middle Way, and Dogen's being-time sutra. The third section, "Buddhist Ethics of Consumption," focuses on particular Buddhist principles or virtues that might be useful in developing Buddhist guidelines for consumer choices. These essays draw on classic texts and current initiatives to lift up Buddhist values such as simplicity, frugality, generosity, and nonharming.
My hope for the book is that it provides many springboards for conversation—for Buddhists and non-Buddhists alike. For activists working in the field, I hope these essays will support your own quest for moral direction in the work. For students of Buddhism, I hope this writing will add to your understanding of Buddhism in the everyday world. For all those interested in the speeding train of consumerism, I hope this book adds to your capacity for preventing a disastrous train wreck!
The authors of these pieces have been generous and gracious through every step of the process with me. I deeply appreciate their willingness to work with my editing suggestions with an open mind. They each took great care in crafting their essays, speaking strongly from personal practice experience and knowledge of Buddhist teachings. They have given their best good-faith effort in preparing these essays; all errors that remain are fully my own.
PART ONE
Getting Hooked
Desire and Attachment
1
Desire, Delusion, and DVDs
Joseph Goldstein
SOME TIME AGO, His Holiness the Dalai Lama was giving a series of teachings in Los Angeles. Every day on his way from the hotel to where he was speaking, he was driven down a particular street filled with people selling all the latest high-tech gadgets. At first he just looked with interest at the different things in the windows as he passed by. By the end of the week, he found himself wanting things even though he didn't know what they were! Desire is _very_ strong. It is hardwired into our biology as part of what helps us survive. If even the Dalai Lama sees wanting arise in the mind, we know this is not trivial conditioning.
In the early years of my practice, as I sat in Bodh Gaya with my teacher, Anagarika Munindra, he would often speak of the difficulty of escaping the gravitational field of the world of sense pleasures. Our lives seem to revolve around desire for ever-new experiences, even as we see how fleeting they are. All the things we gather in our lives will inevitably be dispersed. Either we lose interest in them (as so often happens), or they break, or they remain in the corner of some closet until we move or die. Yet the tendency toward accumulation is very strong. Our homes somehow keep filling with stuff.
Covetousness, the wanting mind, the feeling that we never have enough, is seen in Buddhism as unskillful action of the mind. In the framework of the Buddhist cosmology and the different realms of existence, this covetous mind state is most extreme in the hungry-ghost realm. Hungry ghosts are often depicted as having huge stomachs and pinhole mouths, showing how they are incapable of ever feeling satisfied. In our own culture, we might call it "catalog consciousness," obsessively rifling through the pages to see what else we might want. This is "wanting to want," a disease our culture keeps nourishing.
Why do we invest so much energy in acquisition? There may be many psychological underpinnings of this behavior, seeing it as compensatory action, even at times compulsion for some deeper lack. But we can also understand the force behind this habit of accumulation in a simpler way, namely, the profound influence our consumer society has on our minds. It continually reinforces desires and wanting, often co-opting spiritual values to do so. One of the examples I use a lot in talking about desire is a magazine advertisement for a fancy SUV. There on the glossy page is a view of a beautiful couple in front of their expensive car, surrounded by hundreds of objects, all supposedly contributing to their happiness. The caption on the ad reads, "To be one with everything, you need one of everything."
The wonderful paradox of the spiritual path is that transitory phenomena as objects of our desire leave us feeling unfulfilled, while as objects of mindfulness they can become vehicles of awakening. When we try to possess and hold on to things or experiences that are fleeting in nature, we are left feeling finally unsatisfied. Yet when we look with mindful attention at the constantly changing nature of these same things or experiences, we are no longer quite so driven by the thirst of desire. By mindfulness, I mean the quality of paying full attention to the moment, opening to the truth of change and impermanence. We all know that things change, but how many of us live and act from that place of understanding? The more deeply we can see the impermanent nature of reality, the less seduced we are by impermanent phenomena such as consumer goods.
Mindfulness training keeps us focused in a very precise way on the law of dependent origination. Through paying close attention, we can follow the links of how we get caught in desire—sensing, contact, feelings, desire, grasping, and so on. To be released from this chain of dependent origination, we can work to break the connection between feelings and desire. Each link depends on the others; if any of the conditions cease to exist, the entire cycle of desire is disrupted. We can observe the conditioning of contact, noting the feeling of pleasantness, and then stay mindful of that feeling.
One of the things I discovered in my own practice, which speaks to my relation to consumerism, was how desire works on very subtle levels. For example, when I'm on retreat and I find myself desiring a cup of tea, I might be inclined to get up and gratify that desire. This is because I am focusing strongly on the object of my wanting, the cup of tea. But if I shift my focus from the object to the anticipated feeling of satisfaction, I can be aware that it is the pleasant feelings associated with the tea that are really what I am after. It is then much easier to remember that these feelings are fleeting. Remembering this impermanence, I am less hooked by the object of desire. If we focus on the object, which appears to be more real, it is harder to resist the desire; we are more fooled by the apparent substantiality of the object and less able to see its impermanence. When we focus on the feelings, we have a greater chance of remembering the impermanent nature of feeling, thus breaking the link that generates the wanting. Still, the habit pattern of wanting is very strong.
Some might say that the primary emotional motivator for consumerism is greed. But this greed is itself born from delusion. Delusion is characterized by confusion, bewilderment, by not seeing things as they are. We call this delusion of mind "ignorance." A central focus of Buddhist teaching is the suffering that comes from delusion or ignorance, the delusion of holding a fundamentally wrong view. Greed is fed by one particularly strong aspect of delusion, namely, the delusion of a separate, independently existing self. The big question for the Buddha was how to awaken from this ignorance.
We usually think of self-centeredness as a personality problem, something our friends might suggest we go to therapy for. But _self-centered_ has a more fundamental meaning. Self-centeredness occurs when we create or hold a sense of self at the center of our lives, a reference point for all we think and sense and feel. The self-center is the idea or felt sense of someone behind all experience to whom it is happening. Most of us live in the powerful field of this self-center, circling around our hopes and fears, our plans and worries, our work and relationships, and our multitude of possessions.
There are many different descriptions of awakening, but all Buddhist traditions converge in one understanding of what liberates the mind. The Buddha expressed it clearly and unequivocally: "Nothing whatsoever is to be clung to as 'I' or 'mine.' Whoever has heard this truth has heard all the Teachings, whoever practices this truth has practiced all the Teachings, whoever has realized this truth has realized all the Teachings." This is the essential unifying experience of freedom—the heart of liberation: nothing whatsoever is to be clung to as "I" or "mine." Our unfolding experience keeps changing—sometimes it is pleasant, sometimes unpleasant—but the practice of freedom is always the same, namely liberation through nonclinging.
The Buddha pointed out the major arenas of attachment, in both our meditation practice and our daily lives. We can investigate these attachments in our minds, learn how to let them go, and thus practice the mind of freedom. The attachment of pleasant feelings reveals a lot about the power of addiction, fascination, and enchantment. Thus we have my wanting that cup of tea on retreat, or wanting the pleasant feelings it might generate. On a deeper level, we can cling to pleasant experiences in meditation, feelings of great rapture, calm, happiness, and peace.
We can also become quite attached to our opinions and views about things, attached to being right. Clinging to views is subtler than attachments to sense pleasures, which, though they run deep, are usually not difficult to notice. But the views and opinions we hold are often difficult to see, even though they determine how we perceive the world. Attachment or clinging to views, even if they are worthy or just, can create problems and actually be counterproductive. People involved in critiquing consumerism, for example, can be quite attached to their perspectives, attacking others for their actions and differing points of view. This is not good for one's own mental health and is not necessarily the most effective strategy for social change. Nobody wants to hear a diatribe. The energy of that is very draining. In the name of letting go of consumer objects, the critics are actually holding on to views. I think a careful distinction could be drawn here between attachment and commitment. We can be totally committed to social or political change and still keep our minds and hearts open and inclusive.
The deepest attachment that conditions our lives and understanding is the clinging to the concept of self. Whenever we identify with any particular aspect of our experience, we create a felt sense of self. There are many examples of this. We see this clearly in the relationship we have to our bodies and all that we buy to keep them beautiful, healthy, youthful. This body, which we hold and cherish, seems to define our root answer to the question "Who am I?" It is reflected in our fear of death and resistance to aging. We also create a sense of self when we identify with thoughts or when we identify with the stories we make up about our experience. Thoughts are tremendously seductive. When they go unnoticed, they have compelling power; they become the dictators of the mind. Thoughts of the new car we want or the bigger house we must have can carry great weight in determining our actions.
LIBERATION THROUGH NONCLINGING
Although renunciation is a central aspect of the Buddha's teachings, many of us in the West have a difficult time with this idea. Renunciation is not a particularly appreciated cultural value. And even if we are somewhat aware of its value, it may not be all that inspiring. In Saint Augustine's famous prayer, he says "Dear Lord, make me chaste, but not yet." But another way of talking about renunciation is through understanding it as "nonaddiction." Whereas "renunciation" feels like a burden or sense of deprivation, "nonaddiction" implies freedom, which is something all of us want. Using familiar language and awareness about addiction, we can investigate addictions to food, television, to consuming itself. This language helps to identify the problem and suggests the possibility of freedom.
From a Buddhist perspective (not necessarily an economic one), the basic renunciation is internal. In the Buddha's time there were many wealthy people living the good life of that era, who were able through practice to achieve some understanding of the nature of desire. Unless one chooses the monastic path, I don't think it is essential to give up a comfortable lifestyle in order to practice renunciation. The inner work is in letting go, in the renunciation of the wandering mind, of afflictive emotions, of the idea of self. The Buddha taught people in a wide range of lifestyles, from kings to paupers. In one teaching he said that it is better to live in a palace and be free of desire than to be in a cave consumed by the wanting mind. Often the issue was excess, not the consuming itself. At one point the Buddha counseled a king who was a glutton. The Buddha spoke with him about the importance of letting go of that addiction for his own health and well-being. When addiction results in excess, renunciation offers a route to freedom.
Meditative retreat situations provide some support for reducing consumer urges. People come on retreats for many reasons, one being to destress from work, relationships, or personal problems. Consumerism is not usually at the top of their list of concerns. Those who come to Buddhist centers tend to be already preselected for values congruent with reduced consumerism. But even if it is not why they came on retreat, people often find huge relief in being in a situation that doesn't feed the wanting. On retreat they are able to temporarily experience the ease and simplicity of monastic life. That was one of the great things about living in India all those years; we were just living so simply. We all had very little money, and we kept our wants to basic needs. But even in this narrow field, the consuming mind could still wonder—"Oh, where can I get a nice shawl?" Generally people seem to appreciate being in a place where there is not much opportunity to consume.
Silence is another strong support for weakening greed. With relatively little eye contact and no talking, people feel less need to present themselves to other people. The whole self-image machine goes into slow motion. At the Insight Meditation Society (IMS) center there is nothing to buy, no bookstore, no vending machines—there are very few distractions. Yogis are encouraged to stay on the grounds and avoid whatever few consumerist temptations there are in a small New England town. Still, some do wander off in search of a hamburger, or whatever it is they think they need.
Our center, like a number of others, is in a rural setting, so people often do walking meditation out in nature, calmed by the trees and the land. This also helps tame the acquiring mind. When you're out in nature, you are just present with what is there; you feel less need for something to consume. On the three-month fall retreats, being outside is an especially strong support for renunciation. As the leaves turn and the season settles in toward winter, it is a very inner-directed time of year.
Buddhist centers can also be very useful in helping people clarify their motivations. For me, this is an essential aspect of practice and understanding. A Tibetan phrase expresses it well: "Everything rests on the tip of motivation." There is a significant difference, both in how we feel and in the effect on others, between actions motivated by greed and those motivated by generosity—even when the outward action appears to be the same. The consequences of each motivation will be very different, both in the moment and in the long run. Given the importance of motivation in affecting the results of our actions, it becomes essential that we actually know what our motivations are. This is not easy. If we stay unaware, we simply play out all the habits of our conditioning, including the way we have been conditioned as consumers.
People who come on retreat can study their motivations deliberately and then use this capacity in the world to clarify their reasons for action. Motivation can be very subtle and thus can benefit from awareness training. It takes a lot of practice to look closely at our intentions. Most of us tend to think that basically our motivations are pure, but it is much more complex than that. More often they are mixed, conflicting, ambiguous. This applies to most acts of buying, but really it applies to everything. Media and marketers promoting consumerist messages can play on these mixed motivations and highlight particular internal messages, in effect giving them more air-time. This then makes it harder to recognize and connect with other motivations that may be driven into the background beneath those loudspeakers. I feel that meditation retreats are essential just to give people a chance to study their motivation and develop some clarity that can help them when they return to a more complicated world.
Commitment to Buddhist practice does not necessarily require a radical change in lifestyle. But it may suggest a change in our time allocation that reflects a shift of priorities. People are often amazed that almost one hundred people have been coming each year to the three-month retreats at IMS. They wonder, how do they get the time to do that? When something becomes a very high priority, people figure it out and find the time, even if it takes several years of planning. In general though, after meditation retreats, even highly committed Buddhists continue to live in the way they're accustomed to. It is very unusual to see students simplify their lives drastically, give away all their belongings and savings, and become monks or nuns, although I have seen this happen. Even short of such a level of letting go, everyone can cultivate renunciation in the form of practicing greater generosity.
The practice of generosity can serve as a corrective to addictive consumerism. Generosity enacts the quality of nongreed; it is a willingness to give, to share, to let go. It may be the giving of time, energy, resources, love, and even in rare cases, one's own life for the benefit and welfare of others. Generosity weakens the tendency of attachment and grasping and is intimately connected with the feeling of lovingkindness. People who experience the power and joy of generosity will also experience its effect on consuming. The cultivation of generosity offers a very strong antidote to the wanting mind and would be a powerful corrective if taken up in a widespread way across our culture.
REDUCING HARM
So we can ask the question: Within our culture, what constitutes excess? Are we consuming much more than we actually need—even if we are not leading a renunciate lifestyle? We can also ask, what is excess in the context of our culture within the global economy? These are two different questions, for what may appear to be commonplace or moderate in most homes in America would be seen as excess in the context of the global economy. We can use these questions either as bludgeons of self-judgment or as thoughtful inquiry into our lives and the choices we make, including our choice of what to consume. Recently I purchased a DVD player. But since I already had a perfectly good VCR, was buying the DVD excessive? Does it represent greed? It may be completely ordinary in many American households, but do I need it? These are questions that are, at the least, worth asking.
In order to survive, we have to consume, but by what guidelines do we choose what and how much? The first and most fundamental principle to apply is nonharming. Often this becomes a matter of education. People don't usually know what harm is caused by the products they use or which brand is most harmful. I have heard of a project in the making that could be helpful in this regard. Someone is developing a reference tool, somewhat like a palm pilot in design, that could call up product information from a computerized network as you shop. You could plug in "Cheerios" and it would tell you the social and environmental impacts of producing this cereal. This would give you some basis for your decision; otherwise you just don't know. It would be the equivalent of the guidebooks published by Coop America and others that evaluate products for relative degree of harm and social responsibility. This could significantly raise the level of awareness for a shopper concerned about nonharming.
Sometimes we know something is harmful, but we don't know it deeply enough. There is a great need for education here, similar to the educational process in this country about smoking. For years people knew smoking was unhealthy, but it took years and years of repeating the message to generate society-wide levels of understanding. It required a certain critical mass with a consistency of behavior across society to start changing things. People may know what is good to do, but until understanding reaches some critical mass, social behavior probably won't change.
Let's look at these criteria in relation to what we literally consume, that is, our food. Debates about this have been alive as far back as the time of the Buddha. One monk in the early sangha (the Buddhist community of followers) urged the Buddha to make a rule saying all monks should be vegetarian. Instead, based on his own experience, the Buddha found the middle way between extremes of self-indulgence and unnecessary austerity. He recognized that within certain guidelines, it was important for the monks to accept any food offering as they went on their alms rounds. They were not to ask that an animal be killed for their food or accept meat if an animal had been killed especially for them. But if a family was sharing what they had cooked for themselves, then it was all right for the monks to receive it.
How do we apply this in our culture today, where food is neatly packaged in the market and there is not much connection with its source? Some people who recognize the harm in raising and slaughtering beef refrain from eating meat. Others for health reasons may need to eat meat. Some people, such as those in many native cultures, embrace the larger cycles of birth and death in nature and act from that understanding. There is no one right answer to this question of what to eat. Our task is to investigate different options, not holding the taking of life lightly, and with whatever we consume to maintain a heart of compassion.
We can extend the questions from consumer products to the consciousness produced by consuming. Even if something does not appear to harm the environment or those who make the product, does it still harm the purchaser or consumer in some way? Once a visiting teacher asked me to check out all the most gruesome videos I could find for him. Although I found the request rather strange, he said the videos provided a way for him to consciously put himself in disturbing situations to see if he could stay free within them. Rightly done, this could be a very strong practice in developing equanimity. Of course, it would also be very easy to rationalize more unwholesome motivation. In more ordinary modes of shopping or consuming, we can watch what is happening in our own minds. If we can bring mindfulness to this arena, then it allows us to make wise choices.
Should Buddhist teachers do more in addressing consumerism as an important current issue? There is a wide range of engagement with this topic among Buddhist teachers. Some address the issues of consumerism and its impact on society very directly; others talk more about understanding the nature and power of desire in the mind. As with all areas of social concern, the more information we have, the wiser our deliberations will be. So a great challenge is finding ways to make this information more available.
One point, though, that I would like to emphasize is the understanding that there is not a hierarchy of compassionate action in the world. Somebody meditating in a cave for years working for enlightenment is as much an activist as somebody out there fighting overconsumption and waste. This is not always obvious to people. If you think of the Buddha's past lives and then take a snapshot of just one life as a monk meditating in the forest, one might well ask, how was he helping the world? But if we see that one life in the context of his whole journey of awakening and all the compassionate action that followed from that awakening, then we get a fuller picture. The key is motivation; it is not the action itself, because there is a wide range of compassionate action possible, some of which will look like compassion and some of which will not. What is important is the motivation behind what someone is doing and how free his or her mind is in doing it.
Mindfulness is the foundation of understanding. It contributes to wise attention and helps us distinguish what is skillful action from what is unskillful. Without mindfulness, we don't know what our minds are doing or what the effects of our actions will be. As we bring awareness to our lives in the world, we discover on deeper and deeper levels the nature of desire and wanting, the implications of consumer consciousness, and the suffering of attachment. Yet it is right here in every moment of wanting that we find the possibilities of greater freedom.
2
How We Get Hooked, How We Get Unhooked
Pema Chödrön
_This essay was delivered originally as a teaching on the process of attachment. In it, Pema Chödrön addresses how habits and addictions are cumulative forms of attachment protecting us from the insecurity of living in a changing world. Although she is not addressing consumerism directly, her comments offer useful Buddhist teachings on the fundamental processes at work around desire and craving. She explains how refraining from being hooked can open up the possibility for wisdom to arise, allowing more spaciousness in dealing with ourselves and others. With practice, this wisdom becomes a stronger force than attachment, helping us practice goodness and equanimity, Buddhist virtues that counteract the values of consumerism_.
YOU ARE TRYING to make a point with a co-worker or your partner. At one moment her face is open and she is listening, and at the next, her eyes cloud over or her jaw tenses. What is it that you're seeing? Someone criticizes you. They criticize your work or your appearance or your child. At moments like that, what is it you feel? It has a familiar taste in your mouth, it has a familiar smell. Once you begin to notice it, you feel as if this experience has been happening forever. The Tibetan word for this is _shenpa_. It is usually translated "attachment," but a more descriptive translation might be "hooked." When _shenpa_ hooks us, we are likely to get stuck. We could call _shenpa_ "that sticky feeling." It is an everyday experience. Even a spot on your new sweater can take you there. At the subtlest level, we feel a tightening, a tensing, a sense of closing down. Then we feel a sense of withdrawing, of not wanting to be where we are. That is the hooked quality. That tight feeling has the power to hook us into self-denigration, blame, anger, jealousy, and other emotions that lead to words and actions that end up poisoning us.
Do you remember the fairy tale in which toads hop out of the princess's mouth whenever she starts to say mean words? That is how being hooked can feel. Yet we don't stop—we can't stop—because we are in the habit of associating whatever we are doing with relief from our own discomfort. This is the _shenpa_ syndrome. The word _attachment_ doesn't quite translate what is happening. It is a quality of experience that's not easy to describe but that everyone knows well. _Shenpa_ is usually involuntary, and it gets right to the root of why we suffer.
Someone looks at us in a certain way, or we hear a certain song, we smell a certain smell, we walk into a certain room, and _boom_. The feeling may have nothing to do with the present, and nevertheless, there it is. When we were practicing recognizing _shenpa_ at Gampo Abbey, we discovered that some of us could feel it even when a particular person simply sat down next to us at the dining table.
_Shenpa_ thrives on the underlying insecurity of living in a world that is always changing. We experience this insecurity as a background of slight unease or restlessness. We all want some kind of relief from that unease, so we turn to what we enjoy—food, alcohol, drugs, sex, work, or shopping. In moderation what we enjoy might be very delightful. We can appreciate its taste and its presence in our life. But when we empower it with the idea that it will bring us comfort, that it will remove our unease, we get hooked.
We could also call _shenpa_ "the urge"—the urge to smoke that cigarette, to overeat, to have another drink, to indulge our addiction, whatever it is. Sometimes _shenpa_ is so strong that we are willing to die getting this short-term symptomatic relief. The momentum behind the urge or craving is so strong that we never pull out of the habitual pattern of turning to poison for comfort. It does not necessarily have to involve a substance or a particular thing; it can be saying thoughtless words or approaching everything with a comparing mind. That is a major hook. Something triggers an old pattern we would rather not feel, and we tighten up and hook into comparing or criticizing. This gives us a puffed-up satisfaction and a feeling of control that provides short-term relief from uneasiness.
Those of us with strong addictions know that working with habitual patterns begins with the willingness to fully acknowledge our urge, and then the willingness _not_ to act on it. This business of not acting out is called refraining. Traditionally it is known as renunciation. What we renounce or refrain from is not food, things, sex, or relationships per se. We renounce and refrain from the _shenpa_. When we talk about refraining from _shenpa_ , we do not mean trying to cast it out; we mean trying to see the _shenpa_ clearly and experiencing it. If we can see _shenpa_ just as we are starting to close down, when we feel the tightening, then the possibility exists to catch the urge to do the habitual thing and to choose not to do it.
Without meditation practice, this is almost impossible. Generally we don't catch the tightening until we have indulged the urge to scratch our itch in some habitual way. And unless we equate refraining with lovingkindness and friendliness toward ourselves, refraining feels like putting on a straitjacket. We struggle against it. The Tibetan word for renunciation is _shenlok_ , which means turning _shenpa_ upside down, shaking it up. When we feel the tightening, somehow we have to know how to open up the space without getting hooked into our habitual pattern.
In practicing with _shenpa_ , first we try to recognize it. The best place to do this is on the meditation cushion. Sitting practice teaches us how to open and relax to whatever arises, without picking and choosing. It teaches us to experience the urge and the uneasiness fully and to interrupt the momentum that usually follows. We do this by not following after the thoughts and by learning to come back to the present moment. We practice staying with the uneasiness, the tightening, the itch of _shenpa_. We train in sitting still with our desires, with our conditioned hooks. This is how we learn to stop the chain reaction of habitual patterns that otherwise rule our lives. This is how we weaken the patterns that keep us hooked into discomfort that we mistake as comfort. We label the spin-off "thinking" and return to the present moment. Yet even in meditation, we can experience _shenpa_.
Let's say, for example, that in one meditation session you felt settled and open. Thoughts came and went, but they didn't hook you. They were like clouds in the sky that dissolved when you acknowledged them. You were able to return to the present moment without a sense of struggle. Afterward you are hooked on that very pleasant experience: "I did it right, I got it right. That's how it should always be, that's the model." Getting caught like that builds arrogance, and conversely it builds poverty, because your next session is nothing like that. In fact, your "bad" session is even worse now because you are hooked on the "good" one. You sat there obsessing about something at home or at work. You worried and you fretted; you got caught up in fear or anger. At the end of the session you feel discouraged—it was "bad," and there is only yourself to blame.
Is there something inherently wrong or right with either meditation experience? Only the _shenpa_. The _shenpa_ we feel toward "good" meditation hooks us into how it's "supposed" to be, and that sets us up for _shenpa_ toward how it's not "supposed" to be. Yet the meditation is just what it is. We, however, get caught in our idea of meditation: that's the _shenpa_ , that root stickiness. This is ego clinging or self-absorption. When we are hooked on the idea of good experience, self-absorption gets stronger; when we are hooked on the idea of bad experience, self-absorption gets stronger. This is why we, as practitioners, are taught not to judge ourselves, not to get caught in good or bad.
What we really need to do is address things just as they are. Learning to recognize _shenpa_ teaches us the meaning of not being attached to this world. Not being attached has nothing to do with this world. It has to do with _shenpa_ —being hooked by what we associate with comfort. All we are trying to do is not to feel our uneasiness. But when we do this, we never get to the root of practice. The root is experiencing the itch as well as the urge to scratch, and then not acting it out.
If we are willing to practice this way over time, prajna begins to kick in. Prajna is clear seeing, our innate intelligence, our wisdom. With prajna we begin to see the whole chain reaction clearly. As we practice, this wisdom becomes a stronger force than _shenpa_. That in itself has the power to stop the chain reaction. Prajna is not ego involved. It is the wisdom found in basic goodness, openness, and equanimity—all of which cut through self-absorption. With prajna we can see what will open up space for less attachment. Ego-bound habituation is just the opposite—a compulsion to fill up space in our own particular style. Some of us close down space by hammering our point through; others do it by trying to smooth the waters.
As students of Buddhism we are taught that whatever arises is fresh, the essence of realization. That is the basic view. But how do we see whatever arises as the essence of realization when the fact of the matter is, we have work to do? The key is to look into _shenpa_. The work we have to do is about coming to know that we are tensing or hooked or "all worked up." That is the essence of realization. The earlier we catch it, the easier _shenpa_ is to work with, but even catching it when we are already all worked up is good. Sometimes we have to go through the whole cycle even though we see what we are doing. The urge is so strong, the hook so sharp, the habitual pattern so sticky, that there are times when we can't do anything about it. There is something we can do after the fact, however. We can go sit on the meditation cushion and rerun the story. Maybe we start with remembering the all-worked-up feeling and get in touch with that. We can look clearly at the _shenpa_ in retrospect; this is very helpful. It is also helpful to see _shenpa_ arising in little ways, where the hook is not so sharp.
Buddhists are speaking about _shenpa_ when they say, "Don't get caught in the content: observe the underlying quality—the clinging, the desire, the attachment." Sitting meditation teaches us how to see that tangent before we go off on it. To engage this training on the cushion, where it is relatively easy and pleasant to do, is a way to prepare ourselves to stay calm and clear when we get all worked up. Then we train in seeing _shenpa_ wherever we are. Say something to another person and maybe you will feel that tensing arise. Rather than get caught in a story line about how right or wrong you are, you can take it as an opportunity to be present with the hooked quality. You can use it as an opportunity to stay with the tightness without acting upon it. Let that training be your base.
You can also practice recognizing _shenpa_ out in nature. Practice sitting still and catching the moment when you close down. Or practice in a crowd, watching one person at a time. When you are silent, you get hooked by mental dialogue. You talk to yourself about badness or goodness: me-bad or they-bad, this-right or that-wrong. Just to see this is a practice. You will be intrigued by how you will involuntarily shut down and get hooked, one way or another. Just keep labeling these thoughts and coming back to the immediacy of the feeling. That is the way to break the chain reaction.
Once we are aware of _shenpa_ , we begin to notice it in other people. We see them shutting down. We see that they have been hooked and that nothing is going to get through to them. At that moment we are experiencing prajna, the basic intelligence that comes through when we are not caught up in escaping our unease. With prajna we can see what is happening with others; we can see when they have been hooked. Then we can give the situation some space. One way to do that is by opening up the space on the spot through meditation. Be quiet and place your mind on your breath. Hold your mind in place with great openness and curiosity toward the other person. Asking a question is another way of creating space around that sticky feeling. So is postponing your discussion to another time.
At Gampo Abbey we are very fortunate that everybody is excited about working with _shenpa_. So many words I've tried have become ammunition that people use against themselves. But we feel some kind of gladness about working with _shenpa_ , perhaps because the word is unfamiliar. We can acknowledge what is happening with clear seeing, without aiming it at ourselves. Since no one particularly likes to have _shenpa_ pointed out, people at the Abbey make deals like this: "When you see me getting hooked, just pull your earlobe, and if I see you getting hooked, I'll do the same. Or if you see it in yourself, and I'm not picking up on it, at least give some little sign that maybe this isn't the time to continue this discussion." This is how we help each other cultivate prajna, clear seeing.
We could think of this whole process in terms of four Rs: _recognizing_ the _shenpa_ , _refraining_ from scratching, _relaxing_ into the underlying urge to scratch, and then _resolving_ to continue to interrupt our habitual patterns like this for the rest of our lives. What do you do when you don't do the habitual thing? You are left with your urge. That is how you become more in touch with the craving and the wanting to move away. You learn to relax with it. Then you resolve to keep practicing this way.
Working with _shenpa_ softens us up. Once we see how we get hooked and how we get swept along by the momentum, there is no way to be arrogant. The trick is to keep seeing. You don't want to let the softening and humility turn into self-denigration. That is just another hook. Because we have been strengthening the whole habituated situation for a long, long time, we can't expect to undo it overnight. It is not a one-shot deal. It takes lovingkindness to recognize; it takes practice to refrain; it takes willingness to relax; it takes determination to keep training this way. It helps to remember that we may experience two billion kinds of itches and seven quadrillion types of scratching with various degrees of intensity, but there is really only one root _shenpa_ : ego clinging. The branch _shenpa_ s are all our different styles of scratching that itch.
I recently saw a cartoon of three fish swimming around a hook. One fish is saying to the others, "The secret is nonattachment." That is a cartoon about _shenpa_ : the secret is—don't bite that hook. If we can catch ourselves at that place where the urge to bite is strong, we can at least get a bigger perspective on what is happening. As we practice this way, we gain confidence in our own wisdom, and it begins to guide us toward the fundamental aspect of our being—spaciousness, warmth, and spontaneity.
3
The Inner Pursuit of Happiness
Ruben L. F. Habito
AS I WORK ON MY COMPUTER, my two sons sit lazily in front of the television watching their morning cartoons. Every now and then I hear them blurting out, "I want that!" These outbursts signal times between cartoon segments when ads for new toys or new brands of snacks are flashed before their eyes. This scenario in my own household deep in the heart of Texas literally brings home the state of American society, aptly characterized as a "Consumer's Republic" by author Lisabeth Cohen. Sometimes my sons are lucky enough to get hold of one of those coveted items as a birthday or Christmas present, or they save up weeks of allowance to buy it themselves. Yet usually within a few days these gadgets are laid aside or relegated to the storage box with piles of other toys acquired in the past. Reflecting on this all-too-often repeated pattern, I wonder: Did they _really_ want that? Already their interest has shifted to another gizmo that has caught their attention in the ads.
Reflecting on what I learn observing my two children, it seems that acquiring a specific object of one's desire brings but short-lived satisfaction. But more significantly, acquisition itself does not quench desire but only heightens desire for other objects not yet in one's possession and thus leads to increased dissatisfaction. In her book on consumption trends in American society, Juliet Schor reports that "the story of the eighties and nineties is that millions of Americans ended the period having more but feeling poorer." Although people tended to have more consumer goods than a decade or two earlier, they had less of a sense of overall satisfaction with their lives. More people felt they were further than ever from their ideal of "the good life," which is linked with owning an array of consumer goods deemed "necessary." Schor's recent book builds upon her earlier, bestselling book, _The Overworked American_ , which characterizes the lifestyle of many Americans as a "cycle of work and spend," leaving people in a chronic state of dissatisfaction and frustration.
It was just such a sense of dissatisfaction that led a young man named Gautama, who lived in northern India around the fifth or sixth century BCE, to set everything else aside and seek a way out. His search took him in different directions until he came to sit under a tree in contemplation. At this point he arrived at what has been described as the "place of peace" ( _santam padam_ ), born out of "the extinction of all craving" ( _nibbana_ ), an experience that transformed him into an awakened one or Buddha. His experience, and the message that drew its source from that experience and his subsequent way of life, came to inspire millions of human beings throughout the centuries to this day.
My main task in this essay is to listen with an attentive ear to what the Buddha taught, to reflect on its implications for living in a globalized culture of consumption, and to look for hints that may break us out of this cycle. I begin with an affirmation that the pursuit of happiness is the corollary to the overcoming of dissatisfaction. This pursuit is an underlying dynamism that motivates human beings in our life projects, in our thoughts, words, and deeds. Taking a panoramic view of human history and contemporary global culture, we can identify several areas wherein human beings have sought and continue to seek this elusive happiness. In short, human history has been propelled in great part by the pursuit of three basic desires: the desire to possess, the desire to know, and the desire for thrill and sustained pleasure. Each of these plays a significant role in today's runaway consumeristic culture. And each is easily observable in our own everyday experiences.
THE ACQUISITIVE MODE AND THE CYCLE OF DISSATISFACTION
The Desire to Have More
Our pursuit of happiness generally leads us in the direction of wanting to have more of the good things of life, thinking that this is what would make us happy. This is a very natural human urge. The very commonness of it makes us vulnerable to manipulation. We are bombarded with images, slogans, and all sorts of signals by the media and by educational, economic, political, and other institutions, leading us to believe that unless we have this or that particular item, we are nothing. And so we strive with all our efforts to acquire those things that we consider conditions for our attainment of happiness. It could be a fashionable house in the right part of town, the dream vacation package, the ideal romantic partner. It could be some kind of designer clothing, or the right brand of shoes, the perfect wine to offer friends. Each thing seems to be the necessary prerequisite for a particular state of happiness.
Social and cultural commentators concur that it is this desire to _have more_ that keeps the economy going and the world running. Author Lisabeth Cohen describes how in the 1950s, following the Second World War, a powerful consensus of government, business, and labor emerged. Their combined message was that "buying everything in sight" was the best way to serve the national interest and the best way to fulfill one's duty as a citizen.
Cohen examines the mass consumption–driven economy-cum-sociopolitical-cultural system of postwar America from various angles. Such a system was meant to "provide jobs, purchasing power, and investment dollars, while also allowing Americans to live better than ever before, to participate in political decision-making on an equal footing with their similarly prospering neighbors, and to exercise their cherished freedoms by making independent choices in markets and politics." Trends in the following decades, however, indicate that what materialized was the exact opposite of these ideals of social egalitarianism, democratic participation, and political freedom. For example, between 1979 and 1997, the richest fifth's average income jumped from nine to fifteen times the income of the poorest fifth. The consumption-driven system also has led to the growing fragmentation and heightened inequality in American society, and these inequalities in turn have brought about disenfranchisement in educational, cultural, and political realms of social life.
In his assessment of contemporary consumer culture, Thomas Hine describes the psychological and sociological mechanisms involved in shopping, noting the pathological tendencies in those who might be called "shopping addicts." An act of shopping can be a manifestation of power, responsibility, discovery, self-expression, and other positive values. But at the same time, it can be a symptom of deeply rooted insecurity and an escape from responsibility or replacement for meaningful action. He suggests how "our insecurities leave us open to psychological manipulation, which in turn keeps the engine running."
The human drive to want more and more things comes from a deeply felt sense of _lack_. Buddhist philosopher David Loy has called this lack a basic character of our human existence in this phenomenal world. Our activities in this world are motivated largely by the need to fill in this inherent lack we feel at the heart of our being. And yet, the more we seek to fill this lack by following our craving to have more and more—in short, living in the acquisitive mode—the less we are truly satisfied, and thus continue in a state of unfulfillment and frustration.
An underlying assumption of the dominant mode of life in today's consumer society is that "you are what you have." Furthermore, if you have it, flaunt it. It is in having this or that particular item, whether it be a Gucci handbag or a nifty Vespa that we find our identity and our worth in life. This mode of life drives us in the direction of wanting more and more, believing that having more is the key to happiness. However, sooner or later we realize that the more we have, the more we still want. And thus we realize that we can never _really_ be satisfied with what we already have. In short, this desire to have more keeps us in a constant state of dissatisfaction. Even in the process of acquiring things we desire, we see that there is always more that we still do not possess. Those who succeed in acquiring most or even all of their prerequisites for happiness may still get the gnawing feeling expressed in the Peggy Lee song: "Is that all there is?"
The Desire to Know More
A second area of craving is the desire to know more, accelerated by the information technology now widely available to the general public. In our computerized culture, the almost universal accessibility of the Internet (given a certain level of economic status) and its varieties of services has opened new avenues of human pursuit. The World Wide Web has also radically transformed our consciousness and opened new horizons of knowledge never before imagined. It is not an exaggeration to say that we are in the midst of a knowledge revolution in human history. The fulcrum of this lies in "information technologies (microelectronics, informatics, and telecommunications) around which a constellation of major scientific discoveries and applications (in biotechnology, new materials, lasers, renewable energy, etc.) is transforming the material basis of our world."
The revolution in information technology that undergirds our twenty-first-century global society is propelled by the natural human desire to know, and to know _more and more_. This desire to know is an inherent aspect of our being human, as Aristotle pointed out long ago. The underlying presupposition is that knowledge is power—the more we know, the more powerful we can be.
The scientific method as a fundamental procedure in our quest for knowledge has ushered in tremendous discoveries about the way things work and has brought about momentous transformations in human civilization. For better or for worse, it has given us enormous power over our natural environment. It has given us the confidence that with adequate knowledge, we humans can control the natural world. Hence we tend to assume that any problem we face can be resolved by further research resulting in further knowledge that will then put us in control. Scientific advances since 1900 have pushed the frontiers of our knowledge further and further out into the expanding universe and further and further into the intricate workings of the subatomic world. With the cracking of the genetic code and the mapping of human DNA, we have attained a radically new level of understanding of the human organism.
There is indeed a certain satisfaction in the acquisition of new knowledge. We all have tasted the feeling of competence in mastering new domains such as a foreign language or a musical instrument. However, as with the desire to _have_ more, the desire to _know_ more is constantly being met by the realization that there is always more still left that is unknown. This only sparks the desire to know even more, drawing human beings in directions where no one has gone before.
If we dispassionately survey our contemporary world, we cannot help but notice the stark contrast between our ideal of universal happiness—the expected outcome of more knowledge and mastery over nature—and the actual realities of our global situation. We cannot help but see an ever-increasing gap between the haves and have-nots, with hundreds of millions living and dying in subhuman conditions. We can't help but see the heightened tension among different sectors of our human community, leading to armed conflicts around the world. We can't help but see the increasingly critical situation of ecological destruction, from ozone depletion to the extinction of thousands of species. All this indicates that we have not been able to harness our knowledge to provide the wisdom we need to live well and be genuinely happy as a global community. The desire to know that drives our mental pursuits presupposes, as well as accentuates, the dichotomy between knower and known. I see the world and other people as "out there," separate from me, and therefore fundamentally cut off from my field of concern as I seek my own happiness.
Never before in the history of the world have we human beings had access to so much knowledge and information. But looking at the history of the last hundred years, the gap between what we know and how to use that knowledge for greater happiness has never been greater. Indicator after indicator affirms that we have not been able to put our knowledge at the service of our communal human well-being. This is a gap that is crying out for redress.
The Desire for Thrill and Pleasure
A third feature in the engine that keeps our contemporary global consumer culture running is the relentless pursuit of thrill and pleasure. The entertainment industry is ever ready to offer the latest kinds of thrills. Reality TV seeks to capture the mass audience with yet another adventure challenge, allowing the ordinary Joe or Jane to become an overnight celebrity. The film industry keeps on churning out new blockbuster films that compete for weekly box-office ratings. Ever newer varieties of video and computer games keep children fixated on their little machines that give them the thrill of competition. The sports industry likewise continues to capture the attention of fans who find their highs in the excitement of competitive spectator games.
And yet, we realize, the more we seek new sources of thrill, the less we feel truly satisfied. We may find momentary enjoyment in these thrills, but it is followed by an inner emptiness that can only be filled with a new source of pleasure. This is literally documented in cases of drug and alcohol consumption. Again, we come to the realization that our search for thrill keeps us in a perpetually dissatisfied condition.
The pursuit of thrill in our contemporary society is fanned by titillating images and attractive offers presented to us on television and through the Web. The fact that these images and offerings are able to sway multitudes, generating huge profits for entrepreneurs and providers, indicates that people apparently feel a need for such thrills. This indicates the inner lack many of us feel, which clamors to be filled precisely by these thrills offered for mass consumption.
But as anyone knows who has sought out some kind of high—whether it be the final play-off of the World Series or the euphoria from homegrown marijuana—these thrills do not last. Eventually the altered state wears off and we are left low instead of high. This then leads us to crave the next high. Hence the chronic state of dissatisfaction is only heightened, as we look to some external stimulus we think will offer that thrill or pleasure, whether it be alcohol, tobacco, drugs, the cinema, television, food, coffee, chocolates, sex, or shopping.
The desire to _have more_ , the desire to _know more_ , and the desire for _more thrill_ and pleasure are basic components of what can be described as an _acquisitive mode of being_. As I have tried to demonstrate, such a mode of being attains not happiness but only a chronic state of dissatisfaction and a heightened sense of frustration. Can we envision a different mode of life, one that leads not to dissatisfaction and frustration but to genuine happiness and contentment? Exploring this question, I turn to a tradition that has addressed this very question for more than twenty-five centuries.
TOWARD A CONTEMPLATIVE MODE: THE INVERSION OF THREE DESIRES
In his process of seeking to overcome dissatisfaction ( _dukkha_ ) and attain true inner peace, the Buddha came to realize that neither the relentless pursuit of desire nor the opposite extreme, self-deprivation through rigorous asceticism and mortification, could lead him to happiness. He arrived at what has been called the Middle Way between these two extremes. This middle way was reflected in his inner stance as he settled down under a tree in contemplation, taking a straight look at things as they are.
It was this contemplative attitude that became the condition for the momentous awakening experience that opened him to the true path of peace ( _santam padam_ ) and that came to define his contribution to humanity as a buddha (awakened one). This experience was a pivotal moment that illumined the Buddha's understanding of reality and transformed his entire life. From this moment on, he no longer was a seeker of truth but was now one who had awakened to the liberating truth ( _dharma_ ). The Buddha's contemplative attitude was foundational to his transformative experience. And in return, his experience of awakening grounded him in the contemplative mode of being throughout his entire life.
How can we describe the features of this contemplative mode that opened the Buddha to his awakening experience? Taking our cue from the three kinds of desire that generate dissatisfaction, we can understand the contemplative mode as an inversion of these three desires.
Awareness of Being
As we begin to see through the inherent contradictions in the acquisitive mode of life, we may come to a point where we are stopped in our tracks, unable to go on with our unsatisfactory habits of buying and consuming. In this pause, there can be an opening. We may hear an inner call, inviting us to change direction. Literally stopping and beholding what is going on—in other words, assuming a contemplative mode—can be the key to an entirely different perspective on ourselves and the world.
Instead of pursuing the craving to have more, the contemplative mode involves an inner attitude of simply beholding "what there is, just as it is." When asked by his followers how they too could arrive at the peace of mind that characterized the Buddha's life, the Buddha is said to have replied, " _Ehi passiko_." "Come and see." This is the invitation to enter a contemplative mode of being.
The instructions are straightforward: simply to behold what is there before us. Following basic guidelines of meditation, or simply sitting and watching our breath with the inner eye of our mind, we may get glimpses of a realm that can only be characterized as "not this, not that." This is a realm not like the one we are accustomed to in our ordinary life with its wants and needs that clamor constantly for our attention. Instead, this is a realm that can fill our hearts with a sense of fullness, a sense of rest, a sense of being truly at home. In this realm we are able to taste a full _awareness of being_.
Let me illustrate how this contemplative mode can arise by comparing two modes of walking. We take it to be common sense that we walk because we want to go from point A to point B. We walk, for example, to get to the other side of the street, or from the parking lot to the grocery store. In this mode of walking, the act of moving our legs is simply a means to get us where we intend to go. We are generally conscious of the time at our disposal to get there, and we tend to hurry so we can get there faster. The value of the walking is then entirely dependent on whether it takes us where we want to go in the allotted time frame. It is a means to an end and nothing else.
There is, however, a mode of walking where the point is simply to experience the pure act of "just walking." In this mode of walking we open ourselves to a realm that goes beyond "walking in order to go somewhere" to experience "walking for the sake of walking itself." Here the act of moving our legs is an event that we are able to experience and relish as such. We may taste the wonder of being able to do this act at all, that is, moving our legs so we maintain our balance, finding our whole body swaying with the rhythm, experiencing the simple and glorious fact of . . . being able to walk.
I should note that this second mode need not mean that we do not actually get from one place to another. True, we may choose to walk in a way that takes us around in a circle within a given space, as in a meditation hall. But we may also choose to walk from the parking lot to the grocery store. Though the setting may be the same, the inner attitude that we bear makes a world of difference. The first mode can be compared with what I have described as the acquisitive mode of life; the second mode reflects a contemplative mode of being. In this mode the walking is totally independent of the linear time spent in engaging in it and can in fact lead one to an experience of the timeless.
Contemplative experience can open one's mind and heart to a kind of satisfaction not to be gained by the acquisitive or time-and-space-consuming mode of movement. It has nothing to do with gaining or not gaining, arriving or not arriving. The contemplative mode offers an inner satisfaction that is not dependent on external conditions and is thus an experience in the realm of the unconditional. Such an experience can lead to a tremendous sense of inner peace and release, freeing one from the shackles of desire for consumer goods. As we walk in the contemplative mode, our sense of inner lack is overturned to usher in an awareness of the fullness of being.
Nondual Knowing
As we take this stance of beholding, simply "seeing things as they are," we may come to that most revolutionary of discoveries in the inner journey of the spirit. Put inadequately into words, this is the discovery that what makes "me" what I am most truly is intimately connected to what makes the world what it is. In short, it is an experiential realization of what the Buddha saw in his moment of awakening. He articulated this insight as "the doctrine of interdependent co-arising" ( _pratitya-samutpada_ ), elaborated upon by Buddhist thinkers through the ages.
Coming to this discovery is to realize, intimately, experientially, that what happens to each and every sentient being in this world happens to my very own self. It means experiencing the pain of each and every being as my own pain and, conversely, each one's joy as mine. It is to undergo a momentous transformation in the way I see the world and myself. The experiential realization of intimate connectedness is _nondual knowing_ , a sharp contrast to the knowledge-acquiring mind. It is this experience of nonduality that can unleash the powers of wisdom to flow out into acts of compassion.
From the contemplative view, as I look at the world, I realize that I am seeing my own self. The world is no other than what I am. And conversely, what I am is no other than what the world is. To know the world is thus not different from knowing myself. As thirteenth-century Japanese Zen master Dogen writes, "I came to realize clearly that mind is no other than mountains and rivers, the great earth, the sun, the moon, the stars." Beholding the mountains and rivers and the wonders of the natural world, I see these as manifestations of mind, the same as my own mind, my own self. From this nondual way of knowing, the leveling of mountains and the cutting of trees, the pollution of rivers, the ongoing loss of species, are not events "out there" but are things happening right at the heart of my being. This causes me deep pain.
The realization that "we _are_ the world" can bridge the gap between our scientific knowledge and the wisdom we need to direct this knowledge to our well-being as we live together in this Earth community. Grounded in the experiential realization that the world is not separate from ourselves, and therefore that the world's well-being is our own well-being, we can harness our knowledge and technological acumen to uproot the sources of individual and social suffering.
Up to this point in human history, we have pursued our desire to know in a way that has given us mastery over the laws of physics, chemistry, biology, and even over our own bodies. The dualistic mode of knowing, while giving us power over nature, has also led to great disparity between the haves and the have-nots of the world. We have used this mode of knowing, for example, to master the techniques and economics of factory farming, raising cattle, pigs, and chickens in large quantities for mass consumption. Engaging the nondual mode of knowing, we empathize with the cattle, pigs, and chickens being mass-produced in this way and _know_ that something is not quite right. This mode of knowing can lead us to question how such a system can treat countless living beings in this way and to question our own eating habits dependent on this system. It can also empower us to take action toward transforming the situation and reducing the suffering.
Nondual knowing is prominent in the cultivation of the contemplative mode. In the well-known _Metta Sutta_ , a scriptural text from early Buddhism, it is described as a stance of being engaged with the world "as a mother toward her only child." This wisdom manifests itself as compassion, grounded in a way of being that offers oneself and one's whole life toward the healing of the wounds of the world. Albert Einstein, a major figure in the human quest for knowledge in the twentieth century, made this connection between knowledge and wisdom:
A human being is part of the whole called by us the universe, a part limited in time and space. Humans experience themselves, their thoughts, and feelings as something separated from the rest, a kind of optical delusion of their consciousness. This delusion is a kind of prison for us, restricting us to our personal desires and to affection for a few persons nearest to us. Our task must be to free ourselves from this prison by widening our circle of love and compassion to embrace all living creatures and the whole of nature in its beauty.
Unconditioned Joy
Cultivating the contemplative mode requires setting aside the pursuit of certain kinds of "thrills" that would obstruct this cultivation. This "setting aside" need not be a heroic act of self-denial and asceticism but can be a simple response to an inner voice, a call of the heart to a deeper kind of joy. It is turning toward an inner satisfaction more satisfying than any pleasure dependent on external conditions or stimuli.
For example, we may be in the habit of leaving the television on to keep us company in a lonely house, or of turning on the radio while driving to occupy our bored minds. But we may come to a moment when we see this dependence on directionless external stimuli for diversion as truly distasteful, depriving us of a deeper pleasure. This deeper pleasure is what we taste in moments of silence and simple attention to what is going on around us. Setting aside the pursuit of thrills through external stimuli is a response to that inner voice inviting us to a deeper kind of satisfaction.
Following this inner call, we may be led to search further by reading books on spiritual practice. Reading such books may begin to fill our hearts with yet a new longing—the longing to become a spiritual person, finding satisfaction in spiritual instead of material pleasures. But this itself can throw us into another cycle of dissatisfaction. We read book after book and find our minds filled with ideas that we are not able to incorporate into our way of living. We may also easily fall into what Chögyam Trungpa called "spiritual materialism," or perhaps, "spiritual consumerism." We may be misled into thinking that we are "worth something" because of the many spiritual books we have read, considering ourselves better than others caught in the pursuit of more tangible thrills.
But we may also come to see that all this pleasurable Buddhist reading is not really making any significant dent in the cycle of dissatisfaction that led us to the reading in the first place. We realize that we have done enough reading and that it is now time to take another significant step. Having looked at the menu from various angles, it is now time to set the menu aside, order our food, and then begin to eat. It is this insight that leads us to embark on some form of contemplative practice that can yield more sustained satisfaction.
Finding a community of contemplative practice, with a reliable teacher who can serve as a spiritual guide, can take us to new levels of experiencing joy in our lives. As we engage seriously in contemplative practice, we hear an inner voice inviting us toward a satisfaction that is deeper than anything external stimuli can offer. As we take up spiritual practice of the contemplative mode, we begin to relish a new kind of fruit in our life. A most apt way of describing this fruit is _unconditioned joy_. This can be felt in various degrees of intensity, from the mild sense of inner tranquillity after meditation practice to an intense ecstatic experience whose effect and implications can be felt throughout the rest of one's life.
This experience of unconditioned joy can begin to enter one's life even in the midst of the normal struggles of day-to-day existence. It is not based on a change in external factors in one's life; it is not dependent on some condition we impose or suppose. At best one can perhaps acknowledge it as a gift, a gift of the universe to one who is disposed to receive. This unconditioned joy can be triggered by something as simple as the sight of a tree or the smell of a flower. One can perhaps say that it is a deeply felt affirmation of the fact that "it is good to be." And this affirmation is one that stands in spite of the ups and downs of life, in spite of the actual condition we are in or the state of the world. We can also describe it as experiencing a dimension that is unconditional and universally available to anyone, anywhere, regardless of social or economic status, age, gender, physical condition, ethnic origin, and so on.
Alan Clements, who lived in Burma as a monk for a number of years and now teaches in California, describes it this way:
The practice of meditation became a wonderful new way of life. I was amazed to see how awareness put eyes and ears where there had been none. It enhanced perception and revealed greater nuance and dimension. Sounds were accentuated. Colors became brighter. Tastes, more subtle and sweeter. Smells more fragrant. At times it felt like every cell in my body was undulating with orgasmic bliss. Watching the fog lift in the early morning was a dance in itself—the play of photons, like tiny prisms refracting thousands of infinitesimal rainbows on the eye. The smell of the gardenia bush just outside my window became a symphony of textured scents. I fell in love with the simplicity of just being.
Even a small taste of this unconditioned joy can free us from the driving desire to keep seeking thrills in manifold ways. We will be able to see through those impulses that urge us to buy this or that or seek the thrill of diversionary recreation to fill an inner lack. In fact, we may even come to realize that those cheap thrills are almost distasteful compared with the inner joy experienced in "simply being."
THE INNER PURSUIT OF HAPPINESS
I began this essay with an affirmation of the pursuit of happiness as an underlying dynamism that motivates human thought, word, and deed. Most of the time we humans are trapped in the delusive idea of a self that is separate from the world, leading us to pursue an elusive ideal of happiness. Caught in a cycle of dissatisfaction, we stay locked in the acquisitive mode, hooked on the desire to have more, to know more, and to experience more pleasures and thrills.
Seeing through this cycle of dissatisfaction can become a turning point in our lives as it was in the life of Gautama Buddha. It can enable us to hear an inner voice, calling us to a different definition of happiness. This is an inward way that can take us from the dissatisfaction of not having and bring us to an awareness of the fullness of being. It can connect our pursuit of knowledge of the objective world with the knowledge of our own true selves, opening our lives to the cultivation of wisdom and compassion. It can also redirect our pursuit of thrills and pleasures to the inward journey that will open to us the exquisite taste of "the simplicity of just being," an experience of unconditioned joy.
These experiences are not available in the shopping mall, but they are available with every step we take. We have the choice to transform these three driving desires in each act that relates to consuming. Strange as it might seem, we can actually take the basic drives behind consumerism and turn them around to pursue the Buddha's path. This is not only possible, it is crucially necessary to reduce the rising suffering in the world caused by our mindless consumer habits. As we replace the acquisitive mode with the contemplative mode, we will be in a "win-win situation," overcoming our own suffering and dissatisfaction and at the same time helping to reduce the cause of others' suffering.
4
Young Buddhists in Shopping Shangri-la
Sumi Loundon
I NEVER UNDERSTOOD the importance of Martha Stewart's products until I bought my first house. In a quest for the perfect curtains to grace my new box window, I visited many stores in the mall. When I finally found my dream curtains, my heart fell. Window treatments, I discovered, are expensive—forty dollars for one curtain! Then my mother told me about Kmart. I was overjoyed to find a wide array of tasteful treatments at much lower prices. Feeling satisfyingly domestic, I hung the new yellow curtains in my kitchen and went to bed. My thoughts were awhirl with planning my next shopping trip in search of area rugs, lamps, and bookshelves. Then I stopped myself. Previous nights had been marked by an easy floating off, remembering friends and thinking about something I'd read—meaningful thoughts. Now my mind was seized with a kind of acquisitiveness I had never experienced before. What had happened to the values of frugality I absorbed from my counterculture childhood?
I was raised by staunchly anticonsumer parents in the 1970s. We lived in a small Zen community in rural New Hampshire that grew its own food, pressed its own tofu, and used hand-me-down toys and clothes for its many kids. Our large house had the sparest of furnishings, many of them from donation or handmade from old lumber. Imagine being a child in those circumstances! Such a place gave me reverence for any object that could be mine. Nothing was disposable. Everything should be shared. One took only what was truly needed. It wasn't until I was seven that I ever stepped into a department store. Because most things were brought by one or two staff to the community, no one needed to go out to buy things. Most items were in bulk, without brand names, such as sacks of flour and beans and huge boxes of powdered milk.
Though we were laypeople with families, my counterculture parents and their friends cultivated a monastic-like asceticism to attain the highest realization. In contrast to my peers who were raised in single-family homes with a certain consumer diet, I had been brought up with material starvation and Buddhist rhetoric that still undergird my sensibilities. That rhetoric, birthed in the religious experimentation of the sixties, taught: "Buddhism teaches nonattachment. Worldly things create attachment. Therefore, we should not have things." My father was so antimaterialist that when I cooed over a little mirrored music box, he saw my expression of desire as grounds for throwing the box out. He would sometimes sing Madonna's "Material Girl" as a way of getting me to deny that I was materialistic.
Twenty years later and still a Buddhist, my attitude toward consumerism might be surprising for someone raised in a self-sufficient community with generic goods and meditators' mind before materialists' matter. The fact that I bought a house, have a retirement plan and dental insurance, and own a new loveseat is a sharp contrast to my parents, who at my age consciously rejected these things in pursuit of awakening.
Today I have a complex relationship to consumerism. On the one hand, I feel almost nauseated walking through Kmart. With thirty brands of shampoo in different colors and smells, consumer culture feels excessive to the point of decadence. On the other hand, the severity of the anticonsumerism I endured as a kid bordered on deprivation. This internal conflict around consumerism is heightened when I shop in a Buddhist boutique. Today's kapok-filled zafus are prettier than the newspaper-bound-with-masking-tape one my parents made for me, but is a hand-stitched, Egyptian cotton, organic-dyed, silk-edged, monastery-made, pricey cushion with color-coordinated zabuton necessary to my meditation success?
For a number of years, especially as I went through an elite college with many privileged kids who grew up near malls, I thought that I might be the only young person who felt ambivalent about consumerism. In graduate school, when I began searching for and interviewing hundreds of young Buddhists in America, I found that I was not alone. Like mine, my peers' relationship to consumerism is complex. To explore this complexity, this chapter draws upon my own experience and anecdotal evidence. While this writing is not based on a comprehensive survey, I hope to provide an impression of my generation's attitudes toward consumerism as well as some initial reflections on what they may mean.
YOUNG BUDDHIST ATTITUDES
Unlike the childhood of my parents, my generation has had greater exposure to two opposite dimensions around consumerism, both bequests of the baby boomers. On the one hand, we have been raised with recycling (at home, in schools), with some ideas about environmentalism (one can buy Sierra Club greeting cards at any store, read about global warming), with access to theories about consumerism (reading Marx in high school), and with exposure to sophisticated understandings of psychology (such as Daniel Goleman's). On the other hand, we have been the most heavily marketed-to generation of consumers. Once retailers discovered that brand affinity begins as early as age three, they aimed their advertisements to children specifically to inculcate consumer values and label loyalty. Given that my generation has been lobbied from both sides, it is not surprising to find young Buddhists who are disgusted, delighted, or at ease with consumerism, or some combination of these conflicting attitudes.
Within this contemporary context, baby-boomer Buddhists have provided frameworks for placing consumerism in a dharma path. Reading articles by baby-boomer Buddhists such as Ken Kraft and Allan Hunt-Badiner as well as books such as _Dharma Rain_ , young Buddhists absorb a range of lessons. Significantly, baby-boomer Buddhists themselves have changed their relationship toward consumerism, just as my parents rejoined the comfortable class in the eighties after asceticism in the seventies. As a result, today's young Buddhists select from more than forty years of models. Some are still inspired by early writings such as Jack Kerouac's _The Dharma Bums_ , which puts forward one type of relationship to possessions, while others might pick up a later writing. Yet, even while my generation takes its cues from baby-boomer ideals, many are creating their own philosophies.
Although I found there are as many views on consumerism as there are young Buddhists, it appears that young Buddhists fall roughly into three camps: nonconsumers, at-ease consumers, and conscious consumers. The first group consists of young people who have taken up a monastic path, either emulating it as a layperson or receiving traditional ordination. Counterintuitively, although these young Buddhists, who are as Buddhist as they come in the West, live materially simplified lives, I would not consider them to be _anti_ consumerists. Many are not likely to picket Kmart or go to an antiglobalization rally or read _Adbusters_ or _Utne Reader_ , nor are they likely to buy farmers' market produce over agribusiness goods. One person told me that his monk friends actually get excited about a trip to the mall to purchase the latest computer software! Therefore, because of the nonawareness of consumerism as an issue in their dharma path, I would characterize most of the young, ascetic-leaning Buddhists today as _non_ consumerist rather than as anticonsumerist.
One example comes to mind: I remember a freshman at my college who came from a middle-class background. His dorm room had as much stuff as other students'—skis, posters, stereo, clothes, knickknacks. He began attending a morning meditation group on campus. He became so interested in the practice that he shipped himself off to Japan, meditated like crazy in the Rinzai lineage for two years, and came back as a monk. After I had graduated, I visited him at the dorm his senior year. His room was completely bare except for a laptop and two thin blankets spread on the hardwood floor. He wore a neatly arranged gray monk's robe that he had sewn himself. However, the motivation behind his asceticism had more to do with the value of a simple life in cultivating enlightenment than with being _against_ American consumer values.
My college friend's adopted ascetic life reflects a trend among many young people who get turned on to the dharma. Introduced to Buddhism through a college course or meditation class, reading a beginner's book on Buddhism, attending a public talk, they waste no time in going right for the ultimate goal of awakening. This includes shedding all material excess from earlier years, even what might normally be considered material necessities. The simplicity of an ascetic life, they say, allows them to focus on the important goal of full awakening. Some say that simplicity gives them the freedom to dedicate themselves to helping others instead of concerning themselves with a house, nuclear family, and wealth-generating profession. One young nun wrote that having a shaved head relieved her from having to think about buying shampoo or choosing a hairstyle. Still others come back from Buddhist-studies programs in Asia and, having seen that others do with much less and are actually happier people, decide to simplify their own lives.
The second camp might be termed anti-anticonsumers or at-ease consumers. This tiny group of young Buddhists is aware that Westernized Buddhism has a lot to say about rejecting consumerism but chooses to remain a part of consumer culture nevertheless. There is a sense of guilty pleasure in rejecting anticonsumerism reflected in what James Silberstein writes:
My girlfriend and I recently had a discussion about consumerism, a word which comes off pejoratively as sounding greedy and animalistic, lacking in reason or awareness. After we discussed our disgust with the idea of being a consumer, we both admitted to being full-fledged, card-holding members of the cult of consumerism.
I can identify with this feeling. Sometimes it seems as if the rhetoric on anticonsumerism is delivered so vehemently that one seesaws between agreeing and saying, "Whatever. Let's enjoy ourselves." It may be that this anti-anticonsumerism sentiment follows a larger trend: after a decade of consciousness around fat-free foods, the American public seems to be enjoying a fad in comfort foods such as deep-fried Twinkies and deep-fried cheesecake, items even more fatty than those in the pre-anti-fatty-food era.
In conversations with young Buddhists, I wasn't surprised to find those for whom consumerism wasn't a big deal (nonconsumers) or those for whom anticonsumerism had become a turnoff (at-ease consumers). I _am_ surprised that I have yet to meet young Buddhists who are actual anticonsumerists! Investigating this a little further, I found that there are two types of young Buddhists who begin at different ends—as anticonsumers and as unaware consumers—but arrive at the same place: conscious consumerism.
Some conscious consumers have preexisting anticonsumer opinions into which Buddhism later plays a role. Hilary Miller, fifteen, writes,
Personally, I have felt anti-consumerism sentiments, and was, even before I discovered Buddhism, planning to get rid of many of my things and live more simply. Still, it was difficult to do so because I was so attached, inexplicably, to most of the things I owned. Buddhism helped me free myself from the tyranny of these objects, and I honestly don't miss them. Getting rid of them was actually liberating.
Among anticonsumers who become Buddhist, an unexpected thing happens: radical anticonsumer views soften. A twenty-one-year-old who describes himself as an Eco-Anarchist-Buddhist writes,
I was always really "anti-consumerism," but I think that Buddhism has helped to replace consumerism with something more positive. At one point reading Marx and _Adbusters_ magazine drove my anti-consumerism. Now, I have just learned to be happy without trying to constantly grab everything I see and buy it. When I can see clearly, I find that I don't need these things.
Likewise, Corey Flanders, a Nyingma practitioner in his thirties, writes,
Before I became a Buddhist, over seven years ago, I remember reviling consumerism as if it were necessarily an evil or negative expression or symptom of greed. Now I'd say that Buddhism has shaped my attitude in that I am much more accepting of consumerism. I think it's pretty much a natural impulse for human beings to search for and acquire that which they believe will make them happy. There is something pure and true about consumerism, as it is a barometer of that impulse and therefore a powerful metaphor which may serve to help one's understanding of human life and drives. This understanding, for me, is a cornerstone of compassion. I mean _I want_ the SUV and _I want_ the beautiful clothes and _I want . . . whatever_ , and I can recognize the patterns of consumerism in myself and, consequently, in others.
Dan Fisher, a graduate student at Naropa University, makes a similar point in reflecting that Buddhism has changed his attitude toward consumerism in that he doesn't see the practice of each as mutually exclusive: who he is as a Buddhist is who he is as a consumer and vice versa. Thus, anticonsumerism is seen as too extreme for a system that advocates a middle path, so anticonsumers who become Buddhist adopt a more positive stance toward consumerism.
Other conscious consumers have benefited from dharma teachings that move them from mindless consumerism toward consumer awareness. Young Buddhists say that teachings on desire and nonattachment are influential. In addition, the Buddhist doctrine of interdependence leads young Buddhists to consider how consumption affects not just the mind but the environment. Seunghee Ham, a Korean high school student, writes that when she came to an adult understanding of Buddhism, she consciously changed her behavior:
When I grasped the idea of interdependence, it became clear to me that my own life depended on so many elements that I could merely be the combination of all those around me. This realization has kindled my passion to preserve the environment, the biggest sacrifice of consumerism. I now lecture my brother to take short showers, rummage through the trash bag for anything recyclable, and most important, spend less.
This contemporary type of consumer awareness is milder than that of the Buddhists of my parents' generation, who, as young adults, sharply critiqued consumer culture by radically changing their habits, through handmade goods, farming, recycled clothing, generic and bulk foods, self-sufficiency. Perhaps the moderated views of these young Buddhists are the result of the baby boomers' influence, since most of the anticonsumer baby boomers have themselves relaxed the anticonsumerism of their early twenties. For example, I am surely less anticonsumer today because my parents have returned to a middle-class lifestyle (now my mom has dental insurance, a reclining loveseat, and horror of horrors, a new, not-cheap, car!).
This is not to say that Buddhism today doesn't give rise to radical anticonsumer positions. It does. But it appears that at some point in the development of their views, young Buddhists come to a middle ground. Jeff Wilson, Web editor for _Tricycle_ , captures this growth:
At first, the convert Zen I imbibed came with a strong rhetoric of simplicity and nonattachment, which led me to criticize people caught up in the samsara of endless consumption. If true peace and happiness came only from within, related to the mind and not one's possessions, then consumerism seemed like a very literal form of disease and madness. Later, as I began to notice that a lot of the teachers of convert Zen themselves had fancy cars and expensive altar ornaments, I began to think about whether it was possible to live a life of nonattachment to both consumerism and anticonsumerism, especially since at the end of the day we all must operate within the real world.
Though here I simply describe the current attitudes of young Buddhists, I predict that conscious consumerism will fuel the dominant ideology as my generation matures. Where can we go with conscious consumerism? Is it simply an easy way out, allowing us to be comfortable consumers and sanctimonious Buddhists at the same time? Or does it help us approach consumerism realistically, preventing us from falling into the self-centeredness of the antiworldly dharma bums or the severity of anticonsumerism among young baby boomers? Is this a middle path simply because the two ends of the debate have been drawn up by American decadence and radical anticonsumerists? Or might we be pioneering a truly balanced approach that wisely accommodates individual psychological, spiritual, and economic needs with larger communities' environmental and social justice needs?
CONSUMING BUDDHISM
The conscious consumerism I find among my Buddhist peers is heightened when it comes to the material dimension of Buddhism itself. At an idealistic level, young people see Buddhism as a philosophy, science, psychology, and practice, not a religion associated with an abundance of products that one can buy. Given that Buddhism teaches nonattachment, where is the place for a teak altar set or an expensive Buddha statue? For this reason, some students disparage "boutique" Buddhism and the way Buddhism has become popularized through chic Zen clothing, Samsara perfume, a rock band named Nirvana. I myself went through a phase of disgust as I watched the principles from my Zen commune—intimate, immediate, practiced—become mainstreamed, stereotyped, and seemingly watered down by deskset rock gardens, Yoda's lines in "Star Wars," and _Dharma & Greg_. I felt I could understand why Catholics objected to the crucifix necklace fashion that gripped teens in the late eighties. I didn't want the heart of my religion ripped out by consumer culture. I'm not the only one who feels this way. Again, from Hilary Miller:
Has anyone else noticed the new trend? Malas (Buddhist prayer beads) have been turned into some kind of cheap new jewelry. I see them daily at my school, often on the wrists of people who strike me as very un-Buddhist (although I know we all have Buddha nature, some people hide it really well). Sometimes I have an almost irrepressible urge to go up to one of these people and politely inform them that they are wearing a copy of a religious tool. What really annoys me, though, is not the people that wear them (they are merely ignorant, not malicious), but the people who first manufactured these bracelets. Obviously they knew that their product had Buddhist origins or they would not have named them "karma beads." Why does our society have to commercialize everything in this way? . . . What right do people have to sell religious items like costume jewelry? I try not to be bothered by it, I really do, and I succeed for the most part. But I just don't understand why the people who manufacture these things don't understand that what they are doing is insulting.
At one time I shared Hilary's dismay, yet as I have gotten to know the different paths by which young people are drawn to Buddhism, my view has changed. For many young people, the first contact with Buddhism is precisely through consumer avenues. Monster book chains have a wide selection of books written in accessible language, from personal (Dinty Moore's _The Accidental Buddhist_ ) to scholarly (Don Lopez's _The Story of Buddhism_ ), from practice (Bhante Gunaratana's _Mindfulness in Plain English_ ) to popular (His Holiness the Dalai Lama's _The Art of Happiness_ , which made a quiet appearance on an episode of _Friends_ ). I would estimate that more than half of all young people first learn about Buddhism through a book, and often that book was checked out from the local public library. The Beastie Boys, a rock band that has done some Buddhistic songs and whose lead singer, Adam Yauch, is a dedicated Buddhist, may have done much to draw young people to Buddhism. Young people find the Buddha figure, with that peaceful enigmatic smile and gentle but attentive pose, to be more attractive than the crucified Jesus from church. These statues invite young people to ask why the Buddha looks like that. Films such as _Kundun_ , _Seven Years in Tibet_ , _Bulletproof Monk_ , and _Little Buddha_ have also been a powerful popular Buddhist introduction for young people. These movies offer some basic doctrines around rebirth, karma, inner peace, and freedom that young people are curious about in their search for meaning.
"Hard-core" Buddhists, who do intensive meditation retreats or have a more philosophical style of Buddhism, tend to dismiss the value of consumer-Buddhist stuff—books, statues, music, movies—in initiating someone into the path. Yet, important seeds are planted from that initial consumer contact, and these should not be dismissed. For some young people, the seed may lie dormant for several years. When a crisis arises—death in the family, a major breakup, a car accident—that seed can germinate in the person's process of finding meaning and purpose. Although I personally did not come to Buddhism through a material source, many highly committed young Buddhists began their journey with the things that consumer Buddhism sells. It has taken me some time to see the value of this.
Despite the wide-ranging discourse in Buddhist magazines, living-room meditation groups, and casual conversation on how Buddhism is being cheapened by Buddhist materialism, young people seem to take a conscious consumer approach with Buddhist goods, as they do with consumer goods in general. Connie Pham writes, "The dharma is not something you can buy or sell; it's free for the taking. So despite threats of 'spiritual materialism,' ultimately the dharma, like everything else that sustains life, is free." Corey Flanders considers, "Is Buddhism becoming too consumeristic? No. How can a way of practice become consumeristic? Consumerism/Western materialism may be pulling Buddhism into its structure, using it to make money, but that is natural. That is its function. It will try to co-opt whatever it can for its purpose." Jeff Wilson reflects, "In the West, we hear lots of dire warnings about Buddhism becoming consumeristic. It seems like they are being called for out of a romantic notion of what 'pure Buddhism' should be, which always strikes me as an impossible ideal. If people wish to consume Buddhist goods, so long as they don't do so in support of illegal practices (such as stolen Asian artworks), that's okay." If young Buddhists continue to develop a philosophy around conscious consumerism, then we will also need to think about how Buddhist products are regarded within that.
YOUNG BUDDHIST ATTITUDES IN ASIA
The Buddhist students at University Sains Malaya in Penang have two large shared houses just near the campus. The living rooms have been converted into meditation spaces with Buddha altars, while some of the dedicated students live upstairs. The cohousing bulletin board has the same lists one finds in Western communities: chore assignments, community meetings, telephone messages. Yet, inquire as to the students' majors and one finds that these dedicated young Buddhists concentrate on economics, computer programming, communications, and science. These majors lead to successful middle-class professions. The students in Penang wear white shirts and slacks and have conservative haircuts. Young Asians in places like Penang, many from lesser circumstances than Western youth, aspire to be middle class, own a home, have professional standing, and acquire enough things to live comfortably.
In contrast to the Penang students, Buddhist students in Western universities choose majors in religion, anthropology, arts, and history. These majors lead pretty much nowhere practical (I write this as a fine arts major myself). The students of Buddhist groups in the West usually wear decidedly nonmainstream clothes—sometimes even the Asian clothes that Asians themselves no longer wear—and redefine the limits of hair. Many of the Western youth have the opposite goal from their Asian peers: having grown up in conventional American society, they reject it and seek alternatives.
While Buddhist youth in both Asia and the West are highly committed to their faith traditions, their dispositions around consumerism and material goods are strikingly different. The wide gap between these two cultures suggests that being Buddhist does not perforce give rise to a view on consumerism. For the young Asians in developing countries whom I met, the compatibility of being Buddhist and striving for success and material stability is not a burning question. Likewise, I have not found consumerism to be a big concern among first-generation Asians in America who are also seeking to establish a basic, middle-class life here. It turns out that young Asians from wealthy families have dispositions more aligned with young, affluent Westerners.
I find this contrast fascinating. Why, among certain Buddhists, is the question of consumerism so big? Why do young Western Buddhists, second-generation Asian Americans, and well-off Asians highlight certain dharma teachings—on desire, nonattachment, interdependence—and relate that to consumerist culture? We might take two things away from this correlation.
First, I suggest that those from good circumstances are nearly overwhelmed by American consumerism. Thus, Buddhism's nonattachment may be the diet for consumer gluttony. A high school Buddhist wrote, "I wonder if there is a growing movement of youth who are tired of materialism and propaganda aimed at us and the culture the corporate businesses are trying to sell?" For people like this, perhaps Buddhist teachings offer tremendous psychological relief and are a remedy for societies that have become excessively affluent.
Second, the sociological issue of class appears to be a motivating force in how Buddhism and consumerism have become intertwined. For example, not all traditions of Buddhism, as they have evolved in America, speak to consumerism. Soka Gakkai not only tolerates material success but also includes ways to achieve material success through chanting practices. Could this encouragement be why Soka Gakkai International–USA has had much greater success reaching lower socioeconomic classes—thereby including a greater diversity of ethnic groups—than have Zen, Theravada, or Vajrayana lineages? Given that an ethics of conscious consumerism is dominant among middle-and upper-class young Buddhists, perhaps we should not assume this ethics automatically applies to everyone. Or, in developing this ethic further, we may need to consider the psychological effects of economic class as a motivating force.
While traveling in Malaysia, I was struck by the fact that Malaysians want material goods just as much as Americans. If they have the means to get them, they will! Greed seems to be human, not specifically American. The same thing applies to Buddhist goods. There are just as many Buddhist items for sale in Asia as there are in America, if not more. If anything, one finds even tackier stuff. We are upset about malas hawked as power beads? Check out Buddha cell phone straps, Buddha car talismans, Buddha mouse pads, monk dolls, monk stationery, and so on that can be found in any temple or mall boutique. We in the United States might deal with our ambivalence around Buddhist goods by reflecting on the place of these goods for Buddhists in Asia.
REFLECTION
Doing a little fieldwork for this essay, I recently returned to Kmart. On my way, I stopped by Home Depot to check into buying a new water heater for my house. I must say that buying a water heater does not create the intense craving mind of consumerism. It's practical, it's necessary. I did not feel fussy about the fact that water heaters came in only one color (white), for example. I did not feel defined by my water heater. It was a clean, clear, and stress-free shopping experience.
I then went to Kmart partly because I had some real needs—we're tired of using a cup as a ladle—and partly just to wander the aisles and see if anything leaped out at me as being a necessity. I came to the socks section, hoping to buy something basic but stylish. I was proud of myself for not checking Lands' End online first. No, I thought, no one really sees socks, so I will buy what is functional and long lasting so as not to waste resources. But after searching the entire wall of socks, I could not find anything I liked. I felt myself growing fussy and annoyed. Can't this store stock itself right? I began looking at the other customers who were walking around in a daze at all the stuff. I heard a man ask his wife if there were any Martha Stewart versions of their desired object. I sighed, leaned on my cart, and headed for the checkout counter, where one could buy, just in case I forgot, American flag stickers. "Oh, yeah," I thought, "this is what consumerism is about: creating an identity through what we buy, being dissatisfied even with abundance, and being a good, all-consuming American."
There is no question that I am grateful for some of the anticonsumerism views I was raised with on the Zen commune. At the same time, I won't be raising my own children in such deprived circumstances. Fortunately for my generation, we have many more avenues in which to realistically infuse Buddhist principles into a conscious consumerism. We have decent socially responsible investing funds. There are established social activism groups who make a real difference. We have access to abundant alternative food vendors who are socially and environmentally conscious. In colleges, there are plenty of courses on environmentalism, Buddhism, media awareness, and social responsibility as well as student organizations devoted to activism. More so than for our parents when they were young, we can take jobs in nonmainstream professions and get paid for our work. Young Buddhists can take advantage of these opportunities, bestowed by the baby-boomer Buddhists. At the same time, we should become more conscious of our dominant consumerism views and perhaps critique and develop them into a theory.
In the meantime, I can't wait for Martha Stewart to develop her own line of meditation cushions.
5
Marketing the Dharma
Thubten Chödrön
WHEN WE TURN to spirituality, we may think that we're leaving behind the corruption of the world for higher purposes. But our old ways of thinking do not disappear; they follow us, coloring the way we approach spiritual practice. Since we have all been raised to be good consumers—getting the most while paying the least—we carry our consumer mentality as teachers and students of religion right into our spiritual practice.
Although much of what is said below pertains to newer spiritual students, it also applies to those of us who have practiced the Dharma for years and are now seen as teachers. We, too, must reflect on how consumerist conditioning has influenced us. Until we reach the culmination of the path, we remain imperfect sentient beings and Dharma students.
How consumer mentality influences spiritual practice has been a topic of ongoing interest to me for a variety of reasons. My first Dharma teacher, Ven. Zopa Rinpoche, talked continually about "attachment to the happiness of only this life." He stressed motivation as key to the difference between an action that was Dharma and one that wasn't. Did we act with the thought seeking the happiness of only this life? Or did we act with a motivation that looked beyond our own temporary pleasure? An action seeking only our own gain in this lifetime resembles the actions of animals, he said. Animals help their friends and harm their enemies. Animals want to be comfortable and to be "top dog." If, stripped of rationalizations and justifications, our actions are motivated by such thoughts, then we aren't making full use of our precious human life and the rare opportunity it affords us to practice the Dharma.
These were not easy words for me to hear. Previously I'd thought of myself as a good person, even a compassionate, spiritual one. But when I began to meditate and was honest about my motivations, I was alternately shocked and horrified. But I have been grateful to Zopa Rinpoche ever since, because right at the beginning he imprinted in my mind the importance of being aware of motivations and of consciously cultivating beneficial ones. This is not to say that I have been able to do it. Far more often than not, my mind is overpowered by thoughts of "my happiness now . . . or at least my happiness as soon as possible."
Consumer mentality, in which most of us in the West have been well schooled, is clearly rooted in attachment to the happiness of only this life. As a Dharma student and a so-called "teacher," over the years I have noticed my own tendencies in this area. In writing this piece, therefore, I speak as both a student and a teacher. Although most of the essay is written with the inclusive "we," this "we" is amorphous. It may or may not include you, the reader, or me, the writer, in all its usages. (For example, I don't have children, so the "we" meaning parents doesn't refer to me.) However, I didn't want to say "they," as if I were excluding you and me or pointing the finger at others. So, as you read "we," if the cushion fits, sit on it.
THE SPIRITUAL SEEKER AS CONSUMER
The Consumer Mind
How does consumerism manifest on the part of the student? One element of consumerism is seeking the best product. Thus many of us shop around for the best group, the most realized teacher, the highest practice. We go from this place to that, seeking the best spiritual product to "buy." We want the highest teachings and neglect foundational practices. Viewing ourselves as fully qualified disciples, we don't see much need for basic practices such as ethical discipline and restraint of the senses. Instead, we jump into the most advanced track.
As consumers, we want to be entertained. We'll attend a center as long as the teacher is entertaining—and a teacher must be entertaining these days to attract students. We like to hear interesting stories, told in an amusing way, and we want new and fascinating teachings. When we hear the same teachings over and over again, we get bored and set out to find something new and different.
Our practice environment should be interesting as well, so we seek out exotica. Practicing in the Tibetan tradition, I can say that Tibetan Buddhism certainly obliges this. While in Tibet many of these practices and accoutrements are simply part of the culture, in the West they have become exotic lures. High thrones for the teachers, brocade seat covers, and robes, long horns, short horns, bells, drums, processions, deep chanting, and, oh yes, hats! Yellow ones, red ones, black ones. With all the paraphernalia, how could one ever get bored practicing Tibetan Buddhism? Yet after a while we become jaded and are left with just our own minds, our own suffering. Having little endurance or commitment to practice or to teachers, we move on, seeking something more interesting. We neglect to see that repetition may be just what we need or that exploring the reason for our boredom could bring fresh insights. We also fail to notice that our teachers still do foundational practices and attend elementary teachings given by their spiritual mentors.
Consumer mentality insists on instant gratification of our desires. In spiritual life, we say we want a close relationship with a spiritual mentor, but when that mentor's spiritual guidance challenges our desires or pushes our ego's buttons too much, we stop going. At the beginning of our practice, we profess to be earnest spiritual seekers, aiming for enlightenment. But after the practice has remedied our immediate problem—upset from a divorce, grieving the loss of a loved one, and so forth—and we are happier, our attention shifts once again to seeking happiness from possessions, romance, technology, or career, and spiritual interest fades.
Today's consumer expects things to be easily available and obtainable without much effort. In past ages, spiritual aspirants underwent difficulty to meet teachers. Tibetans traversed the Himalayas to meet wise mentors in India; Chinese crossed the Takla Makan Desert and Karakoram Mountains to attend monasteries and bring back scriptures from India. But nowadays we think, "Why should we have to travel to attend teachings? The teacher should come to us! We have such busy lives we don't have time to go across the country, let alone to another continent." Forgetting that the seeker's very effort and struggle opens him or her to the teachings, we'd prefer that spiritual practice not disturb the flow of our life.
Receiving lengthy teachings or doing complex spiritual practices takes time that modern consumers don't have. Our time is taken up with families, jobs, hobbies, and sports; spiritual practice should not impinge on those pleasures and responsibilities. So we ask our teachers to "modernize" the teachings and practices—to shorten and simplify them—so that they will fit conveniently into our lives. As consumers functioning in a world of supply and demand, we take our business elsewhere if our wishes aren't satisfied.
The Dilemma of Dana
Asian Buddhists traditionally make offerings, or _dana_ , to the monastic community to accumulate merit or positive potential that will bring a good rebirth. Looking at them, some Westerners say, "They're doing spiritual business. They are giving to get something for themselves." Thinking that Westerners are superior to Asians trapped in old traditions, we don't give to the monastic community. Instead we hold to the American work ethic and think monastics should go out and get a job.
When we do give dana (or donations), what is our attitude? At the end of a retreat, someone gives a "dana talk," explaining to everyone that dana is generosity freely given. "Think of all we've received from our teachers during this retreat. They have families, cars, mortgages, credit card bills, and for them to continue to teach us, they need our financial support." Hasn't dana then become another way of paying for a consumer service we've received?
We don't give to support earnest practitioners who don't teach. Instead, we give to teachers when we've received their services. We go through lots of mental gymnastics figuring out how much to give: "Let's see, if someone were to charge for this retreat, how much would be a reasonable price? That's what I'll give." We totally miss the point of dana, which is to take delight in giving and to give from our hearts.
According to the consumer mentality, we pay as we go. But dana is a long-term commitment that is part of our practice. We give because we want to be free from the hindrance of miserliness; we offer dana because we appreciate the teachings and practitioners. When we give dana properly, we don't offer less for a two-day retreat than for a four-day retreat. Instead we give because we want to support practitioners who live simply and devote their time to spiritual study and practice. We give to make the teachings available to new people.
Consumerism breeds self-centeredness. Spiritual practice often becomes centered on "me," my needs, my wishes, what is convenient for me, what works for me. When we go to a religious place or event, we think, "What can I get from this? How will it benefit _me_?" A dharma center, temple, or monastery becomes a place where we go to receive, not to give. If an activity doesn't meet our needs, we don't have the time or money to support it.
I regularly visit an Asian temple in Houston where they hold summer camps for kids. Working in the kitchen, cooking food for a hundred people, are parents, students, grandparents, single adults, and couples without kids. Many people who don't have children are willing to spend four or five days cooking or running children's programs. Why? Because they enjoy being part of a community. They care about children and the future of society. They want to give their time and energy to support something worthwhile for others. Giving is part of their spiritual practice, and they relish it. They enjoy giving, in contrast to consumers who enjoy receiving.
Why do Westerners have trouble creating community? After all, most of us feel a deep longing for community, but still we keep our distance and maintain our autonomy. My guess is that this has to do with the _c_ word, the word we are very frightened of. No, it's not _cancer_ , although that undoubtedly is frightening. The _c_ word we mistrust is _commitment_. If we commit, our shopping around ceases. We have responsibility not just to others but to ourselves. We commit to a daily practice; we commit to attending regular dharma classes in order to nourish our hearts; we commit to attending yearly retreats. We commit time to plan activities at the dharma center, monastery, or temple. We commit energy to plan the Sunday school program instead of just dropping our kids off in the hope that someone else will teach them the dharma. We commit goodwill to serving our teachers and fellow practitioners. This cuts into our time to be with family, to watch TV, go to the gym, talk on the phone, do e-mail, browse catalogs, frequent the mall, and go on vacation. In short, it requires that we divert time that ordinarily goes toward worldly pleasure into time leading to dharma happiness.
Somehow we mistakenly think that commitment means being trapped. In fact, when we make wise, well-thought-out commitments, they free us. They enable us to enter deeply into our practice and shed our defenses before our teachers and fellow practitioners. We develop trust in others and ourselves and learn to be fearlessly open. And most of all, we stick with a teacher and a practice long enough so that the dharma can actually transform our minds. As one student said, "We keep showing up, whether we're happy or unhappy, whether we understand the teaching or not. We keep coming, instead of getting discouraged or distracted." Only with commitment can we actually taste the dharma.
The Enchantment of Status
In a consumer society, people derive status from using certain products. Similarly, being close to a famous Dharma teacher uplifts a student's spiritual status. Having that teacher stay in our home, ride in our car, bless our religious objects, sign a photo, and so forth gives us something to display to others. These days one of the best ways to become close to a teacher is by being a big donor, thus obliging teachers to see you in order to show their appreciation. We wouldn't want to give anonymously and miss a possible reward.
We also gain status by possessing valuable spiritual items. We buy beautiful statues and exquisite paintings of religious figures, which we display on elaborate altars in our homes. On the altars, too, are photos of ourselves with various spiritual masters. When dharma friends visit, we make sure they admire our collection of artifacts, but when relatives visit, we discreetly cover them to avoid their inquiries. We have the latest spiritual books (preferably autographed by a famous author), a comfy meditation cushion (or two), and the requisite prayer beads (made of crystal or stone, not plastic, and blessed by a holy being).
In addition, we collect spiritual events. We proudly rattle off a list of retreats we have attended or initiations we have taken and advise new students about which events and teachers are mediocre and which they must not miss. As experienced connoisseurs, we critique retreat centers for newcomers. We boast of attending large teachings by famous teachers and mention that as a teacher was making his way through the crowd, he stopped to greet us, or while he was sitting on the Dharma throne, he smiled directly at us. Meanwhile, we pat ourselves on the back for being such sincere practitioners.
Similar to the status-seeking attitude is one that idolizes great figures. In consumer society we worship movie stars, sports stars, and political leaders, thinking that everything they do is wonderful. As teenagers we wanted to emulate them; now, as semicynical adults, we idolize them for awhile and buy the things they advertise. But later, when we see their human failings, we blame them and become discouraged.
The same happens with our Dharma teachers. For a while we are in love with our guru: He's so wonderful; his compassion makes the room shine. She's so humorous and warm. He's an incarnation of a very high yogi. She's clairvoyant. We sit around and drink tea and talk about our teachers, telling stories about cute incidents, reciting tales of their great qualities. Sometimes there is subtle competition over who has the highest teacher or who can tell the greatest stories. We revel in newcomers' wide-eyed fascination as they listen to us; we're jealous of those who have better stories.
When our teachers do things we don't agree with, or worse yet, when their behavior appears all too human, we feel betrayed. We are disappointed or indignant, just as when we discover politicians' scams, movie stars' mental illnesses, and sports stars' greed. But we don't realize that our previous attitude was a setup for our present feelings.
What is it in us that makes us seek someone who is perfect? And what does "perfect" mean, anyhow? Does it mean that the person does what we want when we want him to do it? Does it mean she agrees with all our opinions and ideas and lavishes praise on us? I believe this tendency toward idolization relates to the consumer mentality that seeks "the best, or your money back." We have a steady diet of advertisements that condition us to become enthralled with grand expectations of happiness when we buy _this_ product, vote for _this_ candidate, see _this_ film, or attend _this_ game. We bring our unrealistic wishes for perfection and satisfaction into our spiritual practice, projecting them on teachers and meditation practices.
SPIRITUAL MENTORS AND CONSUMERISM
Marketing the Dharma
Consumer mentality influences teachers as well. In a consumer culture, advertising boasts about the excellent qualities of a product. Following this pattern, notices of Dharma events don't just announce an event but actively sell a product, that is, the teacher or the teaching. Most ads display an enticing photo of a spiritual master who is either smiling radiantly or looking wisely into the distance. He or she, the ads declare, is a highly realized, well-respected, fully accomplished master. The topic being taught is a secret teaching that in the past was given only to a select number of qualified disciples. It is the supreme teaching by which previous masters have attained enlightenment. You can receive this for a mere $99.95 plus dana for the teacher. Register early to reserve a seat or you'll be left out. What happened to the age-old custom of humble masters who kept their qualities hidden?
With sincere motivation, informing people who could benefit from a spiritual teaching or retreat is valid and necessary. Can this be done without hype in a culture that thrives on hype? This is a dilemma for many of us because we came to the Dharma partly because of a dislike for the hype and hard sell of consumer society. We want to let people know about Dharma events so they can benefit from the teachings, but we prefer simple announcements. However, these get lost amid the many attractive ads and fascinating flyers. For teachers to draw people to Dharma events, they need to have a title or two, and they must appear "high" or important. His Holiness the Dalai Lama has remarked that people who are unknown in Asia come to the West and suddenly become lamas and rinpoches with a string of titles before their name and a retinue of devotees behind them.
Personally, I find this issue difficult. _Venerable_ or _bhikshuni_ indicates I'm a monastic (at least in my tradition, though _Venerable_ is used differently by others). That's fair enough, because I've been ordained since 1977. However, I have nowhere near the qualities of my teachers and therefore do not want people to address me as "lama," a title that in my tradition is reserved for well-respected teachers. On the other hand, some people who are much newer in the dharma are called "lama"—sometimes because their tradition uses the word differently, sometimes for other reasons. So people ask me, "How come you're not a lama?" When I explain why I don't use that title, they think I'm odd, because in a Western consumer culture, we are taught to display our qualities and make ourselves look good.
To market a product, it must be appealing to potential buyers. The Buddhist teaching of skillful means—teaching according to the disposition and interests of the students—is necessary to guide people on the path. But when do skillful means degenerate into pleasing students so that teachers will have more students? Do we omit particular ideas or teachings or explain them away because potential students don't like them and will stop coming? How much do teachers water down the scriptures in the name of skillful means, when our motivation is actually attracting and maintaining a large following?
There is much danger in this, because it is easy to teach something that looks like Dharma but is a mixture of Dharma and our own ideas and preferences. Sometimes we aren't even aware we do it, because we receive great praise from numerous students, who say, "Your teachings are wonderful!" And since more people are coming to our talks and more people are buying our books and tapes, we think what we're doing must be good.
Success Is in Numbers
In a consumer economy, success is measured by numbers. Thus many spiritual teachers hope attendance at teachings will be high, dana will continually increase, their books will sell well, and invitations to speak on television and radio programs will be plentiful. To what extent do teachers decide where to teach based on the amount of dana they will receive? Is it just coincidence that many teachers go to wealthy communities? How many teachers go to developing countries or to lower-income areas in our own country where dana is meager?
Financial resources are necessary to spread the teachings. How can teachers procure support consistent with right livelihood? Do we drop hints, flatter, or subtly coerce people so that they offer money to us or to our organization? Do we give donors extra perks that are denied to other devotees who may be more sincere but not as well off ?
For monastic teachers, the issue of personal livelihood is much simpler. We don't need a lot because our precepts set parameters on our lifestyle. We don't have many or diverse clothes, we don't wear jewelry or cosmetics, we don't own a house or a car, nor do we have children to support. For lay teachers with families and a middle-class lifestyle, this is trickier.
But both lay and monastic teachers have organizations that support Dharma study and practice and sometimes social welfare projects as well. As someone trying to start an abbey in North America, I struggle with this. As an individual monastic, I didn't need much. I was careful not to view people in terms of who had money and who didn't. But to begin a monastery, more is needed. Many people have suggested fundraising ideas that I have vetoed because they involve pressuring, schmoozing, or giving perks to those who give. I would like people to donate to the abbey because they value the Buddha's teachings, appreciate monastics, and want to see the Dharma flourish in the West. I want them to give because they take delight in giving and feel good about contributing to worthwhile projects. How can I share my enthusiasm for the abbey in a respectful way that accords with my own principles?
THE DISADVANTAGES OF SPIRITUAL CONSUMERISM
Consumer mentality in spiritual students and teachers brings disadvantages to both ourselves and others. In terms of ourselves, it draws us away from actualizing our deepest spiritual aspirations. As mentioned earlier, the distinction between dharma and nondharma actions is made primarily in terms of motivation. Motivations seeking only the happiness of this life are considered worldly because they focus on our own immediate happiness. Motivations aspiring for good future rebirth, liberation, and enlightenment are spiritual because they seek longer-term goals that benefit self _and_ others.
When describing a mind seeking the happiness of only this life, the Buddha outlined eight worldly concerns. These eight fall into four pairs: (1) delight in receiving money and material possessions; displeasure or upset at not receiving or being separated from them, (2) delight in praise, approval, and ego-pleasing words; displeasure at criticism and disapproval, (3) delight in having a good reputation and image; displeasure when they are tainted, and (4) delight when contacting pleasurable sense objects—sights, sounds, smells, tastes, and tactile objects; displeasure when encountering unpleasant sense objects. When I examine my mental states, most of them consist of these eight. Personally speaking, I find having a pure spiritual motivation is actually quite difficult. I hope that others who suffer similarly from worldly motivations aren't afraid to admit it to themselves and others. Only through being honest with ourselves can we purify our minds and hearts.
Consumer mentality in spiritual seekers is clearly involved with the eight worldly concerns. While it is often masked by clever rationalizations, it still enslaves us to the happiness of only this life. When that mind is operating, true spiritual practice cannot occur. We may come to the Dharma with sincere aspirations and devotion, but when old self-centered habits creep into our motivations, we lose what we cherish the most. We may put a lot of time and energy into activities that look spiritual but aren't because the motivation is tainted with the eight worldly concerns. In this way our consumer mentality can sabotage our spiritual practice and noble aspirations.
Perhaps most distressing is the harmful impact spiritual consumerism can have on others. Dharma teachings have been passed down for centuries by practitioners who took great care to preserve their true meaning expressed accurately. The consumer mentality threatens this purity by enticing teachers to "adjust" the meaning of the teachings in order to draw bigger crowds or to have a better reputation. This deprives future generations of spiritual instructions that are true to their source. It can cause others to lose faith in the efficacy of practice because they see teachers speaking one thing but acting the opposite. That is, we talk about the disadvantages of samsara and generating the determination to be free from it, but we act in ways that show our craving for samsara's pleasures. Seeing this, students may think that the teachings don't really work, that the Dharma is a sham. This devastates their possibility for enlightenment. In addition, consumer mentality allures spiritual institutions into creating structures that harm the very people they promise to help. This occurs because the purpose of the institution shifts subtly from serving others to self-preservation.
REMEDIES
In the _Pathamalokadhamma Sutra_ , the Buddha said:
_Among humans, these things, namely_ ,
_Gain, loss, status, disrepute, blame, praise, pleasure, and pain_
_Naturally are impermanent, uncertain, and liable to change_.
_The wise, ever mindful, understand these things_
_And contemplate them as always shifting and changing_.
_Thus, delightful things cannot oppress their minds_ ,
_They have no reaction to disagreeable things_ ,
_They have abandoned all liking and disliking (for worldly concerns)_.
_Further, they know the path of nirvana, dust-free and without sorrow_ ,
_They have reached the other shore of existence and know this correctly_.
One of the foremost antidotes to the eight worldly concerns is the meditation on impermanence and death. By seeing pleasure from the eight worldly concerns as transient, we lose interest in them. By seeing the worldly concerns as uncertain, we are disinclined to exert so much energy into procuring and protecting them.
Struggling for worldly happiness is wearying. We may work very hard to attain the four pleasures and be free from the four displeasures, but we are not necessarily successful. Why? Because we can't control the external world and everything in it. Therefore, it is more valuable to transform our minds. By freeing the mind from attachment, hostility, and ignorance, we will be able to be internally content no matter how much wealth we have, no matter what people say about us, and no matter what we experience. Attaining stable peace—nirvana—is the purpose of Dharma practice.
Part of the remedy lies in asking ourselves, "What does it mean to be successful?" We have been conditioned that the eight worldly concerns constitute success, but do they? We know people who are successful by worldly standards—they have wealth, good relationships, status, and sense pleasures galore—but many of them are miserable. Are these people actually successful? Isn't a better measure of success our internal experience of peace and joy? If so, we need to focus on developing this through spiritual practice.
So whether our consumer mentality functions in the shopping mall or the meditation hall, I propose that we try to catch it when it arises and bring our minds back to what is truly important: compassion and wisdom. Let's revive appreciation for the traditional model of a practitioner—a renounced being who lives a life of simplicity and humility, sincerity and endeavor, kindness and compassion. Let's choose teachers with these qualities and cultivate these qualities in ourselves. Let's keep our spiritual institutions on track by having only as much organizational structure as needed to facilitate the teaching and practice of the Dharma.
Buddhists are attempting to introduce Dharma values and establish a substantial role for the Buddha's teachings in Western culture. The consumer mentality is a great obstacle to reorienting people toward spiritual values and aims that would benefit them. Our collective challenge is to practice and teach the Dharma in ways that not only benefit contemporary culture but also preserve the purity of the Buddha's teachings.
6
You Are What You Download
Diana Winston
LET'S IMAGINE THE BUDDHA ON FOOT, traversing dusty northern India a few hundred years before the birth of Christ. Wandering and spreading the word from village to village, stopping only during the rainy season, he is followed by a retinue of shaved-head men and women, all of whom see him as the Holy One, the Enlightened, the World Knower. Each word from his mouth is like nectar to the disciples, quenching their thirst for knowledge, leading them to the supreme happiness. The great sage carries a begging bowl, a razor, a second set of robes, and a worn-out but still functioning laptop with an extra set of batteries. Even the Buddha needed to check his e-mail.
This image may not work for you. Never mind the anachronism. In truth, it's hard to imagine the Buddha surfing the Web. He was an oral tradition kind of guy, for starters. If the Buddha were around these days, I bet he would have a lot to say about Internet technology and its effect on our minds. Does the Internet oppose his teachings of moderation, restraint, nonconfusion, and nongreed? What about the Buddhist precept against clouding or confusing the mind with intoxicants? Is the Internet an intoxicant, sending us further into the delusion of separateness, wanting, control, and self? To answer these questions, the Buddha would point us computer-age denizens directly to our own minds. It's all there, in this fathom-long body, so he said.
He might ask us: Does it matter what you fill your head with? From the Buddha's perspective, the answer is unquestionably yes. Everything affects us. The law of karma reminds us that each action—no matter how tiny—has an effect. And effects are cumulative: "With single drops of water, the water bucket fills." What kind of mental habitat do we want to create? What kind of self (to use Buddhist language) gets constructed each time we add another drop of water, possibly from a questionable source, into our mind? And might the accumulation of those drops drive us into activity we might not be too happy about later, such as Web shopping for antique dinnerware?
The popular belief, so I hear, is that we don't need to worry about what goes into our heads. We forget everything. Watching violence on television does not necessarily reproduce violent acts in the real world, the theory goes. After all, we have natural filters, we humans are infinitely adaptable, and smart to boot. We'll forget the unimportant or awful stuff and retain what really matters, like which cable station is which number on the channel changer.
My own experience as a meditator, spending hours and hours observing my mind, has shown me without a shadow of doubt that we _are_ affected by what enters our minds, although we don't always see it right away. If we feed our minds with greed-inducing information, we are certain to get more greedy. The Internet, once hailed as a revolutionary, time-saving communication technology, has turned out for the most part to be a time-wasting, greed-inducing, glorified shopping channel. As with most things in America, consumerism reigns. And our poor minds pay the cost.
THE CLOUDED MIND
I'm a bit of a meditation junkie. I gravitate toward long periods of structured silent retreat, say, three months at a time. I practice vipassana, or insight meditation, where I observe the moment-to-moment experience in my mind and body: my breath, body sensations, thoughts, and emotions. On these retreats I meditate in silence for sometimes fourteen hours a day, every day, no break. I am not supposed to talk to anyone, read, write, watch TV, open a newspaper, or go online. The point is to clear the mind of the usual distractions of everyday life in order to see where my mind is clinging or creating a sense of "self," and then to find freedom through letting go. So on retreat I empty out my mind, and in all that residual mental space, everything I ever ingested floats to the surface. Yes, it is still in there, although it's hard to say where.
On long retreats I remember the tiniest supposedly insignificant experiences, like the time I fought with my friend Karen when we were four because she wanted to color the entire coloring book red and I protested for variety's sake; or my dad teaching me to listen to rain; or the wallpaper in my bedroom and the way the light shone in between the tree leaves and created moving shadow puppets on the wall; the smells and views of the little hill town in India where I lived for six months; and the time I first kissed someone, who shall remain nameless.
While meditating, my mind has yielded at all hours of the day, without relief, unending rounds of seventies commercials, television jingles, Broadway musicals, "The Brady Bunch" and other TV theme songs, monologues from acting class, bad rock and roll, previous discussions, good rock and roll, songs from summer camp . . . _the ants go marching one by one, hurrah, hurrah_. . . . They have not gone away. Worse, when I try to sit still to find peace and calm, they come back to haunt me. (I will say, however, that in all these years of meditating, quantitative algebra has yet to materialize.)
No, this mind has not forgotten. It is all in there, especially strong and violent stuff. An avid fan of Salman Rushdie, I once snatched up the first novel of his former wife, Marianne Wiggins, with anticipation, assuming great minds must think alike. Before long I found myself unable to put down an oeuvre on cannibalism. The plot chronicled a group of young girls who, shipwrecked on a desert island, resort to dining on each other. I have scarcely encountered in literature anything as horrific as the little girls gleefully roasting the forearms of the ship captain and devouring the ghastly morsels. I quickly put it out of my mind. Or so I thought. A few years later, in the midst of another long meditation retreat, graphic replays from Wiggins's book tortured me. For a week I walked the halls of the meditation center like a wraith, tormented by images I couldn't exorcise. Ultimately they played themselves out, thanks to vigilant mindfulness. I followed the experience with a heartfelt vow: From this day on I will never take anything into my poor mind that I don't want to see later.
Are meditators encouraged to hold to a basic level of ethics because you might not like what you see otherwise? If you are morally in good shape, maybe you don't spend hours on the cushion engaged in remorse, regret, and guilt. But what if you're not? _I shouldn't have told her that story, but it was just too good to keep to myself_ , or _I should never have shoplifted the Bonne Bell lip gloss from CVS; the ants go marching two by two, hurrah, hurrah_. Ethics gives us a framework to abide by. As part of our personal ethics, we can lean toward simplicity, renunciation, and generosity rather than complication, gaining, and consuming. Thich Nhat Hanh's interpretation of the fifth precept invites us not to cloud our mind with _any_ kind of intoxicant, including TV and the Internet, in addition to the usual drugs and alcohol listed in the Buddhist texts. If we try to follow this precept, we may try to avoid online stimulants and the apparatus of shopping in order to maintain some peace of mind. We can create a life infinitely less cluttered with stuff—internally and externally.
But if we do find ourselves inexorably drawn to the Internet, what happens when we deliberately imbibe excessive, violent, stupid, pointless, titillating, and prodigious information in a direct link from our computer to our brain? As an Internet user, my already full mind is privy to vast new fields of information, stories, poems, bad jokes, sites, commentary, porn, pet projects, hoaxes, dating opportunities, music, chat rooms, sweepstakes offers, commercials, products, advertisements. _Do I need more stuff in there?_ I have hundreds of books I haven't yet read. I have interesting friends whose brains I haven't picked, countries I've never visited, films still to see—and libraries, remember them?
Now I cannot help but think Internet thoughts. My everyday discussions refer to links and URLs and sites. Once I commented to a friend that our conversation had become a Web site. We headed in one direction and a tangent sent us off in another, which led to another, and so on. We were clicking conversational links. "Would you hit Back?" he asked me. "I'm lost."
What do we want in our minds? More junk? If so, log on. Do we really want to keep jamming in this useless, vaguely entertaining, often not even true, never-ending information? It will stay in there, I guarantee. And it will come out to haunt us. The question is, will it make us better people? Yes, yes, I know, we can learn very important things from the Internet. Alternative press has flourished, as has alternative political campaigning. I have access to new media studies, hip peace events in Bangladesh and Colombia, left-wing critiques of the war of the month. They used it in Chiapas. They organized with it in Seattle. I am not denying any of this. If you think I'm only complaining, you are missing my point.
But what kind of karma is being created from daily, less-inspired use of the World Wide Web? What sort of self is being constructed? Will the Internet make us ethical, kind, generous, or compassionate? Will it make our minds and lives more spacious and relaxed? Or will it inflame our greed, leading us to consume? With all that ingested junk, and access to much, much more, how does the Internet affect our basic ability to free our minds? Is it a tool for enslavement or for liberation?
DEPENDENT (OR NOT) ORIGINATION
On the day I realized that I could have anything I wanted over the Internet, I bought ten new books, a subscription to a simple-living magazine, and a pair of black leather boots, and sent myself the daily quotes of the Buddha. The Buddha sent me an e-mail about the law of karma. He said actions have results. If I plant a plum pit, I will get a plum tree. If I practice greed, I will be more greedy. If I practice generosity, I will be more generous. Buddhism 101.
The Buddhist teachings explain on a microscopic, almost neurological level how attachment works and the self gets created. We encounter, for example, a desirable object. At the moment of visual, aural, or touch contact with that object, a pleasant feeling arises in our minds or bodies. This pleasant feeling comes from a variety of places—past habit, training, media, standards of cool, socioeconomics, karma, and so on. With this contact, we associate the pleasant feeling with the object. The feeling itself is wonderful. In order to sustain the feeling, we think we need to _get_ the object. We cling to the feeling and then to the object itself that we think has produced the feeling. We get attached, and voilà, the "self" is born.
Another way of saying this is, we feel something nice (pleasant feeling), we reach out for it (craving), grasp our hand tightly around it and don't let go (clinging), and then there is a birth of the self (becoming). It works in reverse too: an unpleasant feeling results in not wanting and ultimately pushing away (aversion). In Buddhist philosophy, this chain of events is called dependent origination—nothing is independently produced. This chain is happening continuously at such a rapid rate that we are seldom aware of this process. They say it is the driving force by which we live our lives. We are unconsciously responding to pleasant or unpleasant stimuli, but all we know is that we have to have the new DVD player.
Dependent origination teaches how we automatically grab for an object to stop the aching and sustain the pleasantness. In effect, we are trying to put an end to our suffering, which is certainly understandable. The chain can seem hopeless—we are controlled by an unconscious process, running toward pleasant experience and away from what is unpleasant. But this is where mindful awareness comes in, which is really the key. Mindfulness is the part of our mind that knows exactly what is happening when it is happening. It is present, aware, and connected to the moment. It has a liberating power in that it can help us to see clearly. Through the power of mindfulness, it is possible to short-circuit the cycle and prevent the automatic response. If at any moment we apply mindful awareness to the cycle of contact, pleasant feelings, wanting, and clinging, we need not move on to the next link of the chain.
We can notice _Wow, I want a pair of boots_. We can feel the feeling of desire in our bodies (aching in the chest or gut area, pounding heart) and notice the accompanying thoughts ( _they're perfect, I can't live without them_ ). Then we can apply mindfulness to these sensations or thoughts. When we see them clearly for what they are—merely thoughts and sensations, not truths about ourselves—the mind may let go. We may relax some, soften the belly, notice: "Hey, it's just a thought." By seeing it clearly, the mind can let go and stop the forward thrust into attachment, purchase, and the boot-addicted self.
The revolutionary insight brought to us by the Buddha is that actually it is painful to want. Letting go of wanting stops the pain. Getting what we want only temporarily soothes the wound. Buddhist wisdom teaches us that a desire doesn't have to be fulfilled to make it go away. We can recognize and let go of the desire. We can break the chain. All we have to do is catch a single point on the cycle. _Oh look, there's pleasant contact with a desirable pair of boots! Oh, I feel body sensations of longing for them, hmm. Oh, I feel myself wanting!_ If we can bring mindfulness here, we can break the chain. It is up to us; we are not slaves to an automatic process. We don't have to buy the boots. The desire for them may fade through the power of mindfully witnessing dependent origination.
Part of breaking the chain depends on our ability to have some space for reflection. But what happens when our reflection time is limited? What happens when we throw the speed of the Internet into this equation? Over the last decade, the space between a desire and the satisfaction of that desire has almost disappeared. Back in the Stone Age (before 1994, when the Internet was just a toy for computer geeks and the military), if you wanted something, there was a process. You could think about it, visualize the item, research the product, save money, compare the item at several shops, ask your friends for advice. Yes, there were mail-order catalogs, and I suppose even the shopping channel existed back then, but there was some consideration in the process to get something you wanted. Not that this would necessarily deter you, but in those halcyon days, purchasing an object required work.
On the day of the planned purchase, perhaps you asked a friend to join you, drove to the shop, found parking, discovered the desired object was or wasn't there, or they didn't have your size, browsed other things, talked with a salesperson, stopped for a late lunch, and finally, when descending upon your desired object, perhaps reneged—"Well this may not be exactly what I want after all." Today you peruse the Internet and log on to a shopping Web site. You want something—anything, really. It's the CD you never realized you needed, but now you will die without it. There it is. Great. How much? No problem, it's on sale! You type in your credit card number (or your computer—in true Orwellian fashion—remembers it), hit a control key, and it is yours.
Pleasant feeling, wanting feeling, and instantaneous action—all in just a few seconds. There is no time for mindfulness to prevent the inevitable purchase. We have no time to get free. It is easy to act quickly when there are no obstacles. We don't have to go anywhere, talk to anyone, discuss, debate, consider, or compare. We merely have to press a button.
What happens when space and distance are removed in the buying process? What happens when every possible desire can (appear to) be fulfilled at the click of a mouse? When getting an object is taken for granted in the wanting? When millions of young minds are taught that they can have anything they want whenever they want it? What are they taking into their minds, nonstop, with no filters whatsoever? What happens when these children grow up? What will happen to those sweet Buddhist values of nongreed, compassion, and generosity? We may be in for some trouble. In the new millennium, thanks to the Internet, the process is so sped up that we have no built-in physical moment to break the cycle. Could the Internet and its rapacious commerce be contributing to the breakdown of the social fabric? It seems we have become slaves to an even quicker version of dependent origination. The profusion of objects is endless; we attain them at lightning speed. This is not good news, contrary to all the press.
GO REALITY
There must be an antidote to this proliferation. There must be a way out of the constructed self that has been birthed through a field of never-ending consumer desires nestled among prodigious and useless information. There has to be a way to circumvent the nasty effects and the not-so-desirable self that now has been born. It will require some work. I'm not discounting the difficulties of swimming upstream in a culture addicted to speed and greed, but we have to start somewhere.
We might try a few guidelines for support. We could limit the time we spend on the Web and do our best to stick to it. I like to ask myself, do I really need to read the thirty-fifth analysis of the Patriot Act, or could I live without it? Or we might decide that for every hour we spend online, we spend two hours in nature or with friends. A one-to-two ratio, while arbitrary, seems appropriate, or at least a place to start. Another practice would be to pay close attention to how our mind feels upon unplugging. For me the aftermath is increasingly unpleasant and the groggy spaced-out feeling is becoming less and less desirable. Sometimes after a protracted, riveting session on eBay, I log off only to find I can barely tie my shoes. Oh, right, I have a body. A neighbor stops by and it takes about fifteen minutes before I connect with the actual experience of talking. I am stumbling as if I'm drunk, and my eyes are itchy, as if I've been in a sandstorm. Ultimately I normalize, but the transition period is definitely not fun. I now ask myself on a regular basis, would I rather take a walk or surf the Web? (Don't get me wrong, sometimes the Web wins.)
There is a host of potential practices we could try. We can program our computer so a "mindfulness bell" rings randomly, and the monitor goes blank temporarily, helping us stop in that moment, breathe, and sense the body. We can put little awareness reminders stickered to our computer. We could answer e-mails only on alternate days. If we work in an office, we could invite friends to stop by to remind us to breathe while we are on the computer. In that dreadful endless space between Web pages being loaded, we could perceive it not as a tragedy but as a moment for coming back to ourselves.
As for the consumer end, we might agree with ourselves that we will make no impulse buys on the Internet—everything must be considered within a day. Or if we're really addicted, no Internet shopping, period. But I'm skeptical of the cold-turkey approach. If we really want to get radical and work at it, developing mindfulness will go a long way toward subverting the greed-inducing effects of the Internet. Learn to meditate, attend retreats, practice, practice, practice seeing the mind getting caught in craving, and learn to let go. Observe dependent origination at work in your life as frequently as you can. Notice pleasant sensations. Notice wanting. Notice clinging, notice self. Ultimately, develop mindfulness that's sharp and subtle enough to catch the pleasant sensations _while_ online. That's the advanced practice, of course.
One of my friends, a computer expert for a meditation center, decided to try a personal "computer retreat." For several weeks he meditated five to six hours daily, and when he wasn't sitting he went online, answered e-mail, and attended to his computer responsibilities.
"Were you able to be mindful?" I asked incredulously.
"Well, not to the details of typing and reading, not each finger," he replied. "Of course my mind got sucked in. But in that retreat space, I was able to have a general sense of awareness. I could feel the presence of my body and watch myself when I got sucked in, and I could come back to the bodily experience."
How extraordinary: it may be possible to find freedom while interfacing with the machine. I suppose we need strong framing devices to override the force of habit.
On the ethical level, we have to ask ourselves what kind of person we want to be. Greedy and addicted, or generous and free? It _is_ possible to cultivate the second set of qualities. We actually have the capability to develop our character through practice. We can generate the self we want to be. Who we become depends on each little action we take, one choice or one mouse click at a time. Whenever I fall in love with something I just _have_ to buy—a new sweater, a fancy toaster, or even a doorstop—I ask myself this question: Ten minutes ago, did you even know the item existed? Somehow this simple reminder helps me to let go of the wanting.
In the end it may come down to that Buddhist value of contentment. Being with things exactly as they are and being perfectly content. Not needing anything other than what you already possess within you to be happy. Contentment isn't valued in this high-speed and high-greed culture. If people were content with what they have and who they are, why would they go shopping? Learning to cultivate and acknowledge your own contentment is a revolutionary act in these times. Every time you feel content—in a conversation, a meal, a sunset—really sense the contentment. What do your body and mind feel like? For me contentment holds a subtle quality of well-being, a peace or quiet happiness. My body feels fully present, relaxed. I could be smiling, but I don't have to be. Everything is simply enough. Nothing more is needed to be happy. We can train our minds to settle for less. Just this.
To address the systemic impacts of cyberspace, I thought it might be useful to start an advertising campaign called "Go Reality." It would remind people through television spots, print media, and flashing Internet ads that ordinary life, exactly as it is, is actually _better_ than the virtual world. Posters would display zoned-out kids staring glassy-eyed at computer screens contrasted with other kids romping cheerfully through the woods. Celebrity spots could broadcast: "When was the last time you spoke to your child?" or "Real sex is better" or "Try nature, it's the real thing."
The Go Reality campaign could invade the Internet and promote disruption. Those horrible hijacking ads—the ones for dating and for loans that pop onto your screen when you hit the Web—could be rivaled with hijacking ads of our own. Whenever you go on a shopping Web site, a message could pop up: "Do you really need that?" "Save for your kids' education." "C'mon, you're wasting your money." We could buy banner ads on all the major commerce sites shouting the criminality of excessive shopping. _Reality_ , we could proudly display, _means being okay with things as they are!_
It's a great idea. And I promise to get to work on it right away. But I just heard about a new discount Web site, and, well, sitting back and shopping is a heck of a lot easier than changing the world.
PART TWO
Practicing with Desire
Using Buddhist Tools
7
Cultivating the Wisdom Gaze
Judith Simmer-Brown
WHEN TIBETAN BUDDHIST LAMAS fled the Communist Chinese tyranny in 1959, many came to the West to study, teach, and practice the dharma. The culture they encountered, however, presented special challenges to a genuinely spiritual life. In contemporary America, the dominant obstacle they observed was the predominance of materialism, a lifestyle of acquisition that promotes self-grasping. Tibetan teachers have commented about how difficult it is for American students to practice meditation in a materialistic environment. Observing the difference from his Tibetan home, Khenpo Karthar Rinpoche remarked:
Because Tibet is an untouched and uncivilized country, people are quite happy with the simplicity of life. They do not long for the comforts and luxury of life. As long as there is food to eat and a roof for shelter, they are very happy. With that state of mind, when they go to retreat, their mind is simple and the decision is quite complete. They think, "Even if I die of an illness during this retreat, I will let myself die. Even if I die of starvation during this retreat, I will let myself die. Even if I die from the difficulties and hardship of the vigorous practice, I will be happy to die."
Buddhist scholar José Cabezón has suggested that traditional and contemporary Tibetans are primarily concerned about how material wealth "deflect[s] one from pursuing the true, inner wealth of spiritual perfection." Wealth is viewed as ephemeral, and therefore rather than accumulating it, it is more important to spend and enjoy it while it is available, or to give it away. He refers to the thirteenth-century Tibetan master Sakya Pandita, who reflected that those who have wealth that they neither use nor give away must be either sick or a deprived spirit. "Accumulating wealth without using it is like accumulating the wood for one's own cremation. Those who do so are like bees, who put so much effort into manufacturing their honey only to have it taken away from them." Accumulating wealth accrues many obstacles, for then the wealth must be protected and one's greedy tendencies are exacerbated. When accumulation of wealth is an end in itself, it can divert one from the spiritual path and create negative circumstances for future awakening.
More than thirty years ago my teacher, Ven. Chögyam Trungpa Rinpoche, wrote one of the first popular dharma books in America, _Cutting Through Spiritual Materialism_. While on retreat in a Padmasambhava cave in Bhutan, Trungpa Rinpoche composed a ritual text called the _Sadhana of Mahamudra_ that addressed the way in which contemporary societies are dominated by material concerns. This text was received in a visionary state as a _terma_ , a hidden-treasure text, attributed to Padmasambhava as a contemporary contribution to the "dark age" of materialism. In the book, Rinpoche identified what he considered primary obstacles to spiritual development in the West.
Trungpa Rinpoche described the acquisitive pursuit that binds humans to suffering as the hallmark of construction of personal identity, or ego. To promote this core activity, three allegorical lords of materialism pursue three levels of acquisitiveness: the _lord of form_ refers to physical acquisition, the _lord of speech_ to conceptual acquisition, and the _lord of mind_ to acquisition in the spiritual realm. According to these descriptions, materialism must be challenged or it will co-opt our physical lives, our communities, and our spiritual cores. "Physical materialism" refers to the compulsive pursuit of pleasure, comfort, and security as a balm for all of our problems and concerns. Culturally, it is expressed today in the form of consumerism. "Psychological materialism" seeks to control the world through theory, ideology, and intellect. We mentally create constructs that keep us from having to be threatened, to be wrong, or to be confused, thus putting ourselves in control. In American life, psychological materialism is expressed in science and technology, medicine and psychology. On the most subtle level, "spiritual materialism" carries acquisitiveness into the realm of our own minds, into our own contemplative practice or prayer, sometimes expressed as religious exclusivism or extremism.
In all of these areas, our conscious minds attempt to remain in control in order to maintain a centralized awareness from which to defend a fortified position of power. Through this process, our egos use even spirituality to shield us from fear and insecurity. Rinpoche suggested that spiritual practice is often used for personal gain and protection, an expression of acquisitiveness. What are the signs of such an appropriation of spiritual practice? The _Sadhana of Mahamudra_ identifies how, in our preoccupation with issues of control and power, we become "afraid of external phenomena, which are [our] own projections." What this means is that when we take ourselves to be real, independently existing beings, then we mistake the world around us to be independent and real. And when we do this, we invite paranoia, fear, and panic. We are afraid of not being able to control the situation, and as the text states, "sadness and depression are always with us." These teachings suggest that, through Tibetan eyes, even our spiritual traditions are vulnerable to the acquisitiveness that so dominates our cultural life.
This Tibetan analysis gives much greater depth to concerns about the pervading damage to humanity perpetrated by patterns of consumerism and economic globalization. As communist countries throughout the world collapse, the capitalist global economy is all but unchallenged in its growth. Again and again, when traditional societies become modernized, consumerism presents an irresistible path. Global economic interests are now running the entire world. Do any centers of power still exist that are relatively untouched by this globalized network? John Cobb has suggested that religious peoples and communities have the potential to bring the only remaining challenge to transnational corporations and consumerism. Cobb and others from Judeo-Christian theological traditions have applied themselves to the issues of globalization and challenged Asian and Western Buddhists to join in analyzing the issues as well as engaging solutions.
As an American Buddhist new to economic analysis, I have little to add concerning the complexities of the global economy or patterns of consumerism. But my Buddhist practice and training have taught me one thing clearly: No fundamental transformation can take place anywhere without the joining of inner change and outer change. The pedagogy of "engaged Buddhism" builds on the recognition of the interdependence of all things—the suffering of others is also one's own suffering, and the violence of others is also one's own violence. The basic nature of suffering is seen as continuous throughout the world. For engaged Buddhists, "social work entails inner work, and social change and inner change are inseparable." Thus, opening a text of economic analysis is opening to the suffering of the world before our eyes. Listening to the devastating truths of transnational corporate exploitation is encountering a global network of suffering. In order to work with these appropriately, we transform our personal despair, cynicism, and powerlessness into effective action. International development activist Helena Norberg-Hodge wrote:
As engaged Buddhists, we have a responsibility to examine current economic trends carefully, in light of Buddhist teachings. I am convinced that such an examination will engender in us a desire to actively oppose the trend toward a global economy, and to help promote ways of life consistent with more Buddhist economics.
ANALYSIS AS PRACTICE
Central to any Buddhist analysis is close and mindful contemplation of causes and conditions. Buddhist teachings emphasize that there is no first cause or divine creator responsible for the patterns of suffering we discover in our experience—there is no divinely ordained evil or degradation. Instead, Buddhism suggests that all occurrences and events are a result of multiple causes arising under ever-changing conditions. Consumerism and globalization have arisen from a web of many causes and conditions, no one of which is primary. If one deeply observes causes and conditions and the effects to which they lead, then one can identify the most strategically effective ways to change the patterns of suffering in our world. Any form of suffering can be alleviated if one can properly witness the patterns from which it springs and remove specific causes. What is required is a penetrating analysis to identify those that most influence the results.
Tibetan Buddhist philosophers have developed a particularly systematic method of examining causes and conditions. This paper will draw from the magisterial work by the Nyingma meditation master Jamgon Mipham (1846–1912), called _The Gate for Entering the Way of a Pandita_. Ju Mipham Rinpoche (as he is often referred to) begins his analysis of phenomena by saying:
Nothing included under inner or outer phenomena has arisen without a cause. They have also not originated from an independent cause, an uncaused or permanent creator. . . . The fact that phenomena are produced based on the interdependence of their respective causes and conditions coming together is called dependent origination.
His text divides all causality into two categories, applied here to the phenomenon of globalization: (1) _external_ causes and their effects, observable in phenomena outside one's own mind stream such as cycles of nature, or social and economic patterns such as consumer behaviors; and (2) _internal_ causes and their effects, related to one's own cognitive and emotional patterns and actions such as acquisitive greed and the consumptive behaviors that arise from this greed.
Using the traditional framework of analysis, the first important step is to identify the problem of globalization correctly. What do we mean by _globalization_? The president of the Nabisco Corporation approvingly called it "a world of homogeneous consumption." The goal of economic globalization seems to be an international market in which everyone, no matter what latitude or longitude, eats the same food, wears the same clothing, and derives pleasure from the same entertainment. Because of globalization, people from quite diverse cultural backgrounds throughout the world now consume the same McDonald's food, James Bond movies, Nike shoes, and Coca-Cola drinks. Globalization can also be defined as a network of power, centered in transnational corporations and international financial institutions, that controls the flow of capital in order to promote the financial interests of the power elite to the detriment of all others.
The effects of globalization are threefold. First, sovereign governments no longer exist solely for their citizenry or their own national interests. In order to protect financial interests, transnational corporations have "bought" the executive branches of governments through financing campaigns or bribes. To further ensure power, corporations have also taken control of the legislative branches of government through lobbyists, campaign contributions, and term extensions. Having secured governments, corporate interests set the conditions in which policy is determined and control the flow and content of information.
Second, globalization has deepened the gulf between the very rich and the poor both within nations and globally. The unrestrained market favors the rich over the poor and deepens global inequity, increasing the debt of poorer nations under the banner of development. In spite of market rhetoric that suggests that international development will bring the poor into prosperity, the actual result is an increasing economic apartheid.
A third effect is the destruction of cultural and ecological diversity throughout the world. The impact of globalization on developing countries and rural economies is devastating. The global monoculture is eradicating cultural diversity, replacing locally adapted forms of production with industrial systems divorced from natural cycles. Agriculture has become centrally managed and chemically dependent, creating ecological deserts in many climates. In Norberg-Hodge's assessment, "globalization creates efficiency for corporations, but it also creates artificial scarcity for consumers, thus heightening competitive pressures. . . . Globalization means the undermining of the livelihoods and cultural identities of the _majority_ of the world's peoples."
Such an analysis may at first cause horror, shock, despair, and denial, but this is because there is not sufficient understanding of the phenomenon in question. When such a response arises, it is a signal to go more deeply into observing the nature of the phenomenon. Ju Mipham's method begins with an analysis of the causes and effects, recognizing that all such phenomena are not "givens" but are created through multiple causes. This challenges the view that many with the neoliberal agenda hold: that globalization is an inescapable result of market-driven patterns, a "given" of natural law. For many, the ideology of the market, with its supporting ideologies regarding commodification, market success, and consumption, seem to be forces that have taken on their own reality, an inevitable development of the natural-law market principles. Margaret Thatcher, for example, summed it up with an acronym: TINA, "there is no alternative."
Consumerism is considered a subset of this doctrine of natural law. From this perspective, human behavior is the basis of the entire global economy, for humans have limitless wants and are willing to exchange and even sacrifice in order to fulfill their desires. Driven by basic needs and invented or "fancied" needs, humans are willing to live meaningless, subordinate lives in corporate settings in order to gain temporary gratification derived from satisfaction of those needs. Sometimes the doctrine of the market has been supported by theological justification that it was ordained by God, and that God "implanted self-interest in the human breast as the motive force of progress. By following self-interest we follow God's will. Going against self-interest only inhibits God's plan." With market doctrine elevated to the level of divine revelation, those who challenge globalization become heretics.
When we more closely scrutinize the global economy, we see two things: first, this system has not arisen without cause, and second, there is no single, identifiable cause for this phenomenon. All economic theories point to a variety of factors that have given rise to globalization: it has arisen based on the interdependence of causes and conditions coming together, known as dependent origination ( _pratitya-samutpada_ ; Tib., _tendrel_ ). That such a conditioned process made up of a variety of causal factors has an inevitable course not subject to alteration is not congruent with Buddhist logic. If things have arisen from a cause, they are not permanently abiding, transcendently ordained entities. No matter how daunting or damaging they may appear, their existence is reliant upon their causes and conditions and therefore temporary.
If one can properly penetrate these causes, understanding their inner and outer aspects, it is possible to eliminate the causes and to bring about cessation or transformation. All activism must engage in such an analysis in order to effectively identify strategies to overcome social, political, or economic ills. What is important from a Buddhist perspective, however, is to apply the analysis rigorously, thoroughly, to both inner and outer phenomena until one has identified the strategic causes, the elimination of which will truly bring about transformation. Intellectual analysis is important, but it is never enough. One must also contemplate and meditate in order to fully engage the phenomenon in question.
IDENTIFYING THE CAUSES
Outer Causes
When we look deeply, we discover that there are many causes that have given rise to globalization. These causes link together in a vast network of causes, each influencing the others. The doctrine of the market has created principles of supply and demand, measures of market success, and the commodification of land as abstractions from the human realities in the global setting. Philosopher activist Noam Chomsky argues that globalization is not a result of the "natural evolution" of Smith's principles of the market; rather, it has developed from the explosion of industries that have grown grotesquely through state-supported capital. Industries such as telecommunications have developed in a successful fail-safe strategy of "cost and risk socialized, profit privatized." Subsidies, which began as a public expenditure for a social good, have given unfair advantage to favored industries—savings and loans, the airlines, the Internet, and public power, including oil, electricity, and nuclear power—ensuring their continued growth and economic success. One hundred leading transnational corporations on the Fortune 500 list have benefited directly from state protection and taxpayer subsidy; twenty would not have survived without public bailouts.
Additional causes can be found in the special protections afforded corporations. Many trace these to a Supreme Court decision in 1886 that granted to corporations "honorary" individual rights ordinarily endowed to a human person. This set into motion the "entity" status of the corporation, which has safeguarded special protections for its rights to profit and power. Using this privilege, corporations have extended their control over democratic institutions, communications systems, and commodities to the extent that they would deny the resources upon which people depend for livelihood. David Korten has observed:
Corporations now enjoy unlimited life; virtual freedom of movement anywhere on the globe; control of the mass media; the ability to amass legions of lawyers and public relations specialists in support of their cause; and freedom from liability for the misdeeds of wholly owned subsidiaries. They also enjoy the presumed right to amass property and financial resources without limit; engage in any legal activity; bring liability suits against private citizens or civic organizations that challenge them; make contributions to individual candidates, political parties, and political action committees and deduct those contributions from taxable income as business expenses. . . . Step-by-step, largely through judge-made law, corporations have become far more powerful than ever intended by the people and governments that created them.
Put in Buddhist terms, the "entity" status of the globalized market, which appears to many to be an irreversible and unstoppable force, does not withstand deep observation and analysis. Globalization can be identified as a conditioned phenomenon, brought about through protectionism, subsidies, and transnational control. In short, it has come about through human institutions and decision making, propelled by self-interest and the reduction of value to monetary and commodity status. Because it is a conditioned phenomenon, it can be reversed by strategic change of the supporting conditions. David Korten advocates restoring human rights solely to human persons; others recommend the removal of public subsidies for corporate ventures. An engaged Buddhist approach would be to identify strategic causes that might encourage change, even cessation, of the damaging effects of globalization.
Inner Causes: Desire and Ignorance
Analysis of outer causes and conditions is complemented by the analysis of inner causes and conditions: How is it that I myself contribute to the pattern of consumerism and economic globalization? What causes can I discover in my participation, and what causes can be eliminated in order to bring the global pattern to cessation? In Ju Mipham's analysis, the inner causes are found in two stages: first, through understanding the twelvefold chain of dependent origination based on desire and ignorance, and second, through the profound understanding of emptiness of inherent existence, or _shunyata_.
As we have seen, the global economy thrives through the propagation and practice of consumption, which is the daily contribution of each individual to the success of the global market. From a Buddhist view, consumerism exploits the dual foundations of desire and ignorance, which are the basis for the repetitive round of suffering called samsara. The twelve links ( _nidana_ s) of dependent origination identify an inner pattern of suffering built on the cultivation of desire. Sequential links establish the pattern of isolation, solidification of personal identity, and the impetus to confirm that identity in relationship to things and others. The expression of that impetus arises as desire ( _trishna_ , or _srepa_ ), which Ju Mipham calls "eager craving." The text speaks of three kinds of pleasure seeking: "the eager craving of desiring not to be separated from a pleasant sensation, the fearful craving of desiring to cast away an unpleasant sensation, and a self-sufficient abiding in regards to indifferent sensations." In consumptive pursuits, it is craving for pleasure ( _kama-trishna_ ) that is the most obvious motivation, but when we understand the nature of craving on a more pervasive level, the other two kinds of craving, for existence ( _bhava-trishna_ ) and for nonexistence ( _vibhava-trishna_ ), are also apparent. Purchases are made to advance one's desire for pleasure but also to give meaning and expression to one's very existence—"I shop, therefore I am." Hidden within this craving is also the death wish, the desire to spend to satiation, to bankruptcy, to extinction. Within the very act of consumption is the destructive message that suggests the depth of suffering involved.
An essential insight derived from this teaching on desire is that consumption is inherently painful. Even within the pleasure and drivenness of the consumer's impulse is self-recognition of pain. The purchase event may have a moment of thrill, but the experience is haunted by its fleeting quality ( _anitya, mi-takpa_ ), its intangibility ( _anatman, dakmepa_ ), and its unsatisfactoriness ( _duhkha, duk-ngelwa_ ). Because of its inherent unsatisfactoriness, the true impact of which is not absorbed, the consumer is driven to purchase again and again. From this view, compulsive consumption is truly an addiction that carries the seeds of its own destruction.
Outer and inner patterns of cause and effect are successfully linked by a number of core industries in the global economy that exploit addictive desire. Alcohol and cigarettes are obvious addictions, but we can add to them the sweet-tooth craving fed by Nestlé and Coke, cleanliness fetishes satisfied by Procter & Gamble, and entertainment addictions serviced by Universal Studios. The transnational corporations welcome and nurture new "invented" addictions. As Daly and Cobb observed, "If people's wants are not naturally insatiable we must make them so, in order to keep the system going."
A second inner cause in this teaching is that desire arises from basic ignorance ( _avidya_ , or _marikpa_ ), the "delusion of perceiving incorrectly and in disharmony with the nature of things." This means that underneath our desire, we refuse to actually witness the pattern of how desire always leads to suffering. We do not see the underlying unsatisfactoriness of consumption and how pursuing our desires leads to more and more desire rather than the satiation of desire. The threat of seeing this pattern drives us to greater, more intricate and demanding desires that further obscure our ability to see clearly.
According to Buddhist teachings, it is never enough to address desire alone. Desire will never cease on its own because it is so fundamental to the human condition. When the relationship between desire and ignorance is understood, then we see that the way to transform desire is to transform ignorance. The classic antidote to basic ignorance is the cultivation of insight ( _prajna, sherap_ ), the clear seeing of the pattern of suffering and the arising of the pattern. When these are seen directly and experientially, there naturally grows the wish to abandon desire and to develop alternative motivations in one's life. Gradually the realization dawns that all the factors that have dependently arisen giving shape to consumerism are themselves dependent upon other factors, and those too are also dependent phenomena.
Patterns of interdependence in the global economy are so complex that it is difficult to experientially witness the consequences of desire and ignorance on a personal level. Structural suffering in the global economy seems to be perpetrated by a large, amorphous system. Alan Senauke, of the Buddhist Peace Fellowship, observed, "No one seems to be directly responsible, because it is moved ahead by governments, corporations, and is seemingly anonymous." This anonymity makes the task of Buddhist analysis more difficult, for it is impossible to fully know and comprehend the extent of the causes involved in everyday acts of consumption. Yet, in personally examining these patterns, it is much easier to observe the underlying causes of desire and ignorance.
Inner Causes: Emptiness and Interdependence
If the analysis of inner causes remained focused only on ignorance and desire, one could become excessively austere and judgmental in identifying the remedies to globalization. One might become obsessively driven to stop spending, boycott corporations, and drop out of a system seen to be inherently problematic. However, in the Mahayana tradition of the bodhisattva, or "awakened being" dedicated to the liberation of all, fundamental understanding of causes involves a radical paradigm shift. This paradigm shift pivots around the teachings concerned with emptiness and dependent origination, the second level of inner analysis suggested by Ju Mipham.
From a Mahayana Buddhist perspective, the global economy and our involvement in it through consumerism lack inherent existence and are said to be emptiness ( _shunyata, tongpa nyi_ ). Through outer and inner analysis we understand that the multiple factors that support the global economy, especially consumerism, are extraordinarily fragile. On an outer level, the global economy depends on the factors of law, scale, governmental protection, market principles, and infrastructure. On an inner level, consumerism and our support of the global economy rest on habitual patterns of desire based on all-pervading ignorance. But being so dependent makes this phenomenon vulnerable to change, in fact vulnerable in its very existence. Seeing that phenomena are so fragile and dependent, one realizes that there is no independent entity or phenomenon that can be isolated and identified as consumerism or a global economy. Its "entity" nature is ultimately false, posing to be (as we can see upon further analysis) what it is not. Globalization does not have the status of an ultimate or absolute being, even if we conventionally give it that status. If consumerism were an independently existing phenomenon, it would not have a beginning and it could never be dismantled. In the conventional view, consumerism appears to have always existed and will exist no matter what other changes in our economy occur. Likewise, the global economy appears to be the only economy, in fact the only reality of our time, and it is apparently permanent and indestructible.
In Mahayana Buddhism, the ultimate view of reality is just this view of emptiness. No phenomena have inherent existence, including ourselves. It is not just market economics that have been given misplaced concreteness; it is any kind of market, any kind of economy, global anything. This insight, which may be a stretch in conventional thinking, has implications for anyone approaching consumerism. When globalization is seen to exist as an actual entity, it appears to be intimidating, solid, a definitely unsolvable set of problems. But we have found, on further examination, that it cannot possibly exist inherently. Therefore, a "problematic" approach is also unsuitable. If we view the world as basically problematic or flawed, we become powerless to change it. If we understand the emptiness, the lack of inherent existence of these "problematic" phenomena, we take a more balanced and more confident view. This view allows us to see that because phenomena and therefore suffering do not exist inherently, they can be brought to an end. Ignorance about the ultimate nature of the global economy is the primary obstacle concerning its change and ultimately its cessation.
Seeing this view is not just a matter of analysis, it is a matter of meditation and realization. Meditation practice exposes the chaos and suffering of the world over and over again, but it also exposes the unconditional backdrop against which this suffering is experienced. This backdrop is the confidence that no phenomenon is evil, flawed, or resistant to influence on an absolute level. As Ju Mipham Rinpoche wrote:
Realizing this, you understand that all things are merely an unfailing manifestation of interdependence. . . . They are hollow and false, and are devoid of self-nature. The one who understands that this is so, is unaffected by [beliefs] such as conceptualizing a self in the past, present or future.
From a Mahayana perspective, no problems of human life are intractable. To conclude that they are is to give them more power and reality than they deserve or could possibly have. For this reason, there is tremendous emphasis in Mahayana Buddhism on understanding the nature of the problem deeply, clearly, and unflinchingly. In this view, the global economy is an apparition, an interdependent appearance whose ultimate nature is emptiness.
TRANSFORMING GLOBALIZATION AND CONSUMERISM
How would Mahayana Buddhism address the inequities, the systemic violence, the exploitation that arise from consumer culture and from the global economy? How could it respond to the prophetic voice found in Christianity and in some Buddhist movements? While Mahayana Buddhism does not have a prophetic voice, it does have a clear vision about the problems of human existence. From the outset, the Buddha exhibited awareness of social issues such as war, caste, abuse of power, and unethical activity. The root of all such evils, from his perspective, was a mistaken view about the nature of reality. He remained unconfused concerning his central insight, that social issues cannot be changed without a concerted focus on understanding this root error. The Buddhist teachings on compassion begin with personal clear seeing, but they do not end there.
The reason the compassion teachings go further, must go further, is that in Buddhism one cannot experience durable, unconditioned compassion without a direct experience of the lack of inherent existence of all beings. The enormity of serious issues like globalization and consumerism can be overwhelming, moving one to a sense of urgency. If the urgency, however, is an impulsive response to the unbearable qualities of suffering, the aversion that arises toward suffering could lead one to unskillful acts based on what is called "idiot compassion," the impulsive response with insufficient understanding. This impulsive compassion can quickly become ineffective and cause personal burnout, since continuing endlessly in this way for the benefit of others is exhausting and ill directed. Good intention is never enough; it risks the dangers of impulsiveness and romanticism. Effective compassionate actions must be based on wisdom.
Compassionate action regarding globalization and consumerism can be grounded in the realm of spiritual activism. Having identified as directly as possible the multiple causes of the global economy, one strategically chooses to undo those causes. Such choices about what one can contribute are very individual. One person might make a commitment to meditation practice, cultivating the view of the inherently empty and interdependent nature of globalization and consumerism. Another may focus on changing legal protections or public subsidies for corporate interests. Someone else may focus on small-scale community building within the local region or environment. Whatever the choice, these efforts must be developed patiently, with a clear sense of the magnitude of the project. And from a Buddhist perspective, these efforts must be based in recognizing that every single act of clear seeing or compassionate action reverses in some small way one's ignorance concerning the basic nature of reality. At the same time, all of these actions change in some small way the entire phenomenon of globalization. Activism based on impatience with results, excess urgency, or romantic clinging to alternative outcomes will be limited in outcomes.
In circles of engaged Buddhists, discussions of constructive steps have focused on issues of scale and sustainability. The vastness of the problems of globalization have made it almost impossible to witness the broad-scale patterns of cause and effect. Smaller communities allow members to bear witness, to take ownership and responsibility for the life of the community, and to adjust to change more quickly than large communities—in short, smaller communities are generally more sustainable communities. _Turning Wheel_ , the journal of the Buddhist Peace Fellowship, proposes a number of strategies for reduction of scale, localization, and decentralization. Many engaged Buddhists feel that there is a growing need for the development of political skills among American Buddhists, so that coalitions might more effectively support collaboration with other religious traditions on these common concerns. There is clearly a need for comprehensive spiritually based analyses of contemporary economic, social, ecological, and political systems. Attention to the pressing issues of consumerism and globalization may generate a kind of Buddhist "liberation theology" that would combine the best of contemporary social and economic theory and practice with the full lens of Buddhist teachings.
In addition to spiritually based activism, compassionate action can be applied to the inner work of contemporary American life. Compassionate action can address the negative emotions that arise when one contemplates the phenomenon of consumerism in the context of the global economy. When contemplation is only partial, it despairs of any solution, further reinforcing the basic ignorance that cannot see two things: the patterns of desire that perpetuate consumerism, and the belief in the inherent existence of the phenomena of consumerism and the global economy. Ju Mipham Rinpoche describes this as the cultivation of the "wisdom gaze" of dependent origination. This gaze has the ability to deeply, accurately understand the basic nature of the issue; to clearly see the empty and interdependent qualities of globalization, based on many empty and interdependent causes; and to identify what can be strategically changed so that transformation may take place. Such a gaze empowers us to engage in the patient, compassionate work of relieving the suffering of the world.
8
No River Bigger than _Tanha_
Pracha Hutanuwatr and Jane Rasbash
"THE WORD _development_ in Pali is _vaddhana_ , which means messiness or making messiness; it can be messy with good things or messy with problems, sufferings, or chaos. In the modern world, development means the world is flooded with material things neglecting the spiritual aspects." These are the words of Buddhadasa Bhikkhu, a renowned Buddhist monk and thinker of Siam. Following on this, Sulak Sivaraksa, a lay Buddhist thinker and activist, claims that consumerism is a new demonic religion. This chapter focuses on the effects of consumerism in Siam and alternative visions and initiatives based on the work of Ven. Buddhadasa Bhikkhu and Ajahn Sulak Sivaraksa, founding fathers of the engaged Buddhist movement in Siam. The structure of this essay is based on the teachings of the Four Noble Truths. This means identifying problems, looking at causes, envisioning solutions, and outlining a path from the present reality to the desirable situation.
THE PERILS OF CONSUMERISM
Four countries in Southeast Asia—Laos, Cambodia, Burma, and Siam—face the conflict between Buddhist and capitalist values. Each is of Theravadan Buddhist background and at different stages of Western-style development. To explore the First Noble Truth, identifying the problems, we will look at how consumerism affects traditional Buddhist societies in Southeast Asia. At one extreme is Siam, wholeheartedly following the Americanization process over the last fifty years. At the other extreme is Burma, trying to close the country to Western domination in every way.
In Yangon, the capital of Burma, if we visit Shwedagon, the most important pagoda of the country, we see Burmese of all ethnic backgrounds—monks, nuns, and laypeople—paying homage to the Buddha. Some pray and meditate; others perform devotions. The pagoda is crowded all day, every day of the year, from as early as 5:00 A.M. until 9:00 P.M. In Bangkok, the capital of Siam, if we visit the Emerald Buddha Temple, we see it is crowded all day, nearly every day of the year, but with foreign tourists. Only a few Thai are there paying homage to the Buddha. Instead, Thai people crowd the big shopping malls in Bangkok, such as Jusco, Lotus, Tesco, and Robinson, every day from opening until closing time. For most Thai these shopping malls are the new temples and consumerism is their religion, even though if asked they will say they are Buddhist.
What does it mean for the Thai to have consumerism as their religion? It means they define who they are by what they buy: wearing the right brand of dress, owning the right brand of watch, driving the right brand of car, eating at Japanese or Western restaurants, and for the neo–middle class, speaking English to each other. This devotion to consumerism is putting many Thais into debt, especially through the use of credit cards. Credit card companies encourage people to take on debt and then charge them interest that sucks away at their income. If you drive a Toyota pickup and dress like a rural farmer, the traffic police will stop you at checkpoints and and ask for money. But the next day, if you drive a Mercedes Benz and dress in a Western suit, the same policeman will bow his head to touch the tires of your car.
With few exceptions, the monks of Siam are naively welcoming this new religion, blending it with Buddhism as an unavoidable friend. The Thai Buddhist sangha that is supposed to generate Buddhist values of simplicity, generosity, and compassion is now almost completely under the spell of consumerism. Many monks compete with each other to possess consumer goods such as mobile phones, BMWs, and portable computers; others are obsessed with raising money from their newly rich parishioners to build ever-bigger Buddha statues and superfluous religious halls.
Whatever your social status in Siam, you have to climb to the top. If you are from a farming family, you must not be content with being a farmer. You have to buy education to escape from being a farmer to become someone else. If you are a monk, you have to climb up the sangha hierarchy or make yourself famous and have many followers. The whole ethos of Thai consumer society, especially the media and the education systems, inflicts a sense of inferiority. No matter who you are, you are never good enough. From a Buddhist perspective, this is a basic form of alienation. This existential sense of not being good enough ( _vibhava-tanha_ ) has been stimulated by Western-dominated media and advertising to such an extent that young people in Siam reject who they are. Helena Norberg-Hodge explains this phenomenon of cultural alienation very clearly and powerfully in her book _Ancient Futures_. Such alienation stems from the illusion of self competing and comparing with others to define who you are ( _mana_ ). The consumer monoculture feeds on this human weakness. To have consumerism as a religion means that the aim of individual life and of society is to gain unlimited wealth, power, recognition, and sensual pleasure. The Buddha warned his followers not to cling to these four worldly temptations. Yet the present social structures supporting consumerism encourage people to run after them madly.
In contrast to Siam, Burma has been greatly damaged by an authoritarian military junta and, luckily or unluckily, closed to the outside world for more than half a century. This means that except for the few corrupt top military families and some leaks through the Chinese and Thai borders, consumer monoculture has touched the lives of ordinary people very little. The Buddhist values of simplicity, generosity, compassion, and detachment from worldly success are still intact for most Burmese. Meditation practice is widespread, not only among the monks but also throughout the lay community. The Burmese are proud to wear colorful _lunghi_ rather than the Western trousers and skirts that have been adopted in Bangkok and many other parts of Southeast Asia. Yangon street markets are full of producers selling indigenous vegetables, largely home-farmed and grown without chemicals.
Of course, with any small opening to the outside world, the big multinational corporations rush in and pollute the beautiful cities with advertising for Marlboro, 555 Levi's, Tiger beer, Phillips, and Sony, thus spoiling the verdant natural scenery. We do not know whether future democratic leadership in Burma will be aware enough of the dangers of consumerism to stop this trend. It is also a big question whether Americanization in Siam and the Philippines will rush into Burma once the country is opened. At least at this moment, Yangon, with its intricate old buildings and greenery, is much more beautiful than Bangkok, one of the most polluted cities in the world. Once renowned as the Venice of the East, a mystical city of canals and golden spires, Bangkok today is full of unfinished construction sites, ugly new buildings, superhighways, and shopping malls that are tearing the heart out of local communities.
In Siam, development over the past fifty years has overemphasized economic growth without adequate consideration for environmental sustainability, social justice, cultural diversity, and spiritual well-being. This economic growth has been possible only by gradually challenging the traditional Buddhist worldview and replacing it with consumerism. During the Vietnam War, when Americans wanted to prevent Siam from becoming communist, they sent "experts" to be advisors to the various Thai government departments. They urged the Thai government to request the Buddhist sangha to stop giving teachings on contentment ( _santosa_ or _santutthi_ ). If people were content and happy, they wouldn't want American-style development. To follow the new economic path of consumerism, they would need to feel that their way of life was inferior, underdeveloped, not good enough. Unfortunately almost the entire Buddhist sangha was tamed to follow this heretical suggestion except for Buddhadasa Bhikkhu, who saw the dangers of consumerism more than fifty years ago.
The government, business circles, and multinational corporations have used the education and mass media systems and gradually become very successful in uprooting basic Buddhist values from Thai society. Many thousands of self-reliant villages were persuaded to join the cash crop economy, and most are now in debt due to lack of control over the price and costs of their production. After decades of development, more and more farmers have lost their land to absentee landlords or to middlemen who trade their products. Debt-ridden villagers are migrating en masse to the big industrial areas to work in factories and the building trades. As rural communities disappear, people are robbed of their sustainable livelihoods as well as the social security of traditional ways of life. Children of even the better-off farmers are now leaving the countryside for big cities, where they will face further alienation and loss of community. In an abortive attempt to fill this void, the estranged turn to the instant gratification of consumerism, including abusive use of drugs and sex.
A few rural people and poor urban dwellers manage to join the middle class and live a material life with modern conveniences such as private cars, televisions, mobile phones, DVD players, modern houses, and so on. As competition is the name of the game, urban consumers are never satisfied with what they have. Soon the new car will be obsolete, the new computer must be upgraded. Many business executives live a stressful life, going to bed with a handful of drugs to help them sleep. Then they are up before five in the morning, feeding the children on their way to school, arriving in a fancy car that gives the children status.
From a Buddhist perspective, this cannot be a healthy way of life, as one is always driven by greed ( _lobha_ ), anxiety and aggression ( _dosa_ ), and the delusions of individualism and competition ( _moha_ ). Moreover, this way of life is a life without community. In Buddhism a person cannot grow without a supportive community. A higher quality of life based on generosity ( _dana_ ), compassion ( _karuna_ ), and respect for others ( _samanttata_ ) cannot be developed in an individualistic society. Without the maturity of these healthy qualities ( _kusalamula_ ), however successful you are in terms of wealth, power, and recognition, you still experience a deep sense of lack, loneliness, and isolation.
CRAVING AND CONSUMERISM
We turn now to the Second Noble Truth to look for causes of the problem. According to Buddhist analysis, craving is the root cause of all suffering. The very core of consumerism is the amplification of craving, or _tanha_. Traditionally _tanha_ is classified with three aspects: craving for sensual pleasure, craving for existence, and craving for nonexistence. In other words, _tanha_ manifests in the three unwholesome roots ( _akusala-mula_ ): greed ( _lobha_ ), hatred ( _dosa_ ), and delusion ( _moha_ ). Seen in the context of consumerism, _lobha_ is the need to acquire the four worldly states of unlimited wealth, power, recognition, and sensual pleasure. _Dosa_ is the anxiety to acquire these, the fear of losing them, the anger, sadness, and depression (which can turn into aggressive violence) when they are lost or not attainable. _Moha_ is the individualism and competition to attain these four states, the pride when one has them, and defining who you are according to what you have. These modern states of delusion also include endemic low self-esteem and feelings of not being good enough when you don't attain these four states, as well as jealousy when others get them and you don't.
In Siam we can see clearly that _tanha_ does not manifest only on the individual level, as seen in accepted social values. It also manifests as structural violence in the form of the free-market economy, the control of media by transnational corporations, and state mechanisms that favor the rich against the poor. Another form of structural violence is the industrialization process that overuses natural resources for excessive human consumption without compassion to other beings.
To elaborate on _lobha_ , consumerism and capitalism can be explained as modern forms of greed. Capitalism depends on market growth and cannot work without people consuming more and more. Everyone is completely dependent on the "free" yet very unjust market, as is illustrated by the ever-increasing gap between the haves and the have-nots. All over Southeast Asia, seeds of greed are stimulated as people are persuaded to move away from subsistence agriculture to cash crops or paid work. With little control over prices, wages, or work conditions, they struggle to provide for basic needs and fall into a deep unconscious insecurity that is fertile ground for the existential sense of lack at the root of consumer culture. Along the Thai coast, fisherfolk have been living for generations on their daily fishing catches with their small boats and simple tools. In recent years a few modern large-scale trawlers from big companies in Bangkok catch all the fish with superefficient equipment, driving thousands of rural fisherfolk into destitution. This is a clear example of how the greed of big companies supported by the structural violence of the free market can destroy the livelihood of many people.
To elaborate on _dosa_ (hatred), this is related to the lust for power that is so alluring as the sense of lack becomes more apparent. In the struggle for survival and later for the coveted goods, there is a fine line between acquisition, competition, and hatred. On a societal level _dosa_ leads to unjust structures that not only support capitalism but also condone war and human rights abuses. Transnational corporations in Siam appear to have little interest in or accountability to the true needs of the people, seeing them only as consumers of their products. A Suzuki Motor Corporation factory near Bangkok, for example, took advantage of the economic crash in 1997 to lay off eight thousand workers with the pretext of preserving the factory. In reality they wanted to replace the old machines with new technology that used much less labor. During the labor-relations dispute, the government sided with the Japanese company, as they were afraid that the Japanese would withdraw their investment in Siam.
To elaborate on _moha_ (delusion), sophisticated marketing techniques fuel greed and confused views by promoting satisfaction through everincreasing accumulation. Basic needs expand and luxuries become necessities. In Siam and Burma plastic bags have replaced banana leaves to contain food, jeans and modern clothes are preferred to sarongs, then people buy motorcycles and refrigerators, and on it goes. Sadly, it seems that despite this accumulation of material things, the void inside is never filled. Manipulation of this perceived sense of lack is what the capitalist system relies on. Perhaps one of the great delusions is that this is seen as progress. The entire modern education system and mass media in Siam underpin the promotion of _moha_. It makes young people look down on traditional Buddhist values of generosity, compassion, and respect for nature and turn instead to individualism, competition, and a mindset that strives to conquer nature. Television and other vapid media are replacing the traditional role of the elders. In even the most remote Thai villages, people no longer chat with each other in the evening but instead sit in front of a TV screen watching Bangkok soap operas and violent movies from Hollywood.
Of course _tanha_ has existed in all societies at all times since history has been recorded. However, in nonconsumeristic societies past and present, people have learned to curb this _tanha_ so that harm to individuals, community, and nature is kept to a minimum. It is only in today's consumer monoculture that _tanha_ has been eulogized as a desirable value. In contrast to the consumerist worldview, Buddhist teachings advocate reducing and eliminating _tanha_ as the path to happiness. This conflict in views is represented by the following equation:
Happiness can be increased either by satisfying _tanha_ more often or by reducing _tanha_ itself. While consumerism chooses the former and Buddhism the latter, the Buddhist argument is that the more you try to satisfy _tanha_ , the more it will increase. As the Buddha said, "There is no river bigger than _tanha_." This implies that _tanha_ is something ultimately insatiable. A society where _tanha_ is encouraged is Mara's playground, with few winners and many losers. In this process the winners are not real winners, for on the road to acquisition they create oppression and inflict great suffering on many people. The processes of colonization, industrialization, development, and globalization are _tanha_ operating in the macroscale of structural violence.
If we look at the nation-state of Siam, we can see that the social structure is an internal colonization system, where Bangkok imperialism dominates, subjugates, and exploits the whole country culturally, politically, and economically. This is definitely not a nonviolent social structure promoting and encouraging Buddhist values. Instead the social structures of violence ( _vihimsa_ ) promote _tanha_ in the form of greed, hate, and delusion.
Thai activist Sulak Sivaraksa challenges this capitalist trend as unethical:
People believe science and technology will solve everything. The rich will get richer and even the poor will eventually get richer, but I don't believe in this trend. This trend is what I call the Eurocentric trend, which has become predominant because it has the best record in human rights, freedom, individualism, convenience, technology, etc. In this trend right now, Japan is even superseding Europe and North America.
I feel that this trend is fundamentally wrong. Of course it creates something good, but it is fundamentally wrong, because it is unethical. The rich become rich at the expense of the poor and exploit natural resources. Look at the USA. They have 6% of the world's population using over 40% of the world's resources. Japan is also moving in this direction, which means that the gap between rich and poor will increase there too. . . . On top of this the rich are not happy. Fundamentally, this model is ethically and spiritually wrong because people are devoid of peace within. This is why I challenge this model.
As _tanha_ becomes globalized, the scale of suffering has amplified immensely around the world through the spread of consumerism. It is clear from the Buddhist point of view that _tanha_ in the minds of the people works in tandem with _tanha_ in the violent social structures to reinforce unprecedented suffering in the present society.
VISION FOR ALTERNATIVES
Turning now to the Third Noble Truth, from a Buddhist point of view, the way of peace and happiness ( _santisukkha_ ) is to reduce unwholesome aspects of life and society ( _akusala_ ) and encourage growth of the wholesome qualities. In other words, the greed, violence, individualism, and competition that presently dominate society must be curbed, and generosity, compassion, cooperation, and interconnection must be promoted. These wholesome values must be encouraged at both individual and structural levels.
During the left-right political debate of the seventies, Buddhadasa Bhikkhu voiced the strong criticism that the present mode of development was the path to madness and messiness. He proposed that the sangha model be used as an ideal for social reconstruction. He coined the term _Dhammic Socialism_ as an alternative to the present system. He not only presented a theoretical framework but also experimented with creating and living in an alternative community for monks and nuns, which became the famous Suan Mokkh (Garden of Liberation). In contrast to Marxism, Dhammic Socialism sees human beings as part of the natural system, not as the dominating agent. Hence, human beings should live a materially very simple life and devote their energy to cultivating the Buddha potential within.
Buddhadasa's Dhammic Socialism would produce a society that provides an environment for individual growth so that one can be fully human. Buddhadasa spoke about "simple living, higher thinking" as a more attractive ideal than gaining wealth and power. To live this good life he offered detailed methods of self-training and meditation, developing ways to look at the world with a free mind. Buddhadasa felt that a life with limited but enough material well-being was more conducive to fully developing human potential than a life of too much material concern.
Buddhadasa also felt it was important for human beings to live a life close to nature. People should be friends with nature and not try to conquer nature. His favorite saying was that the Buddha was born, got enlightened, lived and taught and died in nature. For him a good society is not one full of artificial artifacts that separate us from the natural environment, as in Bangkok. Rather, the ideal habitat for Buddhist culture is the rural and semiforest life such as at Suan Mokkh. In his own life close to nature, Buddhadasa observed his natural surroundings and came to the conclusion that nature works in a cooperative way. To prove this to visitors, he always pointed to a big tree in front of his hut, where many small trees and plants grew together with the tree, along with a number of wild animals such as birds, squirrels, and lizards. He suggested that human society should be organized in this cooperative spirit. Nature operates under specific laws; the most important of these is the law of interdependence. So, he would say, as human beings we have to understand this and behave accordingly if we want to have a good life and good society. For Buddhadasa, the cultivation of a free mind, cooperative spirit, and living close to nature are practices in harmony with the laws of nature.
Sulak Sivaraksa, in contrast, developed his alternative vision from a different background. While Buddhadasa trained mostly through studying and practicing in the forest, Sulak trained in the United Kingdom in the 1950s, where he became well acquainted with Western ways of argument. His vision of an alternative to consumerism is quite similar in essence, even though his work is based in Bangkok, the center of Thai consumerism itself. He also proposed the Buddhist sangha as a prototype for the emerging countercivilization. For him the sangha in its pure state is an ideal society based on nonviolent ethics where cooperation and egalitarian democracy have remained intact for millennia. Sulak feels that Buddhism must take the issues of poverty and exploitation by the rich very seriously. In his ideal Buddhist society, under righteous and effective decentralized administration, there would not be any poverty. Everyone would enjoy economic self-sufficiency except the monks and nuns, who would intentionally be sustained by the surplus material resources of the lay community. This would then enable the laypeople to be guided by the monks' lifestyle and spiritual progress.
Sulak feels, as did Buddhadasa, that if Buddhists want to play a meaningful role in reinforcing peace, sustainability, and justice in the world, they must question the present consumer monoculture and the violent structures that support it. Though there are no blueprints for a consumerism-free society, Sulak sees the original Buddhist sangha with liberty, equality, and fraternity as the paradigm for lay society to follow. Sulak feels that in the past the Thais followed these ideals, but they have now gone wrong. So, in a way, they need to go back, but that is easier said than done. It is essential, however, to make a very clear stand to confront consumerism and capitalism. In this he feels that Buddhists must work with Christians, Muslims, and others to create a more just and peaceful society.
Sulak's vision for sustainable alternatives is rooted neither in the capitalist story of personal emancipation nor in the communist ethos of collectivism. He is well aware of the potential dangers of misuse of power in both.
At one time people thought the Marxist approach would be the answer. Unfortunately Marxism failed, because instead of using the socialist approach of equality, fraternity, and liberty, the second world used state capitalism, totalitarianism, and centralism.
For Sulak, social engineering, using ideology to change people from without, is not the answer. He feels the spiritual approach has something more powerful to offer. A Buddhist model of development begins with everyone truly practicing to understand oneself. In the Buddhist tradition, this is called _citta sikkha_ , or the contemplation on mind. Meditation is important to attain insight and awareness. Critical self-awareness is crucial for personal empowerment; from this base a critical understanding of communities and society can be realized. To make real and lasting differences, strategies need to acknowledge and transform these unwholesome roots within individuals and societies. A two-pronged approach is required to work on practical social reconstruction and more deeply on the collective psyche or consciousness, where the hazardous lure of consumerism is deeply rooted.
When Asia confronted modernization in the last few hundred years, most of the intellectuals and thinkers, including the Buddhists, rationalized and justified their traditional philosophy to fit into modern concepts. By the time Asia gained independence from Western colonization, most of the Asian elite had lost confidence in their own cultural values. Most Thai elites are now educated in the West or receive Western-style education in Siam. They have come to feel that their society is intrinsically inferior to the West—so they have to adopt all the latest fashions of the West, even progressive Western thought. Buddhadasa and Sulak bucked the trend, and instead of using modernization as criteria for change, they used Buddhist wisdom teachings for their principles. They have offered important leadership in confronting this alienation from intellectual and cultural imperialism and gaining back self-respect for the Buddhist community in Asia.
Buddhist thought advocates that whether you are stupid or clever, man or woman, black, brown, pink, white, or yellow, rich or poor, powerful or powerless, believer or nonbeliever, you have intrinsic buddha nature within you. You do not have to be someone else to be valuable—hence the primacy placed on self-respect ( _hiri-ottappa_ ). Any society with a structure that undermines this self-respect is an unhealthy society. You cannot be "more who you are" by rejecting what you are. This does not mean strictly adhering to traditional roles and responsibilities. It means rejecting the notion of belonging to a _lesser_ race, class, gender, religion, culture, or civilization. Once one is firmly rooted in self-respect, it is possible to make healthy and critically aware choices from among the options offered both by what we inherit from our past and from Western modernity. Working for a sustainable future through political and economic structural change alone is not enough. A new kind of Asian cultural revolution is required to liberate Asia from Western cultural imperialism and from the colonized mentality. This kind of thinking of not being developed enough, and having to catch up with the West, is disempowering and must stop.
INITIATIVES ON THE PATH TO REDUCE SUFFERING
The Buddha prescribed the Eightfold Path of practice as the solution to the problem of craving; this is the Fourth Noble Truth. Buddhadasa and Sulak have both been instrumental in promoting alternatives to consumerism in Southeast Asia as a path to reduced suffering. Buddhadasa established Suan Mokkh as a monastery resisting the mainstream sangha and influenced many others through his writing. Sulak was greatly influenced by Buddhadasa and carried his ethics still further. Each has published hundreds of papers and books and given numerous talks criticizing the present system and proposing alternatives. As an organizer, Sulak has been a pioneer in starting modern nongovernmental organizations (NGOs) in Siam. In his forty years of committed engagement, he has built a network of small organizations based on engaged Buddhist teachings, working in collaboration with different groups. He and his colleagues have actively promoted translation of alternative visions from the West, introducing the Thai reading public to Mahatma Gandhi, E. F. Schumacher, Fritjof Capra, Thich Nhat Hanh, the Dalai Lama, Satish Kumar, Paulo Friere, Helena Norberg-Hodge, and David Korten. Through the Komalkeemthong Foundation and other publishing houses, these alternative voices from the West have strengthened the Thai engaged Buddhist movement. Sulak also took it as his mission to organize seminars and workshops among the progressive middle class, challenging the mainstream development discourse and arguing for Buddhist alternatives to consumerism. His influence in Thai intellectual and educated circles has been tremendous.
One of Sulak's first NGOs, the Thai Inter-religious Commission for Development (TICD), has been effective in supporting grassroots leadership among monks and nuns to promote sustainable development at the village level. Many of the monks and nuns in this network have become well known as initiators of sustainable community empowerment. For example, when modern development and consumerism came to the countryside around activist monk Luang Pho Nan's monastery, the villagers became the victims of middlemen and loan sharks and got into heavy debt. Luang Pho began a campaign of resistance and rehabilitation by using community meditation to raise awareness of the dangers of consumerism. At the same time, he encouraged villagers to form rice banks, community cooperative shops, and community savings groups based on Buddhist principles of participatory democracy ( _vajji-aparihayadhamma_ ).
Not long after Luang Pho Nan started this campaign, the work spread quickly to nearby districts and provinces. Now more than five hundred monks have joined this movement of community revitalization. Villagers can now gradually get themselves out of debt and aim at a self-reliant community life rather than joining the cash-crop economy. One community at Kutchum District, under the leadership of Phra Krusupajariyawat, even started its own community currency. The work of TICD is so important because it helps monks and nuns to understand the structural violence behind the consumer monoculture.
The Spirit in Education Movement (SEM), started in 1995, is another initiative of Sulak and his colleagues'. Its mission is to develop a comprehensive educational movement to counter the trends of globalization and consumerism, using spiritual strength to empower individuals and communities to choose alternative ways of development with confidence and full awareness. This approach is rooted in cultural appropriateness and indigenous wisdom to confront the trends of cultural imperialism that inflict inferiority on people of non-Western origin. One SEM program, the Grassroots Leadership Training (GLT) program, has been ongoing for nearly ten years. The GLT works with marginalized communities in Siam, Burma, Laos, and Cambodia, running three-month training courses with follow-up sessions. The aim of the courses is to empower communities to be self-reliant in terms of basic needs while maintaining their cultural integrity and sustaining a healthy environment.
The empowerment education approach of GLT applies critical self-awareness in a far broader context. This starts with a community-needs analysis to highlight the structural injustices of the modernization process. Tools are given to help communities identify problems and develop sustainable solutions. The real "experts" are seen as those who know and care for their local environment. Staff facilitate problem analysis and reflection, especially in relation to the connection between local and global problems. GLT also offers study tours to innovative projects, introducing appropriate solutions such as sustainable technology and microcredit.
As communities begin to recognize the oppressive forces in society and how they are mirrored within themselves, they move beyond these trends, finding renewed belief in traditional wisdom and regaining their self-confidence and community confidence. This becomes a starting point for locally sustainable futures. GLT alumni are now involved in hundreds of small-scale appropriate development projects and training initiatives that focus on local production for local consumption. At best they hope to help traditional communities not yet marred by the consumer monoculture to protect themselves from the negative forces and make use of the positive elements to revitalize a healthy community life. The idea is to bypass the mistakes of other victimized traditional communities that opened up to modernization without critical awareness.
Though GLT works with participants of several faiths, encouraging spiritual practice according to their own beliefs, the content and process of the training reflect the basic essence of buddhist education (as in Sulak's practice of small _b_ Buddhism)—the Eightfold Path. A large part of the training is to cultivate right view and right thought about internal and external development. Right thought is defined as unselfish, nonviolent, and free of hatred and excessive desire. In order for individuals and communities to develop properly, generosity (or sharing of wealth), power, and recognition are crucial. When conflict arises, a compassionate and nonviolent approach is encouraged.
To practice right speech, GLT students learn methods of reconciliation and mediation and develop understanding of the structural violence of the present media system. Right action refers to the five basic precepts for ethical conduct. The first precept, abstaining from killing, is applied to understanding the cruelty of the industrial production of meat and breeding of animals for consumption. GLT discussions also address the arms industry that supports powerful societies and is linked to many wars around the world. The second precept, abstaining from stealing, takes up the injustice of a national and international economic order that allows the rich to steal from the poor with legal and political legitimacy. GLT participants also learn about alternative economic systems. As for the third precept, abstaining from sexual misconduct, GLT courses investigate the global structure of male dominance and exploitation of women and how the structures of patriarchal greed, hatred, and delusion relate to violence in the world. To address right livelihood, GLT organizes exposure trips to self-reliant communities that practice cooperation to prevent exploitation, as well as sustainable agriculture and handicraft production.
The last three spokes of the Eightfold Path—right effort, right mindfulness, and right concentration—are related to meditation. In order to encourage these aspects, the GLT courses include a weeklong retreat integrating meditation, prayer, or puja practice into the daily schedule. Alumni are encouraged to do regular retreats and daily practice when they return to their communities. In the long term, the Spirit in Education Movement aspires to establish a residential college of sustainable communities for Southeast Asia. It is planned that courses will then devote about one-third of the time to practicing meditation and other serious spiritual practices.
Spirit in Education also works closely with the Assembly of the Poor. This is a wonderful example of a nonviolent grassroots movement challenging the mind-set of modernization and consumerism. Thousands of ordinary people who are victims of development projects work together to raise awareness and challenge the negative impacts of dams, large-scale farming and fishing, and industrial factories. For many years thousands of Assembly members have gathered on a rotational basis to form a large protest village at Pak Moon Dam in northeast Siam. Up against the huge institutions of the World Bank, EGAT (Electricity Generating Authority of Thailand), and the Thai government, this is a story of real hope. The Assembly of the Poor protested the building of the dam to gain fair recompense, as it would drastically impact their traditional way of life. They also protested against wasteful use of electricity in air-conditioning and lighting hundreds of big department stores. However, the dam went ahead, and the lives of the local people, who were largely dependent on fishing and riverside gardens, changed beyond measure as more than two-thirds of the migratory fish disappeared. Undaunted, they campaigned to open the dam and return the river to its previous ecological state. In June 2001 the gates were ceremoniously opened, and very quickly the fish began to return and the people resumed their traditional occupations. But once again the government reneged and now plans to close the gates for eight months of the year.
In Siam, protests are traditionally seen as actions of the political left. Indeed, some of the Assembly of the Poor organizers are from the left movement and did not initially care about Buddhism. However, SEM workers introduced engaged Buddhist monks and nuns to support the movement as educators. The monks and nuns brought a new understanding of the Eightfold Path and also introduced chanting and meditation practice into protest situations. This worked miraculously. It became much more difficult for the police (also Buddhist) to beat or arrest people when they were chanting on the protest site. Once monks and nuns became involved, the Assembly of the Poor officially adopted Buddhist principles of nonviolent action, thus reducing the legitimacy of government use of violent oppression. Even the left-oriented leaders of the assembly now appreciate meditation and take it seriously. The persistent and extremely difficult protests for many years have influenced authorities to rethink and delay building other dams around the country.
Across these years of struggle, the Assembly of the Poor has been a huge conscientization exercise, gradually increasing awareness of the complex interconnected issues relating to consumerism, modernization, and globalization. It has also supported experiments with aspects of self-reliant and sustainable community. There are now initiatives advocating traditional health care and community businesses promoting fairly priced and environmentally friendly local production for local consumption. There is a new focus on using native resources and on self-reliance within families or villages to reduce the outflow from the community. This protest movement has awakened public debate on the differences between modern development and Buddhist values. Using dhammic wisdom to combat the prevailing ideology of consumerism has been very empowering for the protesters, as it shows how consumerism contradicts indigenous values and how dhamma, the base of their culture, can relate to their contemporary political struggle.
A FUTURE WITH LESS SUFFERING
Consumer monoculture is able to dominate contemporary society because individuals have become alienated from their buddha nature, from their culture, and from each other. Driven by greed, hatred, and illusion, we need to find ways to see this _tanha_ to avoid destruction of soil, soul, and society. Empowerment education for grassroots communities and individuals from all social strata providing tools to counteract these trends is crucial. It must address both inner and outer landscapes in understanding _tanha_ in order to give alternative thinking and behavior a chance.
In Buddhist society it is believed that every being embodies buddha nature, the potential to attain the highest understanding, and that we should all strive for this. The poor and marginalized are entitled to the same dignity as everyone else in their struggles. These grassroots initiatives are a light for the future, as they emphasize the importance of critical examination, localization of power, and economic activity growing from rather than deriding indigenous local wisdom. The GLT and other similar initiatives in the region are a vital proactive approach, and the signs are that these will make a real difference to coming generations. The Assembly of the Poor in Siam has perhaps given people the most hope. As ordinary people start to understand the full impact of the situation on themselves and their societies, they gain the confidence not only to rise up in protest but also to find viable and sustainable alternatives.
How much healthier would all our societies be if they were based on value systems that truly advocated sustainability rather than unlimited growth! A society where people help each other out in hard times. A society with no concept of interest. A society where power is shared rather than fought over, that reveres and respects nature rather than controlling and using it as a resource. A society unsullied by the poisons of _tanha_. A society with values steeped in Buddhist wisdom.
Concrete steps are being taken to manifest this vision through initiatives inspired by Buddhadasa Bhikkhu and Sulak Sivaraksa. A good number of committed people are working on these initiatives. They do not have all the answers, but they have a clear awareness of the structural violence and a strong determination to work with the violence within the structures of their minds. They take the path of contemporary bodhisattvas confronting the suffering in themselves and in society in order to work for the liberation of all sentient beings. It is a very challenging yet enriching path—a combination of contemplation and activism, spirituality and politics, humor and seriousness. These committed people are returning to the very roots of the traditional Buddhist teaching and using this power to move toward a wholesome and sustaining future.
9
Taming the "I Want" Mind
Sunyana Graef
ONE SUMMER a Zen practitioner from Poland, who had never been outside eastern Europe, stayed at the Vermont Zen Center for a training period. She was an expert seamstress, and her first assignment was to repair a small sofa. When I asked her to have the work completed by the end of the week, she looked confused, then she became distressed. Why was she so upset? "It's impossible," she said, nearly in tears. "It cannot be done within the time I'm here." What could be the problem? "You don't have the fabric," she explained, "and it could take months to find." When I told her that we would go to a store that very day and get exactly what we needed, she was astonished. Before she returned home, she gave a talk to our sangha about the differences between Poland and the United States. She summed it up this way: in Poland if you need something—be it money, a piece of fabric, a car—you figure out how to do without it. In America if you need something—be it a house, a sofa, a new pair of shoes—you figure out how to get it.
At that time I was building a house, and I felt conflicted to the point of embarrassment about spending so much energy on the project. My parents had offered my husband and me the money to build a home so that we could have more space while our children were growing, and I wanted it to be large enough so that my parents would be comfortable should they ever decide to live with us. Yet I was unsettled about having made a decision to accept their money for what was, essentially, a matter of personal comfort. My preference would have been to live in a tiny cabin in the woods, but with two children and a husband, that was not an option. At one point I called my Zen teacher, Philip Kapleau, and asked his advice on the propriety of owning a large house. He said, "Your students would want you to have it." I wasn't so sure.
Now here was this woman—from a country where even the most common things were not taken for granted—holding up a mirror to our excesses. As our sangha reflected on her experience, we realized that, truth be told, we were spoiled, and we didn't even know it. We live in a land of plenty and have become so accustomed to the abundance surrounding us that we are oblivious to it. We are inundated by material goods to the point that we have become like someone whose appestat is no longer working properly. We eat until we're sick, we consume until we're drowning in . . . what? Things we don't really need or want. The fevered mind of entitlement reigns large in the West—if we want it, we feel we deserve it, and therefore we should have it— _now_! Discomfited by her words, I couldn't help but wonder if I had fallen into the very trap I had so often warned my students to avoid: the trap of misplaced need that turns into greed.
The unbridled consumerism of our culture fosters the belief that all we have to do to be happy is to satiate our desires. Consumerism is surely an addiction; long before we've left our childhood we've become consumerholics, addicted to the drug of _more_. We're a nation of hungry ghosts, wandering through life just like those pitiful beings in the preta realm who, owing to their inexorable greed, have condemned themselves to lives of wretched suffering. Every time a hungry ghost tries to eat something, it turns to poison. Every drop of liquid they ingest turns to fire. Their lives are an unremitting circle of relentless desire followed by excruciating pain. Like poor hungry ghosts, each time we obtain a morsel of something—food, drink, sensory pleasures, consumer goods—we burn internally. Instead of being satisfied, our cravings increase. As our cravings increase, our distressing hollowness grows.
As with any addiction, the first step in overcoming it is to recognize it. We need to see that, to paraphrase Gandhi, happiness does not consist in the multiplication of wants but in their deliberate and voluntary renunciation. The ideal of voluntary renunciation is well known to practitioners of the dharma. The fulfillment that comes through spiritual development does not lie in the realm of desire but in the purification and absence of desires. This is because desires simply cannot be quenched by feeding them. Rather, through capitulating to them, just the opposite happens: they proliferate.
Chasing after desires is like drinking saltwater, the Buddha said. Saltwater can never satisfy your thirst but only increases it. Likewise, desire builds upon desire, so we can never be satisfied. An ancient Hindu teaching describes the heart of a discontented, dissatisfied person as being like a bamboo basket riddled with holes. It is impossible to draw water from a well with such a basket. It will leak, and not a drop of water will remain to quench your thirst. Similarly, when you are suffering from the tormenting thirst of greed and yearning, your contentment leaks away even before your needs have been fulfilled. All that remains is discontent.
Unfortunately, it is not easy to transform habitual behavior and character born from greed and attachment. If it were, then all beings would be content with their rightful share in the bounty of this earth, and our planet would not be suffering from the effects of deforestation, pollution, and overpopulation. But there is a way out. While it is true that the small self is habitually and addictively drawn to objects, and while it is true that habit patterns are immensely difficult to eradicate, the practices of Buddhism provide a path through the morass of longing that surrounds us. Buddhist practice can be an antidote for the addictions of (and to) the spoiled small self with which we are masochistically enamored. It helps us recognize, unmask, and ultimately relinquish this small self, and in so doing we become less vulnerable to the ego's vocal, incessant demands.
Overcoming our firmly entrenched ego-feeding habit is an arduous undertaking; it requires strong measures. This the Buddha provided in the form of a potent medicine called "no-self." Through Buddhist practice we become less identified with the small self; the less self-identified we are, the less need there is to bolster the ego-I with "stuff." By gradually letting go of ego delusion, our sense of separation and alienation dissipates. Ultimately we see that we have everything; nothing is lacking anywhere. "The Buddha had only his begging bowl, yet he was the richest person on earth," said Hakuun Yasutani Roshi.
The foundation of the Buddha's teaching in every sect of Buddhism is the act of taking refuge in the Three Jewels, also called the Three Treasures or Refuges—Buddha, Dharma, and Sangha. In the Zen tradition, taking refuge is a daily act. Every morning begins with the repetition of the Three Refuges, as they form both the foundation and heart of one's spiritual life:
_I take refuge in Buddha, and resolve that with all beings, I will understand the Great Way, whereby the Buddha-seed may forever thrive_.
_I take refuge in Dharma, and resolve that with all beings, I will enter deeply into the sutra treasure, whereby my wisdom may grow as vast as the ocean_.
_I take refuge in Sangha, and in its wisdom, example, and neverfailing help, and resolve to live in harmony with all sentient beings_.
By putting one's trust or faith in the Buddha (the ideal of awakening to our true nature of no-self), by following the dharma (which is the teaching of the Buddha), and by practicing within the context of a sangha (which is the community of followers of the Way of the Buddha), a radical reorientation of one's life takes place. Taking refuge is a powerful means for the transformation of selfishness into selflessness. Through this simple act of faith, one begins to understand how to live a life of wisdom, compassion, joy, and equanimity, free from the addictions of egocentric consumerism.
TAKING REFUGE IN BUDDHA—REALIZATION OF NO-SELF
One of the most effective tools of Zen training is sesshin, sometimes called a Zen retreat. _Retreat_ is not actually a good synonym, implying as it does a peaceful, relaxing rest. That's not a sesshin. _Sesshin_ literally means "collecting the heart-mind." Its purpose is to provide the framework for serious Zen practitioners to make the supreme effort to come to spiritual awakening, thereby realizing the truth of no-self—our buddha nature.
As practiced in the Harada-Yasutani lineage, sesshin is a three-to seven-day period of intense spiritual work centered around _zazen_ , or sitting meditation (a minimum of ten hours daily), chanting (twice daily), and private interviews with the teacher (three times daily). There is also a _teisho_ (Zen talk by the teacher), a work period, meals, and brief rest periods. There is no talking during sesshin. No one leaves the premises for any reason; even going outdoors is discouraged until after nightfall. At the start of sesshin the teacher warns participants to keep custody of body, speech, and mind by looking down at all times, by maintaining inner and outer silence, by eating less than normal, and by carefully guarding the thinking mind. In effect, once sesshin begins, everyone is in a cloistered monastery.
The simplicity of life during those days of intense training is refreshing and liberating. This is one of the things I love most about sesshin: everything is reduced to the essential. I open my closet: there is a robe, an underrobe, a set of work clothes. That's it—nothing else! You have a bed, toiletries, and a set of eating bowls—complete freedom from the tyranny of objects. The food is vegetarian, simple, and similar every day. Paradoxically, eating less, you feel more full.
In such an environment, wants, needs, and desires virtually melt away. I've never heard of anyone spending time at sesshin thinking about clothes, computers, or cars, though there are undoubtedly those who crave sensual pleasures—a soak in a hot tub and a massage around day three would be heavenly! And there is always going to be someone who is struck with a powerful longing for pizza or ice cream. Nonetheless, since there's nothing you can do about it, eventually the desires dissipate.
Sesshin changes your priorities, your perspective, and your life. As you work on letting go of the ego-I, the triggers that set off urges to buy become less compelling and therefore less operational. Where does consumerism come from if not the need to feed this nonexistent self in order to bolster the false image of who and what we are? As you would expect, the deeper the experience of no-self, the more dramatic the change. But even with one or two sesshins, people often experience a subtle dropping away of attachments. Taking refuge in the Buddha, our true nature of no-self, makes this possible.
There are many cases of people who found that their need for such consumer addictions as cigarettes, alcohol, junk food, and passive diversions such as television, movies, and computer games radically diminished or even disappeared completely after sesshin training. Things that seemed important, even essential, before sesshin oftentimes have less appeal at the end of seven days of deep spiritual work.
Sometimes people are bewildered when this happens. We've become so passive about our addictions that we don't realize we have the power to overcome them. For example, a young Zen student called me a few days after her first sesshin. "I haven't smoked in two days," she said. "Is this okay?"
Perplexed, I asked, "What do you mean? Why wouldn't it be okay?"
"Well, it seems strange that I don't _want_ to smoke anymore."
"It's not strange at all," I said. "It's wonderful! Don't smoke!" And just like that, she stopped smoking and never again picked up a cigarette.
More often the letting go is a gradual process. A middle-aged man had been attending sesshin sporadically for close to twenty years. To all appearances, everything in his life was in order. He had a high-powered, wellpaying job, a loving, supportive wife, well-adjusted children. But he was also unhappy and a workaholic. No matter what he did, something kept pushing at him, an inquietude, a sense of alienation. One day he called me to say that he was taking early retirement in order to devote as much time to Zen training as possible. He began attending eight to ten sesshins a year. Within three years, his life had changed completely. He became a vegetarian; he felt more at peace with the world and with himself. His devotion to the dharma was a model for younger students, and his generosity supported the Zen center and helped people attend sesshin and go on pilgrimage. It was as if his intensified training had opened his heart and enabled him to let go of his need to possess and consume.
When you are in sesshin focusing on your spiritual practice, bit by bit you deconstruct and loosen your attachments to the false ideas of self and other. Eventually you come to the realization that there is no thing, no entity, called I. There is no _me_ for things to be _mine_. "It's like robbers breaking into an empty house," an ancient master said. Your identity becomes the whole universe, and you clearly see that "heaven and earth and I are the same root. All things and I are of one substance." You have everything—what is lacking anywhere? When you know this in your very guts, then you never have an urgent sense of want or need. This is taking refuge in Buddha, and with it comes a profound feeling of contentment, equanimity, and joy.
TAKING REFUGE IN DHARMA—CAUSATION AND THE PRECEPTS
Sesshin plunges you into the world of emptiness in which there is no self, no other. Returning to everyday life, you are deposited back into the world of form. The self and all things instantly reappear. Although "form is only emptiness, emptiness only form," it can be a jarring experience to move from the rarefied sesshin realm of emptiness, selflessness, and thinglessness into the discordant samsaric realm of ego, form, and desire. Children want attention, the house needs cleaning, mail is waiting to be answered, there's grocery shopping to be done. Phone calls, disturbing headlines, piled-up work, dirty laundry . . . in less than an hour, the fruits of seven days of cultivating wisdom, compassion, and equanimity seem to fly out the window.
Practicing Zen means being fully engaged and present in the here and now, not separate from the messiness of life. Given that, it must be said that sesshin training by itself is not of much use in ordinary life. After all, we don't go through our days in silent meditation, with downcast eyes and minimal interaction with others. Moreover, during sesshin it is easy to resist the temptation to consume—the only temptations are mental ones, and the only things to consume are the food at mealtimes and sleep (but that's another story). Outside of sesshin it's a different matter. What we need is a way to deal with the commotion and challenges, confusion and pressures of daily existence, not the least of which is the lure of excessive consumption.
Taking refuge in Dharma, the teachings of the Buddha, provides a path that shows how to live a balanced, sane existence amid the uncertainties and seductions of everyday life. The Buddha's teachings are vast, but they can be expressed simply:
_All things are produced by causation_.
_The Buddha has explained their cause and the way to eliminate them_.
_This is his teaching_.
It was this explanation of the dharma that was given by the monk Assaji to Sariputra, who had long been searching for the supreme teaching. Upon hearing these words, Sariputra immediately gave up his search and took refuge in Buddha, Dharma, and Sangha.
Another monk, famous for doing zazen in a tree, was perched on a branch when someone asked him, "What is the essence of Buddhism?" He answered:
_Not to commit wrong actions_ ,
_But to do all good ones_
_And to keep the heart pure—_
_This is the teaching of all the buddhas_.
His questioner said, "Even a three-year-old child knows that." The monk replied, "Yes, but even an eighty-year-old man has difficulty doing it."
These teachings—the law of causation and the basic precepts of moral behavior—are an inseparable continuum. Belief in the law of cause and effect is a powerful impetus for living an ethical, pure, and compassionate life. Moral behavior, in turn, leads to the elimination of pain-producing karma and thus shows a way to end confusion and suffering. Since so much suffering is caused by greed and desire, it follows that observing the precepts and accepting the principle of causation would naturally lead to a reduced need to consume. And indeed they do.
The ten cardinal precepts are all concerned with avoiding volitional actions stemming from greed, anger, and ignorance, which lead to painful karmic effects. They are, as Zen master Bassui said, "a shortcut for entering the Buddha Gate." Interestingly, fully half of them deal directly with consumption: the first, second, and third, the fifth, and the eighth. For example, the decision to follow the first precept will necessarily mean avoiding engaging in any occupation that causes the suffering and death of sentient beings. It means that you will not eat (or cook or purchase) meat, fish, or poultry. It means you will not wear (or buy) leather, fur, down, or silk. In like manner, every single precept can be looked at as a guidepost for living simply, without consuming excessively or unnecessarily. Even the precepts dealing with speech are pointing to a type of mindless consumption: the consumption of other people's time, happiness, and sense of well-being.
The third precept, not to misuse sexuality but to be caring and responsible, is particularly important in this respect. Most obviously, the precept means not to enter into adulterous relationships. It also means not to engage in any sexual relationship in which there is a wide disparity in power, such as teacher-student, adult-child, supervisor-employee, or in which there is a lack of respect or violence. And it means not to use pornography. All consumer addictions are major obstacles to spiritual development; addictions to alcohol and pornography are undoubtedly the most disruptive to serenity of mind.
If any students have the courage to tell me they are indulging in pornography, they do so because they are feeling powerless over this addiction. They desperately want to break free of their lust, as they are deeply ashamed of what they are doing. We discuss the fact that an addiction to pornography violates not only the precept of abusing sexuality but also that of killing, lying, and stealing. Everything we do affects others, including looking at degrading pictures of men, women, or children who were certainly at some point in their lives mistreated, abused, neglected, or were, at the very least, suffering from abysmally low self-esteem. To look at such pictures robs not only them of their dignity but also the one who is looking at the pictures. Thus it is a kind of killing as well as stealing. Then, too, many people who compulsively use pornography lie to their partner about it.
If I ask people how this addiction is affecting their life, they invariably say their partner hates it, they'd be mortified if people found out about it, and they definitely want to stop. Fortunately, if they have taken refuge in the dharma, they already have a powerful tool for overcoming this addiction. They see that the consequences of their actions are painful to themselves and others and that by abandoning that which causes suffering, they can be happier and in a better position to help others. They see that any obsessive behavior keeps them from living freely in the present moment. Instead of being fully aware, they are distracted by intruding fantasies and daydreams of getting the next fix; their mind is not at ease.
I suspect that for Buddhists in particular, with this as with other consumer addictions (drinking, gambling, compulsive eating, excessive shopping), there is a very strong element of shame and secretiveness. I tell my students that if they have secrets, they are protecting their ego. When you protect your ego, you hold yourself back spiritually because so much energy is going into maintaining a facade. One of the principles of twelve-step programs—which are a good model for Zen practitioners trapped in addiction—is to be fearlessly honest. Those students who can admit their powerlessness and call out for help find that this is the first step in freeing themselves from their addiction and changing their life. The courage to do this often begins with taking refuge in the Dharma.
In my own life, it was not addictive behavior that caused problems as much as an oppressive feeling of separation from everyone and everything. As my practice developed, I gradually came to see that my feelings of separation were just that: feelings, and that in fact I was not separate from anyone, anything. Slowly the understanding dawned that everything I did had far-ranging implications, since I was not apart from the world. I began to look more closely at my speech, behavior, and even thought patterns and to consider how they might affect others. It became clear that any choice to consume excessively, be it clothing, food, paper, water, or consumer goods, would have a negative impact on me—it was wasteful, unnecessary, and selfish—and by extension a negative impact on others. I began to take responsibility for my actions in a way I had never done before. I had to admit that my difficulties were not due to fate or someone else or anything else but rather that I myself had made my life the way it was and was continuing to shape my future life.
This realization filled me with a sense of tremendous power—and tremendous dread. There was a feeling of wonder and freedom that came with the understanding that I absolutely had the ability to change my life, but with that came onerous and inescapable responsibility. It was impossible to ignore the effects of my actions or to flippantly say, "It doesn't make any difference," when it manifestly _did_ make a difference, especially in actions involving selfishness or generosity, consumption or renunciation.
In "Deep Faith in Cause and Effect" ( _Shinjin Inga_ ), Zen master Dogen speaks of the importance of understanding causation for one who is practicing the dharma:
Those who study Zen in the Buddha Dharma may wish to start by arousing the thought of enlightenment and repaying the kindness of the Buddha and patriarchs, but first of all they should clearly understand the principle of cause and effect.
Cause cannot be separated from effect, no matter how long it takes for the effects of an action to bear fruit. If we see this clearly, then the palpable sense of the weightiness of our volitional actions and conscious choices causes us to be more aware of the way we live. Awareness in our life leads to awareness of the consequences of our actions. We see that some choices inevitably generate suffering for ourselves and others, while other choices produce happiness. Furthermore, we see that overcoming excessive desire and unrestrained consumerism is directly connected to leading a more joyful, serene existence. The more thoroughly we understand that it is a matter of causality, the harder we will try to avoid evil and do good. In such a way we begin to actualize the Dharma in our everyday life.
TAKING REFUGE IN SANGHA—FAMILY AND COMMUNITY PRACTICE
Living the Dharma gives rise to a better understanding of taking refuge in Sangha. The sangha, a community of practitioners of the dharma, serves as both a foundation and a support for others on the spiritual path. It is encouraging to see how people with many years of dharma experience live their lives. The careful way they use the earth's resources, the simplicity of their everyday life (sometimes even in the midst of wealth and luxury), their generosity, devotion to practice, discipline, patience, energy, virtue, compassion, wisdom, and warmth—all this is inspiring and motivating. It is also a wonderful boon when raising a family to be among such mature people.
At the age of twenty, when I began practicing Buddhism at the Rochester Zen Center, I was not a mature person, nor did I possess any of the virtues that come from steady practice. I was emotionally ungrounded and immature and quite sure that having a child in my state of confusion—never mind the fact that I wasn't yet married—would be tantamount to child abuse. Fortunately for my two daughters, I waited until I was married and in my thirties before starting to raise a family. With greater spiritual maturity, it is easier to make decisions and there is somewhat less angst around child rearing, though you basically have no idea whether or not you are doing well by your children until they are grown, and maybe not even then.
It seems that it is almost impossible to protect children against the aggressive consumerism and peer pressure associated with substance abuse and early sexuality. Being part of a sangha and associating with spiritually developed people provides a bulwark against some of those pressures. All the same, no matter how simply Buddhist parents want to live, no matter how free of acquisitiveness they are, no matter how much they wish to protect their children from the pressures of consumer culture, children have their own needs and their own karma.
Years ago I saw a pertinent article in the _New York Times_ magazine in the "Lifestyle" section. The writers had gone to the apartment of a Zen Buddhist woman in Manhattan and photographed various rooms to show the "Zen style." Looking at the pictures, my jaw dropped, my eyes grew wide. Incredibly, there was practically nothing in her house! Her young son's room was bare except for a bed; the walls were devoid of a single picture, poster, or decoration. No books, no toys, no sports equipment, no musical instruments—there was no sign of life anywhere. And this was supposed to be Zen?! Looking at the pictures, I thought: _This is not Zen; this is bizarre. People don't live like this; kids especially don't live like this_. I wondered if she thought that in order to be a Zen Buddhist you had to live in an empty shell, foregoing all possessions. Maybe she thought that if she didn't have anything, her son wouldn't become attached to consumer objects. It made me think of Layman P'ang, a deeply enlightened ancient worthy who felt so strongly about the corruptive influence of wealth that he threw all his money into a deep river. He did this despite the fact that he had a family to support. (His wife's reaction was not recorded.) If you are single and want to live like that, that is your choice. But it is misguided to impose such an austere lifestyle on children no matter how enlightened you may be. It is important to stimulate children's creativity with books, toys, music, and art. This is not the same as catering to every whim of your child—limits are important. The difficulty is in finding the middle way. So, what's a Buddhist parent to do?
While you might want to deal with the pressures of consumerism by living in an empty house or throwing away all your wealth, there are other, more practical ways to approach this challenge. Children need a certain number of possessions in order to learn about sharing, taking care of things, and respecting property. But even more important, they need the example of their parents. Take, for instance, the problem of drinking, something most parents face with trepidation as their kids enter adolescence. As a point of spiritual practice, if parents strictly follow the fifth precept and don't drink, they will effortlessly communicate to their children the messages of sobriety and clearness of mind. If parents consistently pick up a glass of wine for relaxation or enjoyment, it is only natural that their children will associate drinking alcohol with having a good time. What better thing can parents do than practice what they preach? If as Buddhist parents we drink alcohol, including wine and beer, and yet are trying to get the message across to our children not to drink, it is hypocritical or at the very least confusing. It is much cleaner and easier to just not drink. Of course, not every parent who drinks is going to have children who drink, nor is every parent who doesn't drink going to have children who abstain, but by setting an example you can increase the odds.
In our family the precepts were part of our daily life. Discussing the meaning of the precepts with our daughters and engaging with the questions that came up around them seemed quite natural, and it was excellent training for dealing with consumer issues and moral dilemmas. For me the precepts were a tremendous gift in that they provided impeccable guidelines for daily life. By the time I had a family, I could think of nothing better to do for my children than to follow the precepts to the best of my ability. Now my daughters are grown, but it is a special joy when I see parents bringing their children to the precept ceremonies we hold each year.
Along with following the precepts, I firmly believe that the single most important step parents can take to avoid the excesses of consumer culture is to banish television from the home. When people ask me for child-rearing advice, I tell them just one thing: _Get rid of your TV!_ True, there are some excellent, worthwhile programs on public television, but I honestly do not think the risk is worth it. Television is a dangerous intoxicant, in its own way as destructive as alcohol and drugs. It erodes communication within the family, promotes base values, exposes children to foul language, sex, drinking, and drugs at far too early an age, and interjects destructive, disturbing, violent imagery deep into the mind. Of equal importance, the barrage of commercials on television encourages greedy consumerism. The advertising industry creates desires for unnecessary things by convincing hapless people that they are _worth_ it, they _deserve_ it, they _ought_ to have it. Is it any wonder we grow up believing that in order to be happier, sexier, prettier, more fulfilled, we need the latest . . . whatever? All in all, I cannot imagine why any parents who are practicing the dharma would want their children to ingest the toxic waste they are bound to see on television.
Without TV my children were not exactly clueless about trends—they did attend public school—but they certainly were not much influenced by them either. Instead of spending their time watching junk, they played sports, visited with friends, practiced musical instruments, read books, painted, danced, spent time outdoors, did homework, goofed off, and attended events at the Zen center when they wanted to. My daughters did think that we were a weird family—vegetarian, Buddhist, mother a priest, dad on the school board, no TV, no alcohol—but they weren't angry, resentful, or friendless. In fact, they rather liked our unique strangeness. Our household was exceptionally harmonious, and I am convinced that the absence of television had as much to do with it as anything else.
When you take refuge in the wisdom and warmth of the sangha, the teachings of the Buddha can more easily take root in your life. In time they inform daily interactions with family and community. I have found that taking refuge and following the precepts are ways of working with the forces of entropy on both a personal and a parental level. Our society, with its pressure to consume excessively, pulls us away from our center. This powerful centrifugal energy is unsettling. Always looking outside ourselves, we feel unbalanced, disorderly. The blessing of raising a family with people who are seriously practicing the dharma is that just the opposite energies are at work. Rather than being pulled outward, the centripetal forces of zazen bring one, day after day, back to the center. There is order, and with it comes tranquility.
The values of family and sangha are reflected in each other because sangha is actually an extension of one's family. In our spiritual community, as in our family, we face difficult issues, consumer or otherwise, in much the same way: through respectful discussion and careful listening, trying to maintain virtue, harmony, and equanimity. The sangha of the Vermont Zen Center began with only four people. As a tiny sangha, what was important was the way we conducted our lives and not the things we possessed. Besides, we possessed almost nothing. For close to fifteen years we managed to keep everything on a small scale—no staff, a little house, a tiny budget. But over the years our membership grew, our activities increased, and we developed a pressing need for more space. This became a dilemma for us: Do we limit our growth or raise money to expand our facility?
It was not an easy question to answer. If we were to build new facilities, we faced questions about building materials, scale, design, and ecological impact. Additionally, we would need to borrow money. Part of our practice had been to keep free of debt; Vermont Zen Center has no credit cards. We had worked hard to retire our original mortgage in ten years and had never before purchased anything we could not afford. Suddenly we were considering incurring a huge expense, way beyond our current means. Over and over we asked ourselves: Is this truly need or is it greed? We thought, with so many people suffering from poverty and hunger, do we have the right to ask for contributions and spend this kind of money?
As we debated the merits of expansion versus staying small, we agreed that the only reason for expanding was to increase our ability to help rid the world of suffering. We looked at the root of suffering: greed, anger, and ignorance, in other words, addiction to the ego-I. We concluded that there is no more effective antidote to greed and consumerism, nor is there a better way to help people overcome ego addiction and lead lives of wisdom, compassion, joy, and equanimity, than to expose them to the dharma.
After much discussion, we decided that we would expand. There was a demand for the dharma, and we could better serve people with a larger Zen center. Through the long process of planning and building, we tried to keep costs down, build as "green" as possible, use recycled materials and solar principles, and have a low impact on the environment. While we haven't been able to meet all our goals, we have done our best to build in a responsible way.
I still find it painful to think about the money we have had to spend to expand our center—thousands of dollars for the permitting process alone. But every time I despair, I am immediately filled with the deep conviction that what our troubled world needs now more than anything else is places of spiritual practice. When I was in Japan and saw temples where people had trained for centuries, temples like Ryoanji and Sanjusangendo, Bukkokuji and Sogenji, I had a visceral reaction: _This_ is why the world is still here! If such places did not exist, the world would surely be destroyed. We might not see that or feel that or know that on a conscious level. Nonetheless, I am certain that our planet is intact only because of the efforts of people who let go of their ego delusion, who care more about the welfare of our planet than their right to consume, and who devote themselves to living a wise and compassionate existence.
Part of Vermont Zen Center's mission is to give back to the community through outreach. For example, we open our gardens to the public, raise funds for food shelves and the homeless, work with prisoners, and hold services dedicated to world peace. Some of our fundraising goes toward supporting Oxfam's community programs and paying for the education of a Tibetan child in India. Many sangha members feel inspired to become involved with hospice work, human rights activities, and environmental issues. By making community service an integral part of our practice, we cultivate compassion and selfless giving. It is our hope that the new center will greatly enhance our ability to serve the community. Since generosity and an awareness of the needs of others are remedies for greed, our outreach activities help us as a sangha overcome our consumer addictions.
RENOUNCING DESIRE
The first major ceremony we will observe in our new center is Jukai, the ceremony of taking the Three Refuges, the Three General Resolutions, and the Ten Cardinal Precepts. Twice each year we conduct Jukai; every five years we have Great Jukai. In the expanded ceremony of Great Jukai, participants move through the Center past vivid depictions of the six hell realms.
Participants start with the lowest realms of hell and travel through representations of the hungry ghost, animal, titan, human, and deva realms in turn. At the start of our journey, each person is given a drawing of three animals in a circle: a pig representing ignorance, a cock representing greed, and a snake representing anger. Each animal is biting the tail of the one before them, just as we devour ourselves when we give way to consumer excess. As we walk slowly past the sights, smells, colors, and images of the six realms—some of them frightening, some exquisite, some eerie, some unnervingly familiar—we reflect on the causes of being reborn as a person in war-torn lands or as a starving person, as a dog or a human child, a general or a princess. The consequences of acting on uncontrolled desires stand vividly before us. What a powerful antidote to the forces that drive us to consumerism!
The last realm we pass through in Great Jukai is filled with seductive material comforts and temptations. This is the sweetly scented, beautiful world of the devas. There we linger perhaps a moment longer than in the other realms, enticed by the pleasurable sights and smells. Just beyond is the zendo, where we hear the words of the dharma being chanted by those who have crossed the realms before us. We pass into that tranquil space and, with utmost gratitude, bow down before the Buddha, taking refuge in Buddha, in Dharma, and in Sangha, knowing that this is the path to liberation.
Traveling through the six realms, with body and mind we absorb the teaching on the interrelated causes of being reborn in realms of suffering. We see how our craving and desire in the form of attachment to consumer objects and sense pleasures bind us to the wheel of rebirth. Zen master Dogen's forceful words echo the teaching that has been passed down for twenty-five hundred years: "Do not idle away the time needed for practice, but rather practice in the spirit of a person trying to extinguish a blaze in his hair." Dogen admonishes us to abandon all thoughts of fame and desires, get rid of material goods, part with fields and gardens, renounce everything. "You should renounce them even if you do not possess them. What should be clear in this matter is the principle of being free from them whether you have them or not."
In Tibetan thangka paintings of the Wheel of Life, there is a graphic image of a man with an arrow piercing his eye, depicting the powerful impact of objects on the senses. This impact generates the overwhelming feelings of desire and craving, wanting and greed, which afflict us all and lead to the disease of consumerism. For those who long for freedom from this illness, the Dharma provides a refuge where greed, anger, and ignorance can be relinquished through concentrated effort. The best antidote, therefore, for taming the "I want" mind is the Buddha's teachings, the emphasis on no-self, and the way this no-self is actualized through Zen training.
Anyone who takes up the challenge of walking the path commits to diminishing the "I want" mind. The process is difficult and challenging because it goes against the grain of the "more" ethos of Western society. But ultimately it is transformative and worthwhile. And, really, if we wish to grow in wisdom and compassion, what other choice do we have?
10
Penetrating the Tangle
Stephanie Kaza
GOING SHOPPING can be a perilous mental activity these days. As I wander through the department store, I am barraged not only by a daunting array of goods but also by virtually nonstop moralistic thoughts. A new bedspread— _you don't really need this, the old one's good enough_. A stylish dress— _why would a Zen person need this?_ A stunning carpet— _was this made by enslaved children?_ It goes on and on. The critical voices are all too familiar. As a professor of environmental studies, I am especially plagued by environmental critiques— _if it's not organic, it must be laced with toxic pesticides_. Or _Who knows how far this wood has been shipped and from what decimated forest?_
The koan of consumerism is vast and deep, a tangle within tangles, impossible to completely untangle. Part of the tangle is the resistance, the questioning mind, the nagging thoughts that add up to moral engagement. Sometimes I find myself paralyzed in the co-op, staring at the bounty on the shelves, lost in thoughts of fair trade, farmworkers, and food security. Critiques of consumerism are not new, but as the deluge of products becomes a flood, more and more voices are shouting their concerns.
Some of my own questions come from early training in self-sufficiency in the 1970s; others stem from painful exposure to increasing environmental assault on beloved forests. Still other critiques seem to be part of the social fabric of being American—a puritanical righteousness, a stubborn resistance to corporate control. Can a Buddhist perspective shed any light on this mix of critiques? As in any mindfulness practice, it helps to be able to identify what is going on. _Resisting, resisting, judging, judging_ —these activities of the mind are part of a much bigger historical pattern of moral response to consumerism.
Sociologist Michael Schudson lists five traditional critiques, which provide a preliminary taxonomy of consumer resistance. The first of these is the "Puritan" critique, referring to the early New England colonists who believed people should invest less meaning in material possessions and more meaning in religious pursuits. Puritans felt goods should serve practical human needs but should not be ends of desire themselves. Consumerist attitudes were thought to corrupt people, impairing their capacity for spiritual development.
The "Quaker" critique focuses more on the wasteful nature of the goods themselves. From this perspective, excessive choice and pointless proliferation of products is seen as extravagant and unnecessary. Planned obsolescence, as in the annual new models of cars and computers, is particularly objectionable. If goods cannot be made to endure, keeping the limited resources of the earth in mind, then they should not be made at all. The Quaker critique challenges a core value of consumerism—that more choice is good for consumers and good for the economy.
What Schudson calls the "republican" critique addresses the impact of consumerism on civic society as a whole. In this view a consumerist approach replaces public engagement in politics with private involvement in personal goods. It also shifts a person's identity away from work (what one does) and toward lifestyle (what one owns), promoting individual pleasure over social justice. Historically, the increasing orientation to consumerism has turned people away from social activity. "People abandoned the town square for the front porch, and then later the front porch for the backyard or the television room." This trend is corroborated in the _State of the World 2004_ report with studies showing that overall social health has declined in the United States in the last thirty years despite higher levels of consumption.
The "Marxist," or socialist, critique objects primarily to the exploitation of workers in the capitalist economic system. The production of a common cotton T-shirt, for example, means farmworkers are exposed to intensive toxic pesticides and garment workers in sweatshops work long hours for low wages. From the Marxist perspective, consumerism can also be seen as a distraction or opiate, leading workers to seek satisfaction in goods rather than improve the abusive profit-driven workplace. The last of Schudson's list, the "aristocratic" critique, focuses more attention on aesthetics, attacking mass-produced goods as ugly. That which is rare or exclusive holds the greatest value, thus generating a classist sense of privilege.
Perhaps the strongest critique of consumerism today is being mounted by environmentalists. Thirty years ago concerns about population growth and the earth's limited resources were the primary topics of environmental debate. But since the 1992 Rio Earth Summit, the global South has made it clear that the wasteful consumption of the North is of equal concern. It points out that the North is generating far more significant ecological damage with its high use of water, oil, minerals, and timber. Some have described this as casting an "ecological shadow" on the middle-income and poor classes who bear the burden of the hidden economic and moral costs to the environment. Environmentalists point to industrial nations' oversized ecological footprint. This is the land necessary to sustain current levels of resource consumption and waste discharge. The average American has a thirty-acre footprint—if everyone lived like this, we would need five more planets to support human existence. Though world population may level off by midcentury, environmentalists are concerned that consumption will only keep growing as more and more of the world's population enters the consumer class.
BUDDHIST CRITIQUES
What can Buddhism contribute to these critiques of consumerism? Are Buddhist critiques simply a variation on the commonly expressed critiques above? Or can Buddhism offer a new approach that is helpful in today's galloping rush to consume the planet? Reflecting on this from my own perspective as a Zen student committed to environmentalism, I believe Buddhism offers something distinctive and very useful. As a new religion in the West with growing popularity, Buddhism holds the potential for not only challenging global consumerism but also for offering a practice path to liberation through the very thick of the tangle.
Sorting through my own questioning voices, I find three critiques that clearly derive from a Buddhist orientation. The first critique focuses on the role of consumerism in the process of personal identity formation. The usual idea of self is seen as a significant delusion in Buddhist thought. Consumers in today's marketplace are urged to build a sense of self around what they buy. Consumer goods are symbols of status, political or religious views, social group, sexuality—all of which solidify a sense of self. "I am what I have" has become the operative slogan, using shopping to define identity. Advertising aggressively promotes self-involvement, playing on people's needs for security and happiness. When self-identity depends on products, the need for social acceptance can fuel addictions to brand names, to styles, and even to shopping itself. Consumerism can actually have a negative effect on self-identity, preventing the mind from engaging in more positive life-affirming activity.
From a Buddhist perspective, ego-based views of self are fundamentally mistaken, promoting ignorance and suffering. Deep identification with the separate self as autonomous and fixed prevents us from experiencing the world as relational and co-creative, always in dynamic flux. Material accumulation strongly reinforces this mistaken view. The more we relate to material objects as real and permanent, the more deeply we tend to think of ourselves as a fixed self with specific identity. More attachment, more need for consumer goods to prop up our identity. Or you could take the (false) position that _nothing_ is real or permanent. If nothing is real, then nothing matters, so why not indulge in whatever momentary pleasure you like? With this logic you can successfully avoid engaging the actual relationships of the world that shape and condition your life. If nothing matters, why be concerned about the suffering behind consumer products?
A second Buddhist critique is that consumerism promotes, rationalizes, and condones harming. The foundational principle behind all Buddhist ethics is nonharming, or _ahimsa_ , expressed as the first of the five precepts: "do not kill," or "do no harm." Monks were taught not to destroy "the life of any living being down to a worm or an ant." This precept reflects the Buddhist understanding of interdependence—that the flourishing of life is a complex and ever-changing web of relationality. Killing or harming another being in the web has serious consequences, especially if you do so with the intention to harm. Such an act would show obvious disregard for the true nature of reality.
While consumer good manufacturers may not intentionally choose to cause harm, their actions nonetheless often leave death and injury in their wake. In some cases the choice is deliberate—to clear-cut forests, to pollute waterways, to abuse workers on the production line. Producers justify tremendous harm to many forms of life to meet the bottom line of profit and gain. Slavery is not uncommon even today. Harmful actions produce negative karma, leading to lower rebirths and increased suffering, while minimizing harm leads to positive karma and less suffering for self and others.
Perhaps the strongest Buddhist critique is that consumerism promotes desire and dissatisfaction, the very source of suffering, as explained in the Four Noble Truths. The state of dissatisfaction—clinging, craving, impulse, thirst, attachment, compulsion—could not be more opposite to contentment and equanimity. Craving in its most fundamental sense is the desire for existence. Just to want to exist or be alive is a basic biological drive. Often identified in terms of karma and rebirth, craving is the "thirst that gives rise to repeated existence." Marketers play on this strategically, stimulating this desire to be alive through delicious foods, powerful cars, and exotic vacations. Craving also includes aversion, the desire for _non_ existence. In this case one craves relief or escape from what is unpleasant or undesirable—mosquitoes, for example, or a heat wave or maybe just bad body odor. Marketers take advantage of this too, offering a parade of products that profess to relieve almost any form of human suffering.
Early Buddhist teachings describe the results of desire in terms of four types of clinging or attachment. The first is clinging to sensing and sense objects. Graphic examples are consumer addictions such as tobacco or alcohol and their attendant sensory pleasures. The second is clinging to views and values that reinforce a sense of self. The desire to promote one's views or sense of what is "right" can afflict consumers (as well as their critics). The third result of desire is clinging to actions. Attachment can develop around behaviors necessary to support consumer values. Choosing what to wear, what and what not to eat, and who to please all become part of the consumer's identity, carefully analyzed by market specialists. The fourth, self-clinging, means literally clinging to one's own sense of identity as subjectively experienced. This is the attempt to bridge the sense of fragmentation that arises from experiencing things as separate. Paradoxically, identity building exacerbates the gap it is trying to eliminate and thus can never bring satisfaction.
Of the three Buddhist critiques, we can see that some overlap with traditional critiques yet also offer distinctive contributions to this discussion. The Buddhist critique that consumerism promotes a false sense of self might parallel the Puritan critique of material goods as distractions from spiritual development. The Buddhist concern for nonharming would reinforce the Marxist critique regarding worker exploitation. But the Buddhist focus on desire in promoting an endless cycle of suffering may be the most penetrating critique. Awakening or enlightenment rests on realizing the allpervasive nature of this existence-based drive. Taking up the study of desire in the form of consumerism offers an endless field for spiritual practice. With the structure of this critique firmly in mind, the consumer beset by desire can plunge into the tangle, seeking insight in the midst of confusion.
BUDDHIST METHODS FOR LIBERATION
What, then, are some useful liberative methods to relieve the suffering of consumerism? Taking consumerism as the context, we can look to traditional methods of insight and practice for cultivating enlightenment. Here I offer one approach for each Buddhist critique of consumerism. The first provides exposure to the process of identity formation; the second offers guidelines for nonharming; and the third describes the specific links that perpetuate desire.
Exposing Identity Formation
The first Buddhist critique points out that the problem with consumerism is its constant reinforcement of ego identity. Misunderstanding the self as either fixed or insubstantial misses the empty nature of self. This is almost impossible to grasp through armchair reflection. You need a more vigorous method to challenge the false views of the consumer self.
In Dogen's well-known verse from the _Genjokoan_ , we find one approach to dismantling these false views:
_To study the Buddha way is to study the self_
_To study the self is to forget the self_
_To forget the self is to be confirmed by the myriad things_
_To be confirmed by the myriad things is to drop off body and mind of self and others_.
Zen priest Shohaku Okumura explains that the original Japanese word for "study" in Dogen's text was _narau_. This derives from _nareru_ , which means "to become familiar or intimate with." Dogen approaches this in the biggest sense—studying one's mind, body, sense organs, speech, and social relations as deeply conditioned by self-centered needs. Studying and forgetting the self, in Dogen's view, is fundamental to becoming authentically human.
How does one study the consumer-constructed self? Suppose I really love drinking tea. (I do.) I can study how my self is constructed around drinking tea. I can observe my preferences for a certain brand or tea shop. I can study my pleasure: What delights me about the act of drinking tea? Is it the flavors, the stimulation, the social company? (All of the above.) I can study my memories of drinking tea and see how they add up to a specific subjective identity as a tea drinker conditioned over time.
Looking closely at any one of these aspects of my self as a consumer of tea, I see how dependent my idea of self is on conditions outside my "self." Time of day, quality of tea, source of the water, mind of the tea preparer—all of these contribute to my experience of tea. There is no such thing as my separate self enjoying the separate tea. It is all happening at once. Observing the endlessly connected web of tea conditions and relations, I go beyond the small self. I see myself as part of the co-creating universe, my inflated self-identity as tea drinker busted. The delusion crumbles.
"Self and all others are working together. The working done by self and all others are called our actions." Okumura points out that we think "we" are "driving" a "car." But actually the "car" is "driving" "us." The car we drive is being driven by the oil economy, its parts produced across the globe. Our driving is the action of highway builders, car designers, city planners, and congressional policy makers. All these beings contribute to our existence, poking us to let go of confused views of a separate self.
But how is this "dropping off body and mind?" Dogen's teacher Nyojo said, "Dropping off body and mind is zazen. When we just practice zazen, we part from the five desires and get rid of the five coverings." The five desires come from contact with the five sense organs, generating a false sense of self that is attached to the pleasures or aversions we experience with our senses. The five coverings are the hindrances of greed, anger, sleepiness, distraction, and doubt that keep our minds from functioning in a healthy way. Discarding sensory attachment and hindrances is one path to deflating the consumer self. Studying deeply the myriad aspects of my consumer identity, I see into the delusion of self as consumer, of self as anything separate from anything else.
The insights from studying one type of attachment can be applied from one context of consumerism to another. Studying my self as tea drinker gives me practice experience to study my self as consumer and producer of knowledge, for example. (I am quite attached to my books.) Seeing how self-construction works, I am less gullible to the consumer industry and its endless hooks (including the hooks of books). I can check my psychological conditioning as I lean toward various book purchases. But this self-examination is not in itself the experience of enlightenment. Zazen provides a deeper ground for awakening to the actual experience of the selfless state. This more profound level of insight only strengthens your capacity for seeing through the lures of the consumer self.
Practicing Nonharming
The second Buddhist critique of consumerism is that it promotes harming. This critique raises questions of right and wrong—how do you decide what is harmful in the realm of consumerism? The Buddhist texts on ethical behavior offer specific guidance in the form of the Five Precepts: not killing, not stealing, not abusing sexuality, not lying, and not using or selling intoxicants. The precepts represent practices of restraint, calling for personal responsibility for reducing environmental and human suffering. Taken together they indicate choices one can make to avoid harming others.
I will work primarily with the first precept here, though each precept can apply to aspects of consumerism. The first precept is the practice to abstain from "destroying, causing to be destroyed, or sanctioning the destruction of a living being." A living being is anything that has life, from a small insect to a complex forest. Clearly, every act of consuming raises the issue of harm—just to stay alive we have to eat food that has been killed or harvested. Accepting this paradox, we nonetheless can choose _how much_ harm we want to be responsible for. For example, many people practice vegetarianism because they don't support the harming of animals from industrial agriculture. Others eat organic fruits and vegetables to reduce harm to soil from chemical fertilizers and pesticides. Some avoid fast food because of labor exploitation and human health impacts.
Consumer awareness movements are now promoting "chain of custody" verification that can document the source and treatment of material goods. Forest certification and green building are two arenas where knowledge of production processes have given consumers the option to choose more ethically produced goods. Buying locally often shortens the chain, making it easier to track harmful impacts. Under pressure from students and the Environmental Council, my campus at the University of Vermont is now including green building standards in new capital projects. Our neighboring campus at Middlebury College has used locally certified wood products throughout its new science building.
The precept of nonharming can also be stated as a positive commitment to practice metta, or lovingkindness. One version of the metta verse is:
_May all beings be free from enmity, affliction, and anxiety, and live happily_.
_May all breathing things, all who are born, all individuals of whatever kind be free from enmity, affliction, and anxiety—may they live happily_.
Actively holding this wish for all beings makes it very difficult to participate in their harm. Quite the opposite—you want all beings to flourish and thrive and be free from the impacts of human excess. I think of the blunt checkerboard of clear-cut forests in my home state of Oregon: it has been so painful to witness the fragmentation of the Northwest forest. Offering the metta verse, I wish for kindness to these forests—may they be free from profiteering and politics, may they live happily.
Traditionally the precepts, including nonharming, have been oriented toward individual conduct; the Buddha did not offer a counterpart set of moral guidelines for institutions. Because social structures (governments, schools, churches, and so on) contribute to consumer-related harming, ethical guidelines for social structures would also be useful. Individuals and institutions influence each other. More conscious standards of restraint in public arenas (such as no advertising in schools) can encourage greater personal practice of nonharming, and the reverse can also happen. This means holding social or institutional agents accountable for the impacts of their actions. By taking the initiative here, consumers could reclaim moral integrity that has been eroded by consumerist agendas. It is not necessary for one to have perfected moral practice before asking others to consider their own actions. The point of the precepts is to reduce suffering and to practice interrelationship rather than self-interest.
Breaking the Links of Desire
The third Buddhist critique is that consumerism promotes desire and dissatisfaction, the cause of suffering. A classic method for working with desire is the teaching of the _nidanas_ , or causation. The Twelve Limbs (or Links) of Co-dependent Origination are sometimes portrayed as a wheel of becoming describing the process of reincarnation and rebirth. But these can also be used to describe common patterns of causation that arise in each moment of desiring or grasping. Consumerism utterly depends on this process, reflecting its completely human nature.
The twelve links follow each other in order: ignorance, karmic formations, consciousness, name and form, six sense fields, contact, feelings, craving, grasping, becoming, birth, death, then on to ignorance, and the cycle continues. The pull of each link, based on the strong experience of the one that precedes it, is so powerful that we are continually in the grip of this metapattern. Release from this cycle of grasping and suffering is what the Buddha called nirvana. As consumerism is a never-ending field of desire, it offers an ideal platform for studying the twelve links.
We can start our study at any point in the cycle; for this discussion, let's begin with _craving_ —for the latest Dalai Lama book, for instance. Craving is the experience of being hooked by an object, a thought, or a need and then yearning to grasp it. In the twelve-link cycle, craving depends upon _feelings_ that arise following contact with objects in the sense fields. _I see the book, it feels good in the hand, the words feel good in my mind_. Feeling states in Buddhist psychology are categorized as pleasant, unpleasant, or neutral/indifferent. It doesn't matter so much whether one is happy, afraid, tender, or irritated; for each feeling, one either wants to perpetuate it (usually the pleasant feelings) or get rid of it (usually the unpleasant feelings). Since feelings are impermanent, advertisers or sales agents continually restimulate potential buyers to keep pleasant and unpleasant feelings going. This is done by generating a barrage of _contact_ points for the sense organs, such as colorful displays, flashing signs, tantalizing café aromas. The point of contact is where the object of perception (book), the sense organ (eye and hand), and the sense consciousness (sight perception) come together. The bookstore provides the object; I, as consumer, provide the already conditioned sense organs and consciousness. To slow the production of feeling states and the craving arising from feeling, we can reduce the points of shopping-related contact.
The six _sense fields_ of eye, ear, nose, tongue, body, and mind include both perception and consciousness shaped over time by _name and form_. This is the material form of a being—that is, your body, including your physical sense organs. What you perceive through your sense fields is completely conditioned by your experience. How I read the Dalai Lama's book is conditioned by hearing him speak, seeing his picture, even the memory of meeting him once. Considering the power of the sense fields, I wonder about young children watching hours of television—does their consciousness become dominated by products and brand names?
Name and form are conditioned by previous experiences that mold _consciousness_ and the material form it takes. Such conditioning is well documented for alcoholism and other addictions. Repeated use of alcohol changes people physiologically so they are more attracted to the states induced by alcohol. Apply this conditioning to other forms of excess consumption and you can extend the addictive cycle to luxury foods, designer clothing, and television serials. Advertisers do their best to capture teenage consumer consciousness by imprinting brand-name loyalties for cigarettes, beer, and hygiene products at an early age. Teen product companies even hire teen trendsetters, passing out free samples to establish brand loyalty. Resisting the slogans of consumerism becomes one way to break the conditioning that is being so aggressively promoted. Culture-wide consumer consciousness eventually results in long-term _karmic formations_ , which will require culture-wide attention to transform.
Turning back to craving, we can see how craving perpetuates the other limbs. In craving pleasant experiences, one grasps after their continuation; in craving the absence of unpleasant experiences, one grasps after their cessation. These forms of grasping are especially strong where the ego or sense of "I" attaches to what is craved or avoided. Marketers are masterful at using human grasping to create specialty niches; even green consumers and dharma practitioners are now well-established market groups. No one is immune from having his or her identity needs worked for profit. Breaking the energy in this part of the cycle is especially challenging. _Grasping_ generates _becoming_ : the more one grasps after consumer goods or values, the more one becomes a consumer, leading to " _birth_ " of the self-identified ego that defines life primarily as consumption. Thus we have the phenomena of suburban "mall rats," Tupperware queens, and eBay treasure hunters.
Eventually, of course, the consumer must confront the twelfth limb— _death_ —when the self can no longer be propped up by possessions. Fueled by _ignorance_ of the nature of dependent origination (compounded by massive denial in consumer culture), karmic traces carry over from previous actions or lifetimes. Consider the alcoholic father who models the pattern of alcohol abuse to his son, or the shopaholic mother who fosters an appetite for fashion in her daughter. From generation to generation, consumer consciousness flourishes, feeding the cycle of causation driven by desire.
Observing the nature of co-dependent origination can provide a penetrating tool for analyzing consumerism. The cycle can also be studied in terms of cessation as well as origination. Breaking the driving energy from one link to the next slows down the desire-generating cycle. If you reduce contact with consumer stimulants such as television, your sense fields are less flooded with product messages. If you overcome a debilitating addiction, that craving has less impact on your consciousness. The point here is not that the cycle of causation can be brought to a halt, since beings keep taking form and are conditioned just by existing. But by applying mindfulness, one can observe the process and even learn to unhook from the craving. Each moment of consumption can thus be an opportunity for insight, tasting, if only in a small way, the freedom from grasping and dissatisfaction.
PRAGMATIC RELIEF
The Buddha told his followers that his teachings should offer pragmatic relief for their suffering. If they weren't useful in everyday life, then the teachings were not of value. It seems to me that Buddhist methods of working with consumerism offer very practical methods to address the suffering it generates. Consumerism is a dominant practice field of our times; if the Buddha's teachings have merit, they can be applied to untangle the complex web of all-consuming relations.
For me, this work is an ongoing personal experiment in resisting the invasion of consumer economics and consciousness. Does Buddhism help relieve the suffering of consumerism for me personally? The critiquing voices are never far away, but now I see them as wake-up calls, each one an opportunity for liberation. Hearing about slavery on cocoa plantations, I vow to practice nonharming and reduce my desire for chocolate. Reading about pesticides on strawberries, I vow to support my local organic farmers in the interdependent web. Studying the privilege that comes with first world status, I vow to study the twelve links that perpetuate global poverty.
Practicing deeply with consumerism may provide a very wide Dharma-gate to awakening. Endless desire, endless suffering, endless cycles of consuming. The tangle fills the whole universe—how far into the tangle can the Buddha eye see?
11
Form and Elegance with Just Enough
Rita M. Gross
ASK FOR BUDDHIST ADVICE on almost any topic and you might well receive the answer, "Follow the middle way—not too much, not too little." Western appropriations of this advice almost always focus on the "not too much" component, for good reason. Excessive consumption and runaway greed are extremely evident in many Western contexts. Many sensitive commentators and thinkers struggle with the issue of how to encourage moderation in the face of the relentless message, "Happiness (or safety or security) is just ahead, if only you buy our product." This message is beamed at us nonstop by advertisers hired by multinational corporations seeking to maximize their profits. The quest for moderation in the midst of excess is especially poignant and urgent because so much of the world lives with far, far too little.
However, the Buddhist slogan also contains the phrase "not too little," which is rarely applied in discussions of how to encourage moderation rather than overconsumption. Could guidelines about what constitutes "too little" actually help rein in excessive consumption? This essay will explore such a counterintuitive proposition.
My contemplations of this possibility are taken up in the context of the Buddha's life story, of how he discovered each guideline in turn. What could otherwise seem like abstract speculation becomes concrete when we think about his life and how it unfolded. The canonical stories tell us that as a young man from a wealthy family, the future Buddha enjoyed a life of luxury. Many accounts spare no effort in detailing this luxury: the three palaces—one for each season—the women at his beck and call, even the culture of music and dancing readily available. The young prince was the best at everything he tried—the best archer, the best wrestler, the best charioteer—learned and cultured in all the arts of his day. The stories also say that Siddhartha was protected from any awareness of certain basic facts of life such as illness, old age, and death by his ambitious father, who wanted to ensure that his son _not_ be interested in seeking another way of life.
Siddhartha's curiosity led him to leave his palace, whereupon he saw in succession a sick person, an old person, a corpse, and a world renouncer, the last of whom seemed more serene and contented than anyone he had ever seen. The future Buddha realized that his lifestyle, which could be seen as the epitome of modern pleasures, brought him no real happiness or satisfaction. He decided to leave his life of privilege and set off on a quest for understanding. His lifestyle then swung to the opposite end of the spectrum. He practiced severe asceticism in an attempt to starve himself into true awakening, seeing everything that had formerly promised satisfaction as an enemy to be overcome.
The textual accounts of this phase of the Buddha's life are also quite graphic. He starved himself until, pushing his hand against his stomach, he could feel his spine; he sat between several hot fires on a torrid day. After years of extreme austerity he saw that such a course of action was equally futile, that self-denial was not bringing liberation, contentment, and happiness either. He suddenly realized that a sensible middle path between overindulgence and self-torture would be far more productive. Deciding to bathe and eat food again, the future Buddha endured the scorn of his fellow ascetics but attained enlightenment very shortly thereafter.
It is just as significant that the Buddha found no real peace while practicing extreme self-denial as that he found no real satisfaction in his luxurious palace life. Self-denial is no more effective than self-indulgence in solving the problems of greed and grasping leading to suffering. Suffering due to hunger, thirst, and lack of shelter does not promote spiritual well-being; it only increases attention to the suffering self. And when the deprivation is not self-chosen, the focus on the suffering self becomes all-absorbing, making genuine detachment and tranquillity very difficult. Furthermore, voluntary self-denial often leads to self-righteousness, sometimes based on religious views of the body and material world as unimportant or problematic and therefore to be minimized or avoided. Such a view is simply not compatible with Buddhism as I understand it.
Undue emphasis on not consuming too much can be ineffective and therefore may not be the best course of action. People tend to respond to lectures about the need to cut consumption more often with resentment or guilt than with any actual change in lifestyle. In my view, real lifestyle changes are more likely if the changes lead to a greater sense of well-being rather than a continual sense of restraint and deprivation. Because of this psychology, I suggest that exploring the "not too little" component of the Middle Path has a great deal to add to the commentaries on "not too much" in regard to excessive consumerism. The Middle Path involves not consuming too much, but it also involves a proper appreciation of form, of the phenomenal world, and an accurate understanding of how to work with our embeddedness within that world. That is part of the "not too little" component of the Middle Path. This delicate balance, I suggest, is one key piece of a Buddhist understanding of issues of consumption and overconsumption that may not often be noticed. People may well consume too much precisely because they lack techniques for appreciating the phenomenal world, the world of form. Their greed may well be tamed by learning how to appreciate deeply what they do consume or what needs to be consumed to maintain a dignified life. Greed may be much more effectively tamed by such appreciation than by struggles to curb consumption based on guilt or feelings of obligation.
This insight comes to me from the teachings of my root guru, Chögyam Trungpa, and Buddhist practices I have observed in Asia. At a certain point in his work with Western students, Chögyam Trungpa Rinpoche began to train us in many practices that involved working with and appreciating the phenomenal world. These teachings are especially connected with the Shambhala vision that he began presenting after 1976, but they are also consonant with the general view and practice of Vajrayana Buddhism. He emphasized precision in arranging and placing objects, elegance in decorum and decoration, and concern for whatever would generate a sense of upliftedness. Some of these practices, such as beautiful shrines and shrine rooms, precise shrine room decorum, and treating teachers with respect and care, are traditionally Buddhist, but they had not been emphasized so much in Trungpa's early years in North America. Japanese-style flower arrangements were part of the new wave of material appreciation. Virtually no Shambhala Buddhist program will occur now without beautiful flowers, especially on the shrine and the teacher's side table. Creating and caring for the flower arrangements is part of the rota of work assignments at many Shambhala Buddhist centers. Colorful banners are also common at most events; for newcomers, they just add a sense of elegance, but for older students, each banner has symbolic significance and embodies certain Shambhala teachings.
Some of the other practices seemed less characteristic of traditional Buddhism and have often raised questions from other (Western) Buddhists. Advice about how to dress and how to eat, even how to arrange furniture in one's home, began to appear. Trungpa emphasized dressing well, eating good food, and upholding a general sense of personal decorum and elegance. Jewelry, too, became important, and now the Shambhala community has adopted a whole repertoire of pins that signal something about their bearers to other members of the community. At the concluding ceremony of Level Five of the Shambhala Training program, for example, participants are given a pin, which they are expected to wear especially at Shambhala events. Another pin is given to those who complete Kalapa Assembly, the final program of the Shambhala Training sequence. Part of the etiquette of teaching the various levels of Shambhala Training involves remembering to wear that pin. Though I am somewhat casual about this etiquette, I am careful to remember to pack the appropriate pin when I am preparing to teach a Shambhala level.
Trungpa always emphasized that he was not talking about people spending a lot of money to present a more elegant appearance. Repeatedly, he stated that if one had developed a sense of dignity and style, one could put together beautiful outfits from used clothing. One does not need a lot of beautiful or elegant things; a few such things are far more satisfactory than a large closet full of ill-fitting, garish clothes. The same kind of advice was given regarding food and drink. Enjoying good food and eating with proper table manners was highly recommended. As part of this training, people were also taught how to serve formally both visiting teachers and each other. I have fond memories of programs at which I would be a server one evening and be served the next evening. I also became much more confident of my appearance without worrying about fashion or size. I did find some of the recommended forms, such as Viennese waltzing, rather stiff and unattractive, but by and large I found this training intriguing and helpful. My insight into the wisdom of this advice has grown over the years, until I now think that appreciating form properly is central to undoing habitual greed and overconsumption.
As people took this advice to heart and began to practice it, an aura of wealth began to develop in the Shambhala community. People looked good, even if they were not conventionally attractive, and they also seemed more content. There was less need for more and more. If one truly enjoys, with elegance and dignity, what one needs to consume, there is no need for more. Conversely, if that appreciation is lacking, one will never have enough, no matter how much one has.
Looking around the traditional Buddhist world, I see this aspect of the Middle Path that emphasizes appreciation of the phenomenal world and "not too little" being lived out in many ways. As I have had more experience living with Tibetan Buddhists in India, I have come to wonder if, in fact, Trungpa's advice about elegance and good appearance might not be rather traditional. I now suspect that North Americans who find his advice odd represent North American casualness and informality rather than a cogent interpretation of Buddhist values. On several occasions I have been with a group of pilgrims traveling in India with Khandro Rinpoche. Gently but repeatedly she asks people to dress well, and her helpers explain that the local people make judgments about her based on the appearance of her Western students. On my most recent trip, she really wanted all the women to wear traditional formal Tibetan _chuba_ s (a woman's dress) and even directed a local tailor to make a number of _chuba_ s that the women could purchase as soon as they arrived. (She had even correctly figured out everyone's size.) Unfortunately, some of the women (not students of Trungpa's) insisted on wearing pants anyway on ideological grounds.
It is very common to look at traditional monastic lifestyles and notice the many practices of renunciation. But equally, one could notice aspects of monastic life that carefully delineate the "not too little" component of the Middle Path. One could note the dignity and elegance of traditional robes, perhaps made of patches sewed together, but also made of good fabric appropriate for the climate. In the Tibetan context, bits of brocade on the upper garment worn under the robes are not uncommon, and some are made entirely of brocade. Monastery grounds are well kept, often with beautiful gardens. The buildings are often impressive, adorned with artwork that expresses the vision of the form of Buddhism to which the monastery belongs.
Mindrolling Monastery, in Dehra Dun in northern India, the seat of Mindrolling Trichen, an important Nyingma lineage holder and the father of Khandro Rinpoche, is such a place. The centerpiece of the compound is a 180-foot-tall stupa with four levels inside. Each level contains shrines to different figures important to Tibetan Buddhism and the Mindrolling lineage, including Shakyamuni Buddha, Padmasambhava, and the founder of the Mindrolling lineage as well as all his successors. The walls are covered with detailed murals depicting life stories of important teachers and various mythological figures important to Tibetan Buddhism; statues of buddhas, bodhisattvas, gurus, and _yidams_ (meditation deities) are everywhere. A short distance from the stupa is a comfortable guest house for visitors, with a lovely view of the monastery complex. Perhaps most notable, however, are the grounds, with their many potted flowers and well-kept lawns, a great contrast to the crowded, dirty, and noisy streets just outside the compound. One group of plantings sets off a large pond with a fountain, which is turned on for a few hours in the evening. The entire setting generates a feeling of peace and serenity. Local people, both Buddhists and non-Buddhists, also appreciate the appeal of the compound; it is open during the day, and many local people come to rest, to pray, and simply to enjoy the place.
Clearly these and many other forms go well beyond merely functional needs. One does not need a 180-foot-building to house the ongoing ritual life of the monastery (for which the first floor is used extensively). A pond and a fountain are completely unnecessary from a purely functional point of view. Brocade on the top garment worn under the robes is likewise not necessary. Why does the Middle Path, as expressed in monastic institutions, consistently involve consuming _more_ than the barest functional minimum? There must be some clues embedded in these practices that tell us how properly consuming "not too little" helps us overcome grasping and greed.
Such elegance and beauty in the monastic lifestyle, indeed in religious forms altogether, could be and have been criticized as unnecessary, as somehow inimical to the spirit of Buddhism, with its emphasis on renunciation. Anticlerical and antireligious movements and ideologies, including socialist movements, have made such criticisms of all religions, not just Buddhism. They claim that the buildings and artwork are merely ways to hoard wealth and that such practices demonstrate the hypocrisy of religions, especially those whose founders lived in relative poverty. The money could better be spent on various relief projects, they say. While it is possible to argue that such displays sometimes go beyond the guidelines of the Middle Way into "too much," I would argue that usually they express instead the "not too little" aspect of the Middle Path. The minimum for sheer physical survival is "too little," and trying to live with too little does not lead to peace and freedom. An aesthetic dimension, a way of working with form that expresses elegance and dignity beyond sheer physical survival, does seem to promote true peace, given that such aesthetic practices recur over and over throughout the Buddhist world. But before this point can be fully developed, it is necessary to return to the Buddha's life story and the practice of "not too much."
NOT TOO MUCH
The Buddha's life story provides further clues about the Middle Path. First he discovered that "too much" wasn't satisfactory; then he discovered that "too little" was equally problematic. I think the discoveries have to be in that order, and also that the sequence is especially important for those of us who have plenty of opportunities to consume too much. According to Buddhist psychology, humans have a deeply ingrained habitual pattern never to be satisfied and to always grasp for more. That is the nature of samsara, the ultimately unsatisfying way of dealing with life, which the path of Buddhist practice seeks to remedy. With little advice on how to appreciate form and the phenomenal world, it is not surprising that the religion of the marketplace, the practice of consuming as much as possible in an attempt to allay existential anxiety, is so successful. It appeals to deep-seated habitual patterns that have been ingrained over countless lifetimes, according to the traditional Buddhist perspective. This "religion" features the cultivation of desire and promises that the right car, the fastest Internet connection, and the most convenient loan to cover those purchases will make people feel better. Competing visions of fulfilled desire are offered to consumers, attempting to assure them that if one version of salvation through consumption fails, there will always be another one that might work.
From a Buddhist point of view, this logic is completely and fatally flawed, of course. The cultivation of desire is the problem, not the solution, both because desire is insatiable, as new desires immediately arise to replace those temporarily satisfied, and because the state of being filled with desire is itself painful. It is difficult to imagine how genuine satisfaction could be built on a foundation of denying Buddhism's Second Noble Truth, which states that the cause of suffering is ignorance rooted in desire—exactly what the religion of the marketplace promotes.
Nevertheless, it is difficult even for long-term practitioners to fully grasp the futility of trying to satisfy desire completely, once and for all. The siren song, "next time it will work," is extremely alluring. Without alternative training in renunciation and appreciative consumption, the habitual patterns of mindless and excessive consumption will prevail. Like us, the future Buddha had many opportunities to consume too much, so it is not surprising, and probably necessary that the Buddha first discovered the unsatisfactory quality of consuming "too much" before he could learn the middle path and recognize that "too little" is also a problem.
As is often observed about swinging pendulums and major shifts in behavior, it is usually necessary to go to the other end of the spectrum before things can settle into the Middle Way. Thus, in Vajrayana Buddhism, especially as taught in Shambhala Buddhist centers, the path is regarded as a progressive unfolding, the first stage of which is about renunciation, simplicity, and slowing down so that one can see one's situation more clearly. First, opulent consumption must be renounced. Such renunciation is the necessary foundation for going further, for having the ability to enjoy beauty and elegance without grasping and attachment. If beauty and elegance result in attachment rather than uplifted peace and dignity, then one can hardly claim to be practicing the middle path and not erring on the side of "too little." Rather, one still needs to reach a point where attachment is not the ruling passion and "too much" no longer seems attractive. Given that grasping and greed are endemic habitual patterns ingrained over many lifetimes, such a stage of practice is seen as necessary for most people.
In this initial period of practice, one works especially to see how counterproductive attachment is, how attachment and greed never bring any lasting peace but only increase the amount of pain one experiences. At this stage, learning how to renounce the feast of discursive thoughts, wandering mind, and attachment to one's own opinions is especially important. Though one may renounce things or activities in order to spend time in meditation practice, attachment itself is the primary thing to be renounced. As the Kagyu lineage chant used by Shambhala Buddhists says:
_Renunciation is the foot of meditation, as is said_
_To this meditator who is not attached to food and wealth_
_Who cuts the ties to this life_
_Grant your blessing so that I have no desire for honor and gain_.
Notice that food, wealth, honor, or gain are not the problem, not what needs to be renounced. Rather, attachment and desire are what must be given up. Though renunciation of attachment and desire can be fostered by a simple lifestyle, the main point is to develop a state of mind that is not so consumed by attachment and greed.
This first level of training provides a foundation that is never left behind in the practice of later stages of the path. In fact, one cannot successfully practice later stages of the path without this foundation of renunciation. Most people probably do not take their renunciation to the stage of severe starvation practiced by the Buddha. Nevertheless, things can be appreciated and enjoyed _only_ if they can also be renounced; only a mind familiar with renunciation offers the peace and calm necessary for appreciating elegance and beauty without becoming attached to them. Otherwise one can still be hooked by neediness, and thus the religion of the marketplace continues its reign.
With genuine renunciation in place, the Buddhist alternative to the religion of the marketplace and the need for endless consumption can arise. This is the development of genuine peace, contentment, and happiness, rooted in detachment and equanimity. Sometimes it is not well understood that Buddhists seek genuine happiness rather than some grim stalemate in which desires are held at bay. For Buddhists it is not the case that the best we can achieve is desireless resignation to an unsatisfactory status quo, though Buddhism has been portrayed that way in older accounts. Some Buddhist discourse is suspicious of positive language, which makes it difficult to use terms like _contentment_ or _happiness_. Nevertheless, such terms must eventually be used; the difficulty is to communicate the difference between trying to find happiness based on the satisfaction of desire, which is impossible, and happiness arising from living in the present without expectations and desires. Though these two may sound the same with only superficial acquaintance, they are quite different. Happiness based on the satisfaction of desire is always subject to disintegration, whereas happiness free of attachment can accommodate difficulty and disappointment without disintegrating. Buddhism can never be understood nor can its response to consumerism be fully appreciated if one ignores the central importance of genuine delight and pleasure, contentment, and peace of mind in the overall Buddhist vision of release and fulfillment.
At some point the student on the path does become somewhat detached, somewhat less driven by attraction to phenomena and the consequent grasping and attachment. It becomes clear through experience that the problem has always been the mind that is attached, not the phenomena to which it attaches. This fundamental point is often missed in discussions of attachment and detachment. The phenomena are neutral, not really the cause of grasping at all. Giving them up physically, though, is no guarantee of detachment; yet to a mind that is fundamentally detached, living in their midst does not threaten one's equanimity. This point is especially elaborated in Mahayana teachings, the second stage of the unfolding path of spiritual development as taught by Shambhala Buddhism and other forms of Vajrayana Buddhism.
The Mahayana bodhisattva or the Shambhala warrior is pictured ideally as living in the messy and attractive world rather than in a safer, more isolated place. The attractions and woes of such a lifestyle no longer distract such a warrior as he or she goes about the fundamental task of trying to be of service in such a world. The bodhisattva's ability to live in the world without attachment is expressed in Mahayana art by the crowns and jewels they wear, in contrast to buddhas, who are always pictured wearing monastic robes. The image of the Shambhala warrior goes even further. Although the task of warfare is usually thought to be completely inimical to spiritual practice and attainment, these teachings use the image of the warrior to signify someone who is brave enough to look directly into all experiences, including fear. For the bodhisattva and the Shambhala warrior, things that normally involve intense attachment—wealth and warfare—are transformed through detachment into tools for living in the midst of ordinary people, providing help and comfort.
Vajrayana teachings and practices continue this trajectory. The lushness and sensuality of Vajrayana art and liturgy often seem quite discordant with other forms of Buddhism. Bejeweled "deities" dwelling in palaces of jewels and flowers, often portrayed in sexual union, might seem shocking as representations of enlightenment in many parts of the Buddhist world. Indeed, I have been in Buddhist-Christian dialogues where other Buddhists felt secure enough to voice their skepticism about Vajrayana sexual imagery, saying in effect, "Why _that_ ? It's so embarrassing! Couldn't you think of some other way to express what you Vajrayanists are trying to say?" The Vajrayanist would answer that it is helpful to use the most striking and startling imagery to express a fundamental teaching of Vajrayana Buddhism—that seen as it is, free of the distortions brought about by grasping and attachment, the world is sacred, delightful, and enjoyable. Such images express the fact that the beautiful, appealing, sensuous phenomenal world actually becomes an aid rather than an impediment to awakening when it can be viewed as sacred rather than as a potential trap filled with desire-producing objects. The caution with which phenomena and pleasure must be approached when the mind is still easily seduced by attachment is no longer necessary. Mahayana Buddhists, and Vajrayana Buddhists to an even greater degree, suggest that once renunciation and detachment as states of mind are well in place, it is not necessary to avoid phenomena; indeed, worldly phenomena may even be helpful to the practitioner.
NOT TOO LITTLE
At this point in the unfolding path of spiritual development, the focus switches from "not too much," which is now an intuitive discipline rather than a self-conscious effort, to "not too little." On one level of understanding, this principle is rather straightforward. Buddhists have always recognized that minimal standards of physical and emotional security are necessary prerequisites for the successful pursuit of spiritual discipline. For example, in its discussion of the paramita (virtue) of generosity, the well-known Mahayana training manual _Gems of Dharma_ , _Jewels of Freedom_ states that gifts should be given in proper order: first the gift of material well-being, next the gift of emotional well-being, and finally, the gift of dharma. This point seems rather straightforward; people cannot be expected to practice meditation when they must spend all their time trying to make a living, and it is difficult for all but the most advanced practitioners to appreciate emptiness in the midst of emotional suffering and turmoil. However, it helps explain why Buddhism is initially more attractive to well-off people, not only in North America, but in all situations in which Buddhism has been a new religion.
This suggestion that we must first meet peoples' material and emotional needs before dharma practice can be relevant also serves as a dharmic justification for the engaged Buddhist movement. This movement is regarded with skepticism by some Buddhists, who claim that political and economic concerns are irrelevant to Buddhists. Therefore it is important that the justification for engaged Buddhism be based on traditional dharma teachings rather than values purported to be non-Buddhist.
However, there may be more subtle and radical aspects to the guideline "not too little." To access these dimensions of the guideline, we need to return to contemplation of the practices discussed earlier. Why did Chögyam Trungpa advise his students to dress and eat well? Why did he encourage so much attention to precise and elegant forms? The answer may be found in one of the protector chants of Shambhala Buddhism, done especially in times of turmoil and negative influences. The chant speaks of "the end of the five-hundred-year dark age,"
_When sons do not listen to their father's words_ ,
_An evil time when relatives quarrel_ ,
_When people dress sloppily in clothes of rags_ ,
_Eating bad cheap food_ ,
_When there are family feuds and civil wars_.
The chant goes on to say that these activities provoke the wrath of certain negative forces, which then send turmoil, war, disease, and other calamities to fill the earth. This is an extremely interesting assertion of cause and effect: because of undignified, depressing activities such as eating bad cheap food and wearing clothes of rags, negativity increases. Conversely, acting in a more dignified and uplifted fashion reverses that negativity, which is why Chögyam Trungpa encouraged his students to eat and dress well (but not expensively).
How can the phenomenal world, the world of form, become an ally in the path of spiritual development? What might working with the phenomenal world, the world of form, and paying attention to the "not too little" component of the Middle Path have to do with consumerism? What's the problem with dressing sloppily in clothes of rags and eating bad cheap food? What would its opposite have to do with spiritual development?
The answer has to do with the effect that elegant, beautiful things have on the mind. In Shambhala Buddhist programs a great deal of attention is paid to the environment in which the teachings occur. In fact, the environment is thought to be almost as important as the quality of the dharma talk. It is often said that people usually remember very little content from the first talk they hear. But the overall environment, its dignity and aesthetic quality, along with the friendliness of the staff, are remembered and have a great deal to do with whether people return to the center. Flower arrangements and banners are especially prominent in setting the tone, but much attention is also paid to how various objects are placed in space and how they relate with each other. The Shambhala aesthetic calls for enough space between objects, with the whole pattern being coherent and harmonious. The result is a palpable sense of upliftedness and confidence that contrasts significantly with the depressed feeling that results from a dirty, sloppy, ill-arranged environment. Such an uplifted state of mind is much more conducive to spiritual growth and development than the depression brought about by lack of attention to the quality of one's environment. People may not be consciously aware of the impact of their environment on their state of mind, but the impact still occurs. Buddhists throughout the ages in all Buddhist cultures seem to be keenly aware of the relationship between beautiful, elegant forms and a more uplifted, serene, spiritually developed state of mind. Buddhist art and architecture across continents and traditions offer a potent testimonial to this understanding.
One might ask: "Are sloppy clothes and bad cheap food insurmountable obstacles?" The answer, of course, is no. For various reasons, one may be in a situation in which there is no possibility of clean, attractive clothing and good nutritious food. Then one practices equanimity, the one taste of the fundamental equality of all phenomena, so as not to be thrown off course by such negativities. But when there are alternatives, it is counterproductive not to use the beauty and delightfulness of the phenomenal world as an ally, drawing on its ability to encourage states of mind more in tune with enlightenment. Refusing to take advantage of such aids to enlightenment embedded in the phenomenal world or not knowing how to do so errs on the "too little" side of the Middle Path.
Such practices land us precisely in the middle of the Middle Path—not too much, not too little—and this is very relevant to consumerism. Usually consumerism is thought of as "too much," as erring on the side of overdoing, and in a superficial way that is correct. But why is there so much temptation to overdo? I think it sometimes results from too little appreciation of appropriate forms, of elegance and beauty. We are buried in a mountain of material goods with little sense of how to enjoy what we consume, because we have never been taught etiquette and elegance, because we do not have the practices and forms that would allow us to enjoy phenomena without being tempted to overindulge. As a result, we always want more. With a real understanding of how to work with the phenomenal world, one knows when enough is enough and knows how to enjoy what is enough.
One potent example is that of a flower arrangement. If one tries to put in one extra flower, the whole arrangement can be ruined. Likewise, an arrangement may need one more branch or flower. To enjoy it, to have the flower arrangement work to promote peace and contentment, it must be just right, just enough. But more important, unless one understands the form or guidelines for making a flower arrangement, one will probably not arrive in the middle of the Middle Path. Too little appreciation of beauty and elegance is counterproductive, and, in a situation in which material goods are abundant, underappreciation actually encourages consumerism and overconsumption. Thus, counterintuitively, one of the ways of discouraging consumerism may well be to encourage love of beauty, elegance, and dignity, so that we know how to enjoy the right amount. And I suspect that in many ways such a strategy is more effective than urging people to consume less out of guilt about the effects of their consumption on the rest of the world.
12
Consuming Time
David Loy and Linda Goodhew
The odd thing was, no matter how much time he saved, he never had any to spare; in some mysterious way, it simply vanished. Imperceptibly at first, but then quite unmistakably, his days grew shorter and shorter. . . . Something in the nature of a blind obsession had taken hold of him, and when he realized to his horror that his days were flying by faster and faster, as he occasionally did, it only reinforced his grim determination to save time.
—Figaro the barber, in Michael Ende, _Momo_
TODAY MR. FIGARO'S COMPLAINT is all too familiar. Even with so many labor-saving devices and efficiency measures, how is it that we seem to have so much less time? What social scientists call a "time-compression effect" contributes a manic quality to much of daily life. Increased stress at work and school, sleep deprivation, up to half the U.S. work population suffering from burnout, workaholism (and sometimes death from overwork), no time for family and friends, children left by themselves . . . it's not a pretty picture.
A 1992 survey by the U.S. National Recreation and Park Association found that 38 percent of Americans report "always" feeling rushed, up from 22 percent in 1971. More recently Joe Robinson in the _Utne Reader_ claims that the United States has now passed Japan as the most overworked country in the industrialized world. He reports that the husband and wife of an average U.S. household are now working five hundred more hours a year than they did in 1980. Lou Harris public opinion polls have shown a 37 percent decrease in Americans' reported leisure time over a twenty-year period, leading Harris to assert that "time may have become the most precious commodity in the land."
But could commodifying time itself be the problem? Perhaps our problem with time is not so different from our problem with everything else we consume. By commodifying we convert things into resources for buying and selling. Today the earth and all its beings continue to be commodified in new and ingenious ways, such as the trading of carbon emissions and manipulating the genetic codes of biological species, including our own. With the profound impact of the industrial revolution, life was transformed into labor—work time—to be bought and sold, and hence also valued according to supply and demand. Our accelerating postmodern world has aggravated this development. Because we can never consume enough of it, the most precious "resource" of all has become time.
This suggests that if we want to understand consumerism, we need to understand how and why we consume time. This paper will examine time consumption with the help of the Japanese Zen master Dogen Kigen (1200– 1253) and the German novelist Michael Ende (1929– 1995). Dogen's classic text, the _Shobogenzo_ , includes some of the most profound Buddhist reflections on time, more precisely, on the delusive duality we usually experience between ourselves and time, between events and the time they are "in." Michael Ende wrote many books apparently for children, including _Momo_ and _The Neverending Story_. _Momo_ is a provocative fantasy built on an insightful conceit: What if time _could_ be saved, just like money? By exaggerating our preoccupation with time-saving, Ende reveals why time cannot be saved or consumed and why people who try to do so lose sight of what life is all about.
Dogen's obscure and epigrammatical reflections on time are as incisive today as when he wrote them. _Momo_ was published in 1973, presciently, for only since then has the temporal nightmare it depicts (or predicts?) become our reality. Together Dogen and Ende can help us understand how we consume time today and how we might realize a more healthy alternative.
TIME COMMODIFIED
Life holds one great but commonplace mystery . . . time. Calendars and clocks exist to measure time, but that signifies little because we all know that an hour can seem an eternity or pass in a flash, according to how we spend it. ( _Momo_ , 55)
Momo, the main character in Ende's novel, is a homeless, gypsylike street child who makes many friends because she has the marvelous gift of truly listening to others. As the plot thickens we find her resisting a secret army of men in gray suits who are slowly taking over the world. The author reveals later that they live by literally consuming other people's time. They deceive their "clients" by promising them more leisure in the future from their savings accounts in the Time Bank, but in return their victims must save as much time as possible now by speeding up their work, cutting social life, and in the process destroying all joy in life. The mottoes of the gray men (all too familiar to us today) are "Time is precious—Don't waste it!" and "Time is money—Save it!" (67).
At one point Figaro the barber is in a bad mood, feeling he is a failure and doubting the value of his existence. One of the gray men recommends that he save time by eliminating all the activities that in fact give his life meaning: the time he spends with his elderly mother, his social life, his reading, even his daydreaming. Suddenly he becomes future oriented, with disastrous consequences. "The determination to save time now so as to be able to begin a new life sometime in the future had embedded itself in his soul like a poisoned arrow" (65). Yet by changing his lifestyle he becomes increasingly restless and irritable. "People never seemed to notice that, by saving time, they were losing something else. No one cared to admit that life was becoming ever poorer, bleaker and more monotonous . . . [for] time is life itself, and life resides in the human heart, and the more people saved, the less they had" (68).
The story also targets consumerism of material things. Children turn up with new toys that offer nothing to the imagination, leaving them mesmerized but bored. The gray men tempt young Momo with Lola the Living Doll, a talking Barbie-type doll with a never-ending wardrobe of clothes, accessories, and friends to accumulate. It is the perfect toy to teach children a key economic lesson, that "there's always something left to wish for" (85).
Because of their ability to live fully in the present, children are believed to present a greater threat to the gray men's work than anything else. The men persuade adults to legislate against children's free time, arguing that children are the raw material of the future, so they must prepare to be the experts and technicians of tomorrow. In compulsory prisonlike child depots (modern schools and day care centers?), they are allowed only useful, educational games so that "they forgot how to be happy, how to take pleasure in little things, and, last but not least, how to dream" (167–68).
One of Momo's special friends is Beppo, a poor roadsweeper who is deliberately slow and Zen-like in his total attention to the present moment. In order to sweep all day long he had learned that it's no good to hurry. "You must only concentrate on the next step, the next breath, the next stroke of the broom, and the next, and the next. Nothing else. . . . That way you enjoy your work, which is important, because then you make a good job of it. And that's how it ought to be" (36). Because he takes all the time in the world to answer questions—being determined never to say anything untrue—Beppo is widely believed to be "not quite right in the head," and the gray men get him confined to a hospital. When he tries to escape, one of the gray men appears with the lie that Momo has been kidnapped, but she can be ransomed for one hundred thousand hours of Beppo's hard—and hurried—work. Beppo agrees and is released.
In the meantime Momo takes refuge in the magical residence of Professor Secundus Minutus Hora, where "all the time in the world comes from" (142). A sworn enemy of the gray men, the professor helps Momo find and release the gray men's secret hoard of stolen time-lilies. Deprived of sustenance, the gray men evaporate. The lily flowers fly back "to their true home in the hearts of mankind" and suddenly people find they have plenty of time to enjoy flowers and play.
Everyone's sense of time returns to normal—in _Momo_ , at least. But have the gray men taken over our own world? Ende wrote this fable before he visited Tokyo, where we write this essay and where Ende must have observed the hordes of gray-suited "salarymen" inflicted with the fatal disease he calls "deadly tedium"—a tedium that motivates much of our escapism into consumerism. As this suggests, the gray men are not a Western or a Japanese problem but a modern problem. What does Buddhism have to say about the source of this problem?
TIME OBJECTIFIED
When asked why his disciples were so radiant, Shakyamuni Buddha replied:
[My disciples] do not repent of the past, nor do they brood over the future. They live in the present. Therefore they are radiant. By brooding over the future and repenting the past, fools dry up like green reeds cut down.
Mahayana Buddhist teachings can help us understand our present problem with time consumption by tracing it back to the basic dualism that we experience between things (including us) and the time they are "in." This dualism is in fact a fundamental delusion that contributes greatly to our duhkha, or unhappiness. Fortunately for us, this perceived split between things and their time is not something real or objective but something mentally constructed—which means it can be deconstructed.
The problem is not simply that everything dear to us (including—most of all?—ourselves) will pass away; nor is the solution simply to accept that impermanence. Such a response still presupposes the delusive duality between things and time. As Nagarjuna realized, if there is no permanence, then there can be no impermanence either, because the meaning of each is dependent upon the other: "All things are impermanent, which means there is neither permanence nor impermanence." Without the things that are contained in time, time cannot exist as a container. Without nouns there are no referents for temporal predicates. When there are no things that have an existence _in_ time, then it makes no sense to describe things as being young or old. "So the young man does not grow old nor does the old man grow old."
Is that clear? Maybe not. If there are no things that exist in time, how are you able to read this book? Isn't it because you bought (or borrowed) it last week? Nagarjuna's argument is, typically, too abstract to connect easily with our everyday experience. Here Dogen's more concrete images can help us. Dogen deconstructs the dualism between things and time by reducing each term to the other. On the one hand, he demonstrates that _objects are time_. Objects have no self-existence because they are necessarily temporal, in which case they are not objects as we usually understand them. On the other hand, he also demonstrates that _time is objects_. Time is not an objective container but manifests itself _as_ the ephemeral processes we call objects, in which case time, too, is different from how it's usually understood. "The time we call spring blossoms directly expresses an existence called flowers. The flowers, in turn, express the time called spring. This is not existence within time; existence itself is time." In his _Shobogenzo_ Dogen combines subject and predicate in the neologism _uji_ , which is usually translated as "being-time":
"Being-time" here means that time itself is being . . . and all being is time. . . . Time is not separate from you, and as you are present, time does not go away. . . .
Do not think that time merely flies away. Do not see flying away as the only function of time. If time merely flies away, you would be separated from time. The reason you do not clearly understand time-being is that you think of time as only passing. . . . People only see time's coming and going, and do not thoroughly understand that time-being abides in each moment. . . .
Time-being has the quality of flowing. . . . Because flowing is a quality of time, moments of past and present do not overlap or line up side by side. . . . Do not think flowing is like wind and rain moving from east to west. The entire world is not unchangeable, is not immovable. It flows. Flowing is like spring. Spring with all its numerous aspects is called flowing. When spring flows there is nothing outside of spring.
When time flows, there is nothing— _no thing_ —outside of time. To treat time as a commodity, then, is to be caught up in a delusion that makes us hurry up in order to gain the time to slow down. This is just the trap that the gray-suited time thieves encourage people to fall for. The commodifying attitude that tries to save time cannot help but carry over into the rest of our lives. Understanding time as a resource, to be used like any other resource, means we lose the ability to _be_ time. Having become habituated to hurrying, it becomes difficult for us to slow down, even in situations when hurrying is inappropriate. How many people take their laptops and cell phones with them when they go on vacation? During a quiet afternoon lying on the beach, we still remember all those things we need to do.
Like Nagarjuna, Dogen also emphasizes that the relativity of objects and time implies that objective time-as-a-container-for-things is a delusion. If there is only time, then there is no time. I am being-time when I no longer situate my activities within another, constructed time understood as external to me. In place of the present as a thin, moving line between the immensities of past and future, I live _in_ the "eternal now" when I nondually _become_ whatever I am doing.
Dogen makes this point using the image of firewood and ashes:
Firewood becomes ash, and it does not become firewood again. Yet, do not suppose that the ash is future and the firewood past. You should understand that firewood abides in the phenomenal expression of firewood, which fully includes past and future and is independent of past and future. Ash abides in the phenomenal expression of ash, which fully includes future and past. Just as firewood does not become firewood again after it is ash, you do not return to birth after death.
This being so, it is an established way in buddha-dharma to deny that birth turns into death. Accordingly, birth is understood as no-birth. It is an unshakeable teaching in Buddha's discourse that death does not turn into birth. Accordingly, death is understood as no-death.
Birth is an expression complete this moment. Death is an expression complete this moment. They are like winter and spring. You do not call winter the beginning of spring, nor summer the end of spring.
Because our life and death, like spring and summer, are not _in_ time, they are timeless. If there is no nontemporal being who is born at a certain time and dies at another time, then there are only the _being-time_ events of birth and death. But if there are only those events, with no one that they happen _to_ , then there is really no birth or death, because our notions of birth and death are dependent upon a person that they happen to. Instead, there is "just _this_!"— _tada_ in Japanese. Shakyamuni Buddha is sometimes called the tathagata, literally "the one who just comes/just goes." Or we may say that there is birth-and-death in every moment, with the arising and passing away of each thought and act. Then there is nothing lacking in the present that needs to be fulfilled in the future, and spring is not an anticipation of summer. Each moment, each event, is whole and complete in itself.
In other words, the Buddhist solution to this aspect of our suffering involves realizing that I am not _in_ time, because I _am_ time. What I do and what happens to me are not events in time; they are the forms that time takes right here and now. If I _am_ time, though, I cannot be trapped _by_ time. Paradoxically, then, to _be_ time is to be _free from_ time. Momo is free because she lives in such a timeless world. It is not that she always _has_ time for her friends. Rather, her way of listening to them is loving and nourishing because her being-time is open to their being-time. Figaro overlooks this, trying to save something that cannot be saved because time is not something we can ever _have_.
Momo also shows us that being-time is not only what we _are_ , it is what _we_ are. In individualistic cultures such as most Western consumerist societies, my time is _mine_. I protect and cherish it. I may need to sell a certain amount of it for money every week, but the rest belongs to me. I can spend it however I like; it is part of my disposable income. Today we take this for granted and base all our business and recreational planning on this premise. But premodern cultures show us that such an attitude is not natural or inevitable. Unfortunately, our possessive attitude toward time often encourages an indifference to civic concern, a lack of devotion to the collective that is necessary to address the enormous social and ecological issues we face. Without such collaborative participation, these problems are unlikely to be successfully resolved.
That Nagarjuna and Dogen both emphasize the problematical nature of this duality shows that our problem with time is neither modern nor Western. Contemporary time compression merely aggravates the split further, trapping us more deeply in delusion. Does this mean that objectifying and commodifying time as something we are _in_ is a basic tendency of the human condition? Is this habit common to all cultures? Apparently not. In contrast to Western society, some premodern tribal societies lack awareness of objective time as an abstract reference point outside events. E. E. Evans-Pritchard's classic study on the Nuer of central Africa rather wistfully concludes:
I do not think that they ever experience the same feeling of fighting against time or having to coordinate activities with an abstract passage of time, because their points of reference are mainly the activities themselves, which are generally of a leisurely character. Events follow in a logical order, but they are not controlled by an abstract system, there being no autonomous points of reference to which activities have to conform with precision.
What is new today is modern technologies and forms of social organization that enable us to quantify time much more precisely. Commodification of time was made possible, and perhaps inevitable, by the clock. As clock time became central to social organization, life became "centered around the emptying out of time (and space) and the development of an abstract, divisible and universally measurable calculation of time." The collective objectification of clock time means that now, insofar as we are social beings, we all must live according to this universal standard. The complexities of our social interactions require such a mechanism for their coordination, even though such a lifeless way of patterning time has led to an experience of it that is completely alien to the real world. Alien or not, most of the time we have no choice but to pay attention to the fact that in order to make that 10:00 A.M. class we have to catch the 9:16 bus.
In other words, time today _is_ an objective container for us, for that is the way it has been socially constructed. But to live _only_ according to that collective construct is to "bind ourselves without a rope," to use the Zen metaphor. With clock time, time is objectified and consumed as outside the activity and regulating it. With Dogen's being-time, in contrast, the temporality of an activity is integral to the activity itself. We can sometimes notice this difference in the way music is played. Either the notes march along precisely following the time signature, or we are so absorbed in those notes that we do not notice the time signature at all because the music nondually embodies its own time. The musical example is a good one because it reminds us that the solution is not always to slow down. Some music sounds better played fast. Many sports wouldn't be as much fun if you couldn't run. The point is to find the pace that is appropriate for the activity—or, stated even less dualistically, to let events generate their own temporality. Most of us know better than to make love watching the clock. Can we learn to "make love" to the whole world, in all our activities?
THE LACK OF TIME
If time commodification and consumption have become such a problem for us, why do we distinguish so sharply between clock (absolute) time and the events that happen "in" it? For Anthony Aveni, an anthropologist who studies different time systems, the common drive behind our temporal schemas is a quest for order, which is necessary to secure the cosmos and the self that inhabits it. "Temporally speaking, we desire the capacity to anticipate where things are going, to relieve our anxiety by peeking around nature's corner as far as it will follow." Deeper than the desire for order, however, is what Damian Thompson describes in _The End of Time_ as our "deep-seated human urge to escape from time which, in the earliest societies, was usually met by dreams of a return to a golden past." Christianity changed that by situating us toward the end rather than the beginning of time, thereby promoting a golden future instead. In a crucial step toward modernity, the Italian hermit Joachim of Fiore (1135–1202) conceived of a coming golden age not outside of this world (in heaven) but _within_ this world. This shift eventually gave birth to our modern preoccupation with progress.
Perhaps the difference between a golden past and a golden future is less important than the shared impulse to transcend time as we know it experientially, because its ineluctable course carries us all to a final destination we dread. In a poignant passage, Momo asks Professor Hora if he is Death, and he replies: "If people knew the nature of death, . . . they'd cease to be afraid of it. And if they ceased to be afraid of it, no one could rob them of their time any more" (144). Thompson sums up his study of apocalyptic time by concluding that the human understanding of time is always distorted by death: "The belief that mankind has reached the crucial moment in its history reflects an unwillingness to come to terms with the transience of human life and achievements. Our urge to celebrate the passing of time fails to conceal an even deeper urge to escape from it."
In contrast, the Buddhist tradition begins with Shakyamuni's willingness to come to terms with the transience of human life and achievements. According to the traditional myth, it was Shakyamuni's encounter with an old man, an ill man, and a corpse that motivated his spiritual quest. Zen satori, for example, is sometimes called "the great death" because it involves ego death, "letting go" of the sense of self. From a Buddhist perspective, however, an explanation of time compression and commodification that focuses _solely_ on death denial and symbolic immortality is inadequate.
That brings us back to the Buddhist emphasis on _anatta_ —"no self" in modern terms—the claim that my sense of self is not something that exists independently but is rather a conditioned and ungrounded mental construct. Repression of this uncomfortable fact returns continually as a sense of _lack_ : the feeling that "something is wrong with me." We all experience this but understand it in different ways (I'm not rich enough, famous enough, loved enough . . .). Consumerism plays on this very effectively by offering to fill up our sense of lack with commodities. The implication is always that the _next_ thing we buy will end our lack. Advertising surrounds us with images of attractive, smiling people who obviously feel no lack, and we too can be happy like them if we use the same products.
Another way to describe this sense of lack is that we don't feel "real" enough. If I feel ungrounded, the solution is to (try to) become more grounded, which is where religion traditionally comes in. It usually offers us this answer: Do this or that, and you will be saved. But what solutions are possible in a secular society focused on the individual? Now becoming real depends upon my own efforts— _which require me to use my time well_.
For Buddhism, then, the self is better understood not as a thing but as an ongoing _process_ that seeks perpetually, although in vain, to feel secure by making itself more real. Since the modern, more individualized ego self is even more of a delusion, it is all the more unsatisfied with itself; and then on top of that, it must explain the dissatisfaction. The reason must be that I have not attained my goals. Since the goals I do accomplish bring no satisfaction, I need more and more ambitious projects . . . leading to more and more time compression.
In psychoanalytic terms, the pressure we feel to accomplish something is an internalization of the intentions we project outward into the world. Psychoanalyst Neil Altman noticed his compulsion to accomplish something during his years as a Peace Corps volunteer in southern India. Raised in an individualistic culture emphasizing achievement more than affiliation, Altman, like most of us, had been trained to use his time _efficiently_ :
It took a year for me to shed my American, culturally based feeling that I had to make something happen. . . . Being an American, and a relatively obsessional American, my first strategy was to find security through getting something done, through feeling worthwhile accomplishing something. My time was something that had to be filled up with progress toward that goal.
The more we experience time as objective, the more alienated is the sense of self that is _in_ time and therefore more desperate to _use_ time in order to try to gain something from it. Greater, too, is our awareness of the always-threatening end of our own time through death. Our own sense of separation from time motivates us to try to secure ourselves within it. Yet according to Buddhism, the only satisfying solution is the essentially spiritual realization that _we are not other than time_.
Unfortunately, this self-defeating dynamic has taken on a collective social life that supports our modern preoccupation with economic expansion and technological development. As sociologist Max Weber pointed out, this historical process has become all the more obsessive because it has no particular goal except more and more. Ende also understood this. In a talk given in Japan in July 1985 and later published in the _Asahi Journal_ , he spoke to his urgent concern to set human beings free from the obsession of economic growth. Unfortunately, this obsession is now intrinsic to our economic system, which must keep growing if it is to avoid collapse. The technological challenge of how to produce things has more or less been solved, so the greater economic challenge for the developed or "economized" countries is how to stimulate ever more consumption among those who have the money to buy things.
But is our fascination with that game declining? I wonder if the attraction of the future is collapsing, if we are now psychologically "disinvesting" from both the individual and the collective projects—always future oriented—that we hope will make us real. Without faith in any spiritual alternative, however, we remain trapped in the future because that provides the only way we can think of to address our sense of _lack_. We try to "progress" faster and faster because we do not know what else to do, what other game to play. The more we suspect that we are headed nowhere, the faster we need to run. Fewer and fewer of us still believe that economics or technology will solve our world's problems and lead to a better life. The collective _lack_ project of technological development is questioned by an increasing number of people. For those who still control the dominant institutions of government and corporations, however, the final stage of "progress" has become quantified into a one-dimensional game of economic growth as measured numerically by GNP and GDP.
How else can we deal with this pervasive sense of _lack_ ? If we accept the Buddhist denial of a substantial self, we open up the possibility of a this-worldly transcendence of self, realizing the nondual interdependence of a no-longer-alienated subject with a no-longer-objectified world. Buddhist awakening occurs when I realize that I am not other than that world. One way to express this is that I am what the world is doing right here, right now. This is liberating because it frees me from the self-preoccupation of always trying to ground myself in constructed reality. If _I_ am not inside _my_ body, looking out at the world outside, then _I_ do not need to secure myself. Once _I_ have realized this by letting go of _my self_ there is nothing that needs to be made _real_.
So the final irony of my struggle to ground myself—to make myself feel real by filling up my sense of _lack_ —is that it cannot succeed because I am already grounded in the totality. It turns out that my lack is a _lack_ only as long as I dread it and attempt to fill it up. When I cease doing that, my lack transforms into the source of my creative energy, welling up from a fathomless source. Consumerism is so addictive because it seems to offer a this-worldly, commodified solution to what is basically a spiritual problem. Insofar as we are transformed spiritually, consumerism is revealed as a delusive way of thinking and acting that can never give us the secular salvation or happiness that it promises.
We cannot just ignore collective clock time as a social construction, but we do not need to be trapped within it. We become free of objectified, commodified time insofar as life becomes more playful. That is because play is what we are doing when we do not need to gain something _from_ a situation. When we do not devalue the here-and-now in order to efficiently extract something from it, then there will be the time—the being-time—to smell the roses as we do our work with pride and loving care, as happens at the end of _Momo_ :
People stood around chatting with the friendliness of those who take a genuine interest in their neighbors' welfare. Other people, on their way to work, had time to stop and admire the flowers in a window-box or feed the birds. Doctors, too, had time to devote themselves properly to their patients, and workers of all kinds did their jobs with pride and loving care, now that they were no longer expected to turn out as much work as possible in the shortest possible time. (235)
PART THREE
Buddhist Ethics of Consumption
13
Three Robes Is Enough
Ajahn Amaro
WHEN INDIVIDUALS ASK to take up the life of a Buddhist monastic, at the time of their ordination ceremony they make an agreement with their preceptor, the mentor responsible for their training. This elder says to the candidate: "Those who have gone forth from the household life should be prepared to robe themselves in scraps of thrown-away cloth, to eat whatever food is given to them as alms, to live at the root of a tree as their only shelter, and to use naturally occurring remedies as medicine for sickness. Do you agree to live by this standard for as long as you are a monastic?" The candidate answers: "Yes, I do."
Thus, at the very beginning of intensely focused spiritual training, one commits to train the heart to be content with the simplest standard of living. Of course, life often provides food, clothing, and shelter of a considerably higher standard and one can be very glad of that. Nonetheless, it is quite significant that this opening agreement explicitly links spiritual life and contentment with having little. In so doing, it demonstrates that contentment is a natural expression of spiritual practice.
Furthermore, this agreement is not just made once and then quietly shelved and forgotten. Monastics are encouraged to reflect daily on how they are relating to the use of their dwelling place, their clothing, food, and medical concerns. One is constantly refreshing one's attention to that domain: "What am I taking for granted?" "Do I feel hard done by if someone else gets the better food?" "Am I fussy about which dentist I see?" "Do I choose to wear patchy robes so that I can look more like a genuine ascetic than the others?" And so forth.
Each day Theravada monks in training recite these reflections:
Wisely reflecting, I use the robes: only to ward off cold, to ward off heat, to ward off the touch of flies, mosquitoes, wind, burning and creeping things, only for the sake of modesty.
Wisely reflecting, I use almsfood: not for distraction or for vanity . . . only for the maintenance and nourishment of this body, for keeping it healthy, for helping with the spiritual life; thinking thus, "I will allay hunger without overeating, so that I may continue to live blamelessly and at ease."
Wisely reflecting, I use the lodging: only to ward off cold, to ward off heat, to ward off the touch of flies, mosquitoes, wind, burning and creeping things, only to remove the danger from weather, and for living in seclusion.
Wisely reflecting, I use supports for the sick and medicinal requisites: only to ward off painful feelings that have arisen, for the maximum freedom from disease.
Buddhist monastics are also subject to limits placed on the quantity or quality of their material possessions. In the origin story for the first rule in the discipline that deals with relinquishing inappropriate possessions, the Buddha recounts how he was inspired to set such a limit:
As I was walking on the road from Rajagaha to Vesali, I saw many monks coming along buried in robe cloth—with great wads of extra cloth piled on their heads, on their backs and on their hips. Seeing them I thought, "All too soon these foolish men have come under the spell of over-indulgence with respect to robe cloth. What if I were to set a limit, lay down a restriction on how much in the way of robes a monk should have?"
Then traveling by stages I came to Vesali. There I stayed at the Gotamaka Temple. Now that time was the coldest part of the winter, and I sat outside wearing one robe and was not cold. Towards the end of the first watch I became cold so I put on a second robe and the cold feeling abated. Towards the end of the middle watch I became cold so I put on a third robe and the cold feeling abated. Towards the end of the final watch, as dawn arose putting joy on the face of the night, I became cold so I put on a fourth robe and the cold feeling abated.
I thought, "Those who have gone forth as monastics, even those delicately brought up who might be afraid of the cold, are certainly able to get by with this amount in the way of robes. Suppose I were to set a limit and were to allow just three robes." So, monks, I allow you three robes: a double-layered outer robe, a single-layer upper robe and a single-layer inner robe—thus four layers of cloth.
These basic standards of renunciation, simplicity, and frugality are contained within the code of conduct for all Buddhist monastics. In addition, the Buddha also allowed the possibility of refining this element of spiritual training even further for those who wished and for whom such greater austerities might be useful. This refinement is embodied in the thirteen _dhutanga_ , or optional ascetic practices that the Buddha considered appropriate for his students.
As most people are probably aware, India in the Buddha's time as now was replete with yogis engaging in all kinds of austerities: standing on one leg for forty years, eating only cow dung, letting the fingernails grow until they pierce the flesh . . . the list is gruesome and infinite. Having once been just such an ascetic, the Buddha criticized self-mortification as an end in itself. So when allowing his disciples to take up more austere practices, he was very specific as to what was suitable and what was not. The list of things he allowed included eating only once a day, not lying down to sleep, living only on the food offered on the morning almsround and refusing extra food from the monastery kitchen, living at the foot of a tree rather than in a hut. By this small sample it can be seen that these austerities were designed to challenge the instinctual urges in the realms of food, sleep, and shelter, but they were not physically damaging or repulsive by the standards of general society.
Perhaps the most significant attributes of these austere practices were the stipulations that the Buddha placed around their use. He said that there were five reasons why someone might engage in such forms of spiritual training: (1) in the belief that by experiencing pain and difficulty they are burning up bad karma; (2) in the belief that by experiencing pain and difficulty they are creating good karma; (3) because everyone else does them and one doesn't want to be seen as a weakling; (4) because people praise those who follow such practices and one wants the praise; (5) for the sake of simplicity of living. Of all these reasons, the Buddha said only the fifth was noble and worthy; the other four were based on superstition, wrong view, or foolishness.
SIMPLICITY, MODERATION, AND CONTENTMENT
Although these guidelines are mostly derived from monastic training and lifestyle, it has always been the case that the broader Buddhist community of lay practitioners has taken its lead from and followed the spirit of the example set by the monastics. "Austere practices" and "renunciation" might seem far removed from the lives of ordinary folk holding down jobs, raising children, engaged in the ten thousand dimensions of worldly responsibility, but they embody a spirit of contentment and voluntary simplicity that is of inestimable worth to all.
Two of the most well-known and oft-recited teachings of the Theravadan Buddhist scriptures extol the virtue of _santutthi_ or contentment. These verses, learned by every child in Southeast Asia from an early age, have guided the lives and cultures of Buddhist nations for centuries.
_Avoiding those of foolish ways;_
_Associating with the wise_
_And honoring those worthy of honor. ._ .
_Providing for mother and father's support_
_And cherishing spouse and child_
_And ways of work that harm no being . ._ .
_Respectfulness and of humble ways_ ,
_Contentment and gratitude: . ._ .
_These are the highest blessings_.
_This is what should be done_
_By one who is skilled in goodness_ ,
_And who knows the path of peace:_
_Let them be able and upright_ ,
_Straightforward and gentle in speech_.
_Humble and not conceited_ ,
_Contented and easily satisfied_ ,
_Unburdened with duties and frugal in their ways_.
_Peaceful and calm, and wise and skillful_ ,
_Not proud and demanding in nature_.
_Let them not do the slightest thing_
_That the wise would later reprove_.
_Wishing: In gladness and in safety_ ,
_May all beings be at ease!_
There is a gentleness of spirit that is carried by these words, an encouragement to live lightly and respectfully with all beings. Central to these qualities is the principle of the Middle Way. This is the way of balance: neither neglecting one's own needs nor overinflating them, taking into account the environment we live in and the needs of our fellow beings as much as our own immediate concerns.
Another Buddhist term that is used frequently in reference to this principle is _matannuta_ : moderation, or knowing the right amount. In his illuminating text _Buddhist Economics_ , the contemporary Thai philosopher and social commentator Ven. P. A. Payutto suggests:
Matannuta is the defining characteristic of Buddhist economics. Knowing moderation means knowing the optimum amount, how much is "just right." It is an awareness of that optimum point where the enhancement of true well-being coincides with the experience of satisfaction. The optimum point, or point of balance, is attained when we experience satisfaction at having answered the need for quality of life or well-being. Consumption, for example, which is attuned to the Middle Way, must be balanced to an amount appropriate to the attainment of wellbeing rather than to the satisfaction of desires. _Thus, in contrast to the classical economic equation of maximum consumption leading to maximum satisfaction, we have moderate, or wise consumption, leading to well-being_. [author's emphasis]
This principle of "knowing the right amount" may seem very simple, but as Ven. Payutto points out, it is very broad and deep in its application to our lives. It is as relevant to the marketplace and to the world of householders as it is in the lives of the monastic community. Our need as humans to give our hearts fully to the development of this quality was outlined by the Buddha in the _Ovada Patimokkha_. The Buddha gave this discourse shortly after his enlightenment, when the monastic community was growing and in need of some guidelines for the monks and nuns:
_Patient endurance is the supreme practice_
_for burning up unwholesome states . ._ .
_Restraining all harmful speech, hurting none_ ,
_Being self-possessed in the way of virtue_ ,
_Knowing the right amount in taking food_ ,
_Having a secluded place for sleeping and meditation_ ,
_Making efforts to practice with a pure heart:_
_These are the teachings of all the Buddhas_.
Perhaps the most significant aspect of this teaching was that every single person listening to this discourse was known by the Buddha to be already fully enlightened. That the Buddha felt it necessary to pass on this advice indicates the depth of the human habit of _not_ knowing that subtle, perfect balancing point. It is as if he were saying, "Just because you are fully enlightened doesn't preclude the possibility of over-or underestimating your needs, or overlooking what might be appropriate to time and place." If it is difficult for an arahat, a fully enlightened person, not to overeat occasionally, it should come as no surprise that we also miss the mark from time to time.
The qualities of moderation and contentment have recently come under challenge in Southeast Asia. In the late 1950s and 1960s, as Thailand launched itself into the international marketplace, the Thai government of the time made the extraordinary move of specifically requesting that the leading abbots and teachers of the Thai Buddhist community not encourage _santutthi_ and _matannuta_ in the population.
In their drive to encourage productivity and consumerism, the political powers regarded moderation and contentment as obstacles to their program. Sad to say, most of the monastic community acquiesced to this request, being culturally conditioned to not cause conflict and to maintain the status quo. However, one prominent teacher, Ajahn Buddhadasa, had no fear of those in power. Although he had official ranks and titles, he was not at all worried about losing them if he spoke up. He came right out and openly challenged the politicians, asking them if they felt they were wiser than the Buddha: "Surely the Buddha would never have extolled qualities so highly and universally regarded if they were something that could possibly be harmful?"
Ajahn Buddhadasa showed how greed, selfishness, and wastefulness were actually the more harmful qualities, and that a healthy economy would need to be based on wholesome rather than unwholesome principles. Buddhadasa drew on the early Buddhist scriptures, warning that if the government pursued its chosen policies, it was likely to do more harm than good in the long run. Needless to say, he was heavily criticized for getting involved with politics and rocking the boat, but it was hard for anyone to fault him on his scholarship, his reasoning, or his straightforwardness. His voice was heard, and eventually the government ban on contentment was lifted.
RENUNCIATION IN THE WORLD
Although many of the teachings quoted here come from the distant past, and even in their more recent translations still carry an aura of remoteness and antiquated religiosity, they nonetheless are talking about timeless qualities of the human heart. The greed, love, and wisdom of today are indistinguishable from those qualities as they occurred at the time of the Buddha. We might not habitually think in the language of "seeking sense pleasures" or "renunciation," but try substituting "material dependencies," "addictions," and "voluntary simplicity" and we suddenly find ourselves in familiar terrain.
Perhaps we can see that the spirit of renunciation and letting go of the compulsive pursuit of sense pleasure and material gain are indeed identical with today's aspirations to break free from the dictates of the consumer culture and the anxieties generated by advertising, peer pressure, and complacency. Thus these teachings can carry very useful messages for us here and now.
Raimundo Panikkar, in his book _Blessed Simplicity_ , stated: "Not everyone has the inclination to take up the vocation of monasticism, but all of us have some part of us which is a monk or a nun, and that should be cultivated." This "inner monastic" describes that dimension of our being that is already utterly free, independent, whole—that does not need anything to complete it or for anything to be subtracted from it—and that is full of a radiant love for all beings. The formal outer life of a monastic—peaceful, respectful, unselfish, humble, nonpersonal, nonsexual, nonviolent—is designed to resonate with and support the realization and fulfillment of inner wholeness and self-sufficiency. As Martin Heidegger wrote: "Renunciation doesn't take; renunciation gives; it gives the inexhaustible strength of simplicity." Likewise in the words of Simone Weil, the highly regarded Christian philosopher: "We only possess what we renounce; what we do not renounce escapes us. . . . In general we must not wish for the disappearance of any of our troubles, but instead for the grace to transform them."
Renunciation and contentment were widely extolled in the Buddha's teachings. He realized that even though the majority of his students had no desire to pursue a lifelong monastic vocation, nevertheless the regular employment of renunciate principles would certainly help everyone to overcome the burdens of fussiness and neediness that exhaust so much of our energy and financial resources. The Buddha upheld basic moral standards encapsulated in the Five Precepts. On the lunar quarters he instituted a "one-day-a-week ordination" for those who felt a particular commitment to his teaching and wanted to deepen their insight and broaden their freedom of heart. Observance of the following eight factors forms a foundation for the practice of renunciation, and thus the capacity to choose simplicity.
When the Uposatha observance is complete in eight factors, it is of great fruit and benefit, radiant and pervasive.
1. Here a noble disciple reflects thus: "As long as they live, the enlightened ones abandon the destruction of life and abstain from it; with club and weapon laid aside, they are conscientious and kindly, and dwell compassionate towards all living beings. Today I too, for this day and night, will do likewise. I will imitate the arahats in this respect, and the Uposatha observance will be fulfilled by me."
2. "As long as they live, the enlightened ones abandon the taking of what is not given and abstain from it; they accept only what is given, expect only what is given, and dwell with honest hearts devoid of the inclination towards theft. Today I too, for this day and night, will do likewise."
3. "As long as they live, the enlightened ones abandon sexual activity and live the celibate life, remote from sexuality, refraining from the practice of sexual intercourse. Today I too, for this day and night, will do likewise."
4. "As long as they live, the enlightened ones abandon false speech and abstain from it; they are speakers of truth, adherents to truth, trustworthy and reliable, no deceivers of the world. Today I too, for this day and night, will do likewise."
5. "As long as they live, the enlightened ones abandon wines, liquors and intoxicants, which are the basis of negligence, and abstain from them. Today I too, for this day and night, will do likewise."
6. "As long as they live, the enlightened ones eat only once a day and refrain from eating at night, from untimely meals. Today I too, for this day and night, will do likewise."
7. "As long as they live, the enlightened ones abstain from dancing, singing, musical performances and unsuitable shows, and from adorning themselves by wearing jewelry and applying scents and makeup. Today I too, for this day and night, will do likewise."
8. "As long as they live, the enlightened ones abandon the use of high and luxurious beds and seats and abstain from them; they make use of a low resting place, either a small bed or a straw mat. Today I too, for this day and night, will do likewise."
When, monks, the Uposatha observance is complete in these eight factors, it is of great fruit and benefit, radiant and pervasive.
To his aunt and stepmother, Mahapajapati Gotami (also the former queen of the Sakyan people), the Buddha gave specific advice shortly after her ordination as the very first of his female monastic disciples. He urged her to renounce things that "lead (1) to passion, not to dispassion; (2) to bondage, not to detachment; (3) to accumulation, not to diminution; (4) to having many wishes, not to having few wishes; (5) to discontent, not to contentment; (6) to gregariousness, not to seclusion; (7) to indolence, not to the arousing of energy; (8) to luxurious living, not to frugality." Of such elements arising from material comfort, status, and wealth one should see: "This is not the Dharma; this is not the Discipline; this is not the Buddha's Teaching."
Renouncing excess, appreciating what one has, monastics develop the capacity to render the heart supremely content with whatever the world has to offer.
GENEROSITY, WEALTH, AND FRUGALITY
As a counterpoint to his critiques of greed and materialism, the Buddha praised highly the qualities of unselfishness, generosity, and frugality. In a notable exposition on qualities conducive to harmonious communal living, he taught:
As long as you show lovingkindness to your fellows in the spiritual life, openly and in private, in acts of body, speech and mind; . . . share with your virtuous companions whatever you have received as a rightful gift, even down to the food you are eating; . . . you may be expected to prosper and not to decline.
Regarding the accumulation of capital, the Buddha did not praise or criticize wealth; he was much more concerned with people's actions. Ven. Payutto engaged the Buddha's ideas on wealth to support an alternative model of Buddhist economics.
According to the Buddhist teachings, wealth should be used for the purpose of helping others; it should support a life of good conduct and human development. According to this principle, when wealth arises for one person, the whole society benefits, and although it belongs to one person, it is just as if it belonged to the whole community. A wealthy person who uses wealth in this manner is likened to a fertile field in which rice grows abundantly for the benefit of all. Such people generate great benefit for all those around them. Without them the wealth they create would not come to be, and neither would the benefit resulting from it.
According to early texts, the Buddha taught that the householder who shares his or her wealth with others is following the path of the Noble Ones. "If you have little, give a little; if you have a middling amount, give a middling amount; if you have much, give much. It is not fitting not to give at all. Kosiya, I say to you, 'Share your wealth, use it. Tread the path of the Noble Ones. One who eats alone eats not happily.'" Some people make it a daily practice not to eat until they have given something to others. This practice was taken up by a reformed miser in the time of the Buddha, who said, "As long as I have not first given to others each day, I will not even drink water."
As Ven. Payutto points out, when the wealth of a virtuous person grows, other people stand to gain. But when the wealth of a mean person increases, it is at the expense of those around him. People who grow more and more wealthy while society degenerates and poverty spreads are using their assets wrongly. Here wealth is not fulfilling its true function. It is only a matter of time before something in the system breaks down. If people use wealth wrongly, it no longer benefits others and instead becomes a hindrance, destroying human dignity, welfare, and community. In short, Buddhist teachings stress that our relationship with wealth be guided by wisdom and understanding of its true value and limitations. It is important that we not be burdened or enslaved by wealth. Instead we should be masters of our wealth and use it to benefit others.
The Buddha outlined four kinds of wholesome happiness that come from wealth:
(1) The happiness of ownership—so that one can reflect: "This wealth has been rightly acquired through my own honest efforts"; (2) the happiness of enjoyment—so one can reflect: "I have derived benefit from this wealth and have been able to perform good works"; (3) the happiness of freedom from debt—so one can reflect: "I experience pleasure and happiness as I owe no debts, large or small, to anyone at all"; and (4) the happiness of blamelessness—so one can reflect: "My actions of body, speech and mind have all been innocent and blameless." The wise person, comparing the first three kinds of happiness with the last, sees that they are not worth a sixteenth part of the happiness that arises from blameless behavior.
In another teaching the Buddha listed the benefits of wealth as (1) the capacity to support one's family; (2) the capacity to support friends and peers; (3) the capacity to safeguard one's possessions from thieves, confiscation, fire or flood; (4 and 5) the capacity to support individual religious seekers.
As one might deduce from these teachings, the Buddha was critical of miserliness for being a waste of resources for the community, but also for the individuals who were making themselves miserable, when they could be bringing joy into their lives. There is an early story describing a rich old miser who had recently died, leaving no heir to his huge fortune. The king of Kosala pointed out that the old miser had lived on broken rice and vinegar and had worn the simplest clothing.
The Buddha remarked: "That is how it is, Your Majesty. The foolish man . . . supports neither himself nor his dependents. . . . He does not make offerings. . . . His wealth, accumulated but not used, disappears to no purpose. His wealth is like a forest pool, clear, cool and fresh, with good approaches and shady setting, in a forest of ogres. No one can drink, bathe in or make use of that water."
Even though the Buddha criticized miserliness, he praised highly its wholesome relative, frugality. Once again he considered the _attitude_ behind what we do to be vastly more important than precisely _what_ we do. One of the best illustrations of the skillful employment of frugality comes from an incident that occurred shortly after the Buddha's passing away. Ananda, formerly his attendant for twenty-five years, had gone to the city of Kosambi, arriving near the local king's pleasure garden. When the palace women saw Ananda, they went over to pay their respects and he heartened them with spiritual teachings. They were so inspired that they donated many lengths of cloth—enough for five hundred robes—to their beloved teacher. The king was indignant over the matter and went to see Ananda.
"But what can you, Honorable Ananda, do with so many robes?"
"I will share them with those monks whose robes are worn thin."
"But what will you do with those old robes that are worn thin?"
"We will make them into dust cloths, to line thatched roofs with."
"But what will you do with those dust cloths that are old?"
"We will make them into mattress coverings."
"But what will you do with those mattress coverings that are old?"
"We will make them into ground coverings."
"But what will you do with those ground coverings that are old?"
"We will make them into foot wipers."
"But what will you do with those foot wipers that are old?"
"We will make them into dusters."
"But what will you do with those dusters that are old?"
"Having torn them into shreds, Your Majesty, having kneaded them with mud, we will use them to patch any cracks there might be in the plastering."
Then King Udena thought: "These disciples of the Buddha use everything in a very proper, frugal way, they do not let things go to waste." And with that he bestowed yet another five hundred lengths of robe cloth on the Venerable Ananda.
So, in contradistinction to miserliness, even though one might not be endeavoring to be acquisitive, our skillful relationship with the material world can end up attracting more abundance to us, and the result can be joyfulness rather than misery.
APPLYING THE TEACHINGS TODAY
There are many ways in which the values outlined in all these teachings can be usefully applied to the lives of people today. The principles point to specific ways we can guide our actions and attitudes to lead to the welfare and happiness of ourselves and the world. As we engage issues of wealth, generosity, moderation, and simplicity in the contemporary context of consumerism, we can consider these basic ethical principles taught by the Buddha.
In a discourse given to a layman called Tiger Paw, the Buddha taught that there are four things that lead to the welfare and happiness of family people. First, whatever may be the means by which we earn our living—whether by farming, business, practicing therapy or teaching school, or by some other craft—we need to practice _persistent effort_ : to be skillful and diligent, investigating the appropriate means to succeed at our work. Second, we need to practice _protection_ , to guard the wealth acquired by our efforts and the strength of our faculties. This is taking proper care of righteous wealth righteously gained. It is wise to consider how we can invest or save our resources so that neither thieves nor the government can unjustly rob us, unloved heirs cannot make false claims, and the vagaries of the stock market cannot undercut our gains. Then we will be able to use our earnings to invest in wholesome alternatives to destructive materialism. Third, we should learn the value of _good friendship_ , associating with people who are of mature virtue, accomplished in faith, generosity, and wisdom. This will help stabilize our community and support the ongoing flow of resources. Fourth, it is wise to lead a _balanced life_ , neither extravagant nor miserly, so that our income exceeds our expenditures rather than the reverse. This means reducing debt and managing household and civic budgets wisely.
Further on in this discourse, the Buddha taught that there are four spiritual accomplishments that support a layperson's welfare and happiness. First, we should take up the cultivation of _faith_ , developing confidence in the worth of a spiritual practice. This means trusting in the merits of the teachings and practices that point beyond pursuing self-centered needs. Second, it is important to establish a standard of beautiful _conduct_ based on the Five Precepts. Such moral integrity is a great source of peace and happiness for us as individuals, as well as being a blessing and helpful example to those around us. Third, we should cultivate the practice of _generosity_. With a heart free of the stain of stinginess, one can be generous, openhanded, delighting in giving and sharing, bringing great joy to others. Fourth, we should make conscious efforts to calm the mind and develop _wisdom_ through meditation. The Buddha's understanding of "wisdom" meant seeing into the transiency of experience, the arising and passing away of all phenomena. This insight is noble and liberating and can lead to the cessation of suffering.
As we can see from the many scriptural selections in this essay, the Buddha did not shirk from the world of economics and the use of wealth. But he did drive a clear line down the Middle Way between need and greed. These discourses may seem only tangentially related to the themes of simplicity, consumerism, and greed, but they are nonetheless of deep significance. Such a pattern of living described by the Buddha is the result of the efforts of the person who has truly escaped the cycles of self-centered consumption and who has the genuine welfare of all at heart. Although the appropriate use of the material world can be a skillful means to a well-balanced life, _true_ happiness cannot come from any outside source but ultimately _only_ from within our own hearts. A simple and wholesome lifestyle is certainly conducive to personal happiness, but it needs to be always backed up by genuine attunement of our hearts to nature.
Perhaps this point is best illustrated by the verse that is traditionally recited after one renews one's commitment to the core practice of _sila_ , beautiful, wholesome conduct, as summarized in the Five Precepts. It speaks not just of the rules as outwardly observed but also (and more important) to those modes of conduct as simply the natural disposition of the pure heart.
_Sila, the pure heart, is the source of happiness_ ,
_sila is the source of true wealth_ ,
_sila is the cause of peacefulness—_
_therefore, let sila be perfected_.
For if our hearts are truly attuned to The Way Things Are, then from moment to moment we experience a deep contentment; there is nothing whatsoever that we are lacking.
14
Practicing Generosity in a Consumer World
Santikaro
Good is giving, dear sir!
Even when there's little, giving is good.
When done with faith too, giving is good;
The gift of the righteous gain is also good.
And further: Giving discriminately too is good.
— _Samyutta Nikaya_ , Sagathavagga, Devatasamyutta
THIS CABIN, this frozen river, this breathing in and out, this everchanging consciousness, and much, much more are the natural gifts reminding me of the sources of dana. Out this sunlit window, the Arrow River still flows under more than a foot of ice, joining the Pigeon, which forms the border between Ontario and Minnesota before emptying into Lake Superior. I hear the Arrow rushing as I walk upon it, following animal tracks and an otter's belly slide—what playful joy! Bundled up roly-poly against the cold, I run in sympathetic happiness through the cold biting air, kicking up puffs of snow with my clumsy boots. Winter stillness highlights coarse breathing. Stinging cold on the face deepens appreciation for the warm safety of clothes, cabin, and fire. Eyes feast on the stark beauty of crystalline snow, rusty lichens on cracked cliff rock, leafless birches and aspens, snow-catching firs, river grass adding mellow gold—nothing in me deserves this beauty and wonder, yet it is given, provided, shared.
The sun is a gift of warmth and light even as it sets. The snug cabin was built by nameless others, these days given for my use by Ven. Punnadhammo, the abbot. Paul the steward cooks daily meals and tends to other needs quietly, kindly. Propane gas, candles, and other goods are provided by the community's support network. Trees have given their wood that I may stay warm, even toasty, and survive the minus-fifteen-degree nights. I am clothed in the offerings of Thai, Chinese, Sri Lankan, and American donors. It is all gift. What isn't? Given by others, by nature, by Dhamma.
These gifts lift me out of my little habits and petty concerns, revealing how the gift of Dhamma is so much more than teachings, meditation advice, words. The gift of Dhamma is life, well-being, freedom, and more. It is everything because everything is Dhamma. And Dhamma is all gift, can only be given, never taken. Its nature is to share, recycle, circulate in a mandala of generosity rather than the _samsara-vattha_ of desire.
Dhamma, too, is the greatest gift of my life. May it be a gift for all of society as we struggle for meaning in a world of dollars, logos, oil, and military spectacle. The Dhamma of giving is a disinfectant, a gunk dissolver, an antidote for the monetary values, brand names, and "it's the economy, stupid" that clutch at our hearts and swirl in our brains and taint our blood. Reflecting on dana amid such troubling forces on one hand, and the wonders of Dhamma and nature on the other, I am challenged to increase my own giving and transform my life into something that can be a gift for others.
I write as an American monastic recently returned to Chicago (and now disrobed) after twenty years in Siam. I find myself grappling with the challenges of integrating my Thai experience with the complex American cultural mix of healthy (that is, democratic) and unhealthy (worship of profit) elements. For many years I was supported by poor Thai farm families, middle-class supporters of Suan Mokkh, and kind people in the cities I visited. Their generosity pervades Thai culture, yet often I failed to appreciate the power of the dana they modeled all around me. This essay is part of my own coming to terms with the deeper implications of dana that escaped me for too long.
That money has a big place in the American consciousness is beyond question. That money and wealth play a disruptive and corrupting role in religion is widely acknowledged. The growing accumulation of wealth by the plutocracy foretells increasing polarization and violence in an already violent society. Even middle-class Americans, rich by the standards of most of the world's people, spend much of their money on indulgences, entertainment, and addictions. Consequently, money and its uses, how we think about giving and receiving, how we define our roles as Buddhists within a consumer culture, and how Buddhist groups and centers fund themselves are among the most important moral and practical issues facing American Buddhism in the coming decades.
Dana (giving, generosity) plays a central role in these issues and thus deserves careful examination, especially today, when a capitalist distortion of dana may already be setting in. Here I will consider dana as a core Buddhist value and practice, and examine how it mitigates, redeems, and undermines consumerism. I will also consider how consumerism can undermine and corrupt dana. American Buddhists are keen to adapt Buddhism to their own culture. To the extent that U.S. culture is capitalist, consumerist, and forgetful of history—which I believe is largely the case—adapting Buddhism to U.S. culture will be fraught with peril. This danger may be unique in the history of Buddhism, unlike its earlier adaptations to animist, Brahman, Confucian, Taoist, and Bon cultures. The problem isn't so much adapting to Judeo-Christian culture as to the consumerism-capitalist culture that has apparently taken over the religious culture.
I suggest that dana—in all its wonderful, profound simplicity—is a necessary and significant part of what Dr. Buddha would prescribe for our times. It can be understood without hours of study. It liberates us from acquisitive and protectionist habits. It mitigates individualism and nourishes community. Its meaning spans the most basic levels of practice through to the ultimate. It challenges "me" and "mine," fostering letting go. A reinvigorated and updated understanding and practice of dana can serve as a powerful antidote to consumerism's ills. I see this as essential for Buddhism to stay on course as we navigate this bizarre postmodern world seeking genuine peace and liberation.
DANA IN BUDDHIST TEACHINGS
_Dana_ means "gift, offering, giving, generosity." Dana involves sharing the gifts, benefits, and resources that have come to us—material, intellectual, artistic, social, spiritual—with those worthy of them. Dana means giving things of value where they are needed and when they will be of benefit. Dana involves things worth giving; it is not merely the convenient sort of donation that gets rid of unwanted junk. Nor is it the proud charity superiors give to their supposed inferiors.
Recipients qualify as worthy in various ways. One is genuine need, such as experienced by victims of famine, war, and natural disasters. Orphans, the ill, the indigent, and the poor are also deserving of dana, for their needs are real. They deserve our help, not pity. A special case should be made also for inmates, addicts, and other social outcasts; their needs are profound in many ways. Those who live committed, unselfish lives based in Dhamma are also worthy of support, for example, a doctor serving the homeless or a serious Dhamma student. Most worthy are those who understand that everything is a gift to be passed on, who commit themselves to a renunciate style of life and strive to drop all self-centeredness. With nothing retained as "mine," they keep dana in active circulation and elevate or increase its value spiritually.
The Buddha's own story is marked throughout by generous giving and receiving. His great awakening depends on the dana of Sujata, a serving girl, and Sotthiya, a grass cutter. Her sweet milk-rice and his fresh-cut grass sheaves give the Buddha-about-to-be strength and comfort for the supreme final effort. To these are added gifts of nature—a cool river for washing away accumulated ascetic grime, a friendly forest in which to meditate, the shade of trees, and the copacetic sounds of birds. Finally, the Naga king provides his great hood for protection from weather and malevolent forces. Thus the Buddha's supreme human effort was not entirely individual; it was based on the collective circulating charity of many beings. In return, liberated from personal concerns, the Buddha gave his entire life in service of the Dhamma.
The teaching of dana continued through the sangha founded by the Buddha. Monks and nuns walked nobly out of forests and ashrams, along village paths and city streets, stopping at houses to beg silently. A village child, housewife, or old man offers a spoon of rice, a dollop of curry, or piece of fruit into the bowl of the begging monastic. Not merely a stereotype, the practice still survives today in Southeast Asia, helping to sustain Buddhism as a living reality. The early lay exemplars practiced dana along with meditation and discussion, completing the Four Assemblies of practice (bhikkhus, bhikkhunis, lay men and women) needed for Buddhism to be whole and sustainable.
The Buddha praised gifts given to communities of serious practitioners ( _sanghadana_ ) over gifts given to individuals, even the most exalted of all. Giving to the Thus-Gone-One who needs nothing was valued less than giving to those training in the way, their guides, and the community that keeps this noble way alive. Such dana keeps up the centers of tradition, learning, and cultivation that support all who follow the way, whether home leavers or householders. As individuals, only buddhas can fulfill the highest ideal of practice; with noble community, even struggling members are uplifted so that they can contribute too.
_This is the Sangha of upright conduct_
_endowed with wisdom and virtue_.
_For those people who bestow alms_ ,
_for living beings in quest of merit_ ,
_performing merit of the mundane type_ ,
_a gift to the Sangha bears great fruit_.
Dana is described as the first of three bases of good, meritorious activity ( _punnakiriyavatthu_ ). Besides dana, the other two are ethics and virtue ( _sila_ ) and cultivation ( _bhavana_ ). These nonmeditation aspects are believed more accessible and suitable for householders. The practical effect of this is that dana is seen as a householder practice, while study, practice, and meditation, as well as keeping a more refined ethical discipline, are the realm of monastics. Nonetheless, the three bases of good action apply equally to monastics living with middle-class consumer trappings where meditation is an optional, frequently nonexistent, part of their lives. For today's monastics with more material resources than society's poor, the practice of dana is an act of honesty, humility, and necessity.
Dana is also found among the _parami_ , perfections ( _paramitas_ ). Giving is listed first among the virtues for crossing over, both among the ten parami of Theravada and the six of Mahayana. A remarkable passage in the Venerable Buddhaghosa's _Visuddhimagga_ , a Theravada classic, presages the Mahayana in its explanation of the perfections:
For the Great Beings' minds retain their balance by giving preference to beings' welfare, by dislike of beings' suffering, by desire for the various successes achieved by beings to last, and by impartiality towards all beings. [In other words, the four brahmaviharas, or divine abidings.] And to all beings they give gifts, which are a source of pleasure, without discriminating thus: "It must be given to this one; it must not be given to this one." And to avoid doing harm to beings they undertake the precepts of virtue. . . . Through equanimity they expect no reward. Having thus fulfilled the Perfections, these then perfect all the good states . . . and the Eighteen States of the Awakened One. This is how they bring to perfection all the good states beginning with giving.
The final parami perfected is also the first—dana. What is often portrayed as the most basic virtue also turns out to be the culmination, the last fulfilled before the bodhisattva is ready for a final birth. I take this to show that the spirit of dana runs throughout and perfects all the parami. For the bodhisattva, there is no tolerance, wisdom, and compassion without wholehearted unlimited giving. One must give completely of oneself for compassion and the other perfections to be realized.
DANA AS ANTITHESIS AND ANTIDOTE TO CONSUMERISM
Consumerism is the current dominant form of capitalism, a system that biases capital over labor and money values over other values. Thus it biases the things that make money over things that make meaning, happiness, wisdom, compassion, and other virtues. In our world, consumerism is more than an economic system, more than political economy. It increasingly functions as substitute religion, debased, shallow, and unable to liberate. As the dominant value system, way of thinking, and way of life, consumerism has a powerful influence even on those of us who struggle against its seductive tentacles. Many Western Buddhists disdain the retention of "Asian cultural baggage" but may be unconscious of the consumerist baggage of their own cultures.
Though I view consumerism as a generally harmful ideology, I do not intend to demonize commodities, trade, and markets, as they are necessary parts of any economy. Yet this form of capitalism takes many things (such as acquisitiveness, individualism, frivolity, and waste) to extremes. The purpose of this discussion is to restore healthy values to the systems of trade and finance, that is, to find and recover healthy boundaries between commodities, private property, market value, and money on one hand, and voluntary gifts, circulating communal property, cultural value, and virtue on the other.
In such a context, how can dana retain its proper meaning and place? How is dana central among wise responses to consumerism that foster Dhamma understanding and practice both individually and communally? Further, let's turn this antagonism around. Vice cannot flourish where virtue is strong. By reinvigorating and strengthening the practice of dana, consumerism can be neutralized. We can identify a number of ways that consumerism has an impact on us that also concern how we understand and practice dana. Here I will discuss three: the impact on social values, on community, and on monasticism. Concurrently, I will suggest some ways the practice of dana can counteract consumerism's influence.
Dana as Primary Value
How, then, is the virtue and practice of dana confused and corrupted by consumerism?
_The meaning of my life_
_buying and owning things_
_then throwing them away_.
I use this sort-of haiku as a working summary of consumerism. In it, money and market value are the measure of everything. Meaning and value are derived and abstracted from things that can be bought, that is, commodities. Once abstracted, such value can be distorted, exaggerated, and concocted through advertising. With most media and much education performing this function, we end up in the consumerist society of today. In this particular construction of values, our lives center on what we own, rather than what we are, our character and virtue. Everything becomes commodity, even family and love are mediated by market mechanisms. But how can the market value suffering, compassion, good health, community, loneliness, a peaceful heart, spiritual insight, and liberation?
Generosity is expressed under the influence of other cultural and religious values. Unhealthy value systems obstruct, distort, or pervert it. Consumerism, for example, turns upside down the ethos of a dana-honoring culture. Wherever consumerism is strong, its values dominate and can even colonize religious values. Values of profit, individual pleasure, and egocentric freedom push aside socially cohesive values such as dana. For example, many of the problems in modern Thai Buddhism can be understood by analyzing how consumerist values have been insinuated into customs and practices that were previously Buddhist.
As increasing areas of life are mediated by price-tagged goods and services, the sphere of voluntary giving shrinks. Despite the mantra of "free trade," price tags limit freedom and gratitude. They value things according to one narrow set of criteria and ignore others. Exchanges within the domain of markets are dominated by those with capital and come with the legal backing of contracts, courts, and lawsuits, none of which inspire gratitude. Gratitude, a voluntary response of heart and action that occurs naturally toward generosity, is rare in trades and deals. When economic benefit becomes the primary "good," generosity is marginalized.
In consumerism, economic or trade value is hegemonic. Values constructed out of aesthetic appreciation, love of nature, friendship, solidarity, and spiritual practice are secondary, if not marginal, for these are precisely what the logic of consumerism undermines. Appreciation of and gratitude for these values cannot arise when we are focused on getting the next thing. When we lose track of giving, even Dhamma can come with a price tag, whether for retreats asking hefty fees or for Dhamma books that spin profits for truth-constraining megamedia corporations. Buddhism becomes a growth business and fundraising becomes a major focus of group energies.
True dana is given and received freely as favor, out of kindness. Societies in which generosity is operative, gracious, and strong are motivated by a web of healthy, mutually supportive values. Dana makes an excellent indicator of social health and cohesion. Are we generous in the care and resources we give our children, elderly, poor, and each other? Are we generous with those who appear different because of race, class, religion, or ethnicity? The practice of dana is a direct antidote to the calculations of the market that permeate consumerist lifestyles. Rather than figuring what we can get from an exchange, we focus on what others need and what we can give. When both recipient and giver value the gift in terms of friendship, shared meaning, and Dhamma, we step outside the market's confines. That wins some space for other values to take hold as well.
As we practice valuing things (material and immaterial) without the price tags, we are more able to discern what is truly Dhamma and what is not. We may even learn that the old cliché is true: the best things in life are free. When we donate at a teaching, it helps us listen better, reflect more freely, and feel happy by helping. The donation doesn't earn us anything; it begins the necessary shift from self-centeredness to unselfishness that Dhamma requires. We still must investigate and practice within ourselves, but this can now be less weighed down by calculation.
We moderns tend to mistake complexity for sophistication and intelligence, forgetting the origins of the word _simple_. Dana is simple both in terms of being comprehended easily (children understand it without any trouble) and in its coherence. It need not be complicated; it can unify rather than fragment. Something so simple as generosity allows all to participate regardless of degrees, professional credentials, class, and wealth. Thus it supports democracy and promotes equality. When we put generosity at the center of our lives, we are much more immune to the tricks of consumerism. Dana's simple pleasure reminds us that technoflashiness and endless pseudovariety are fleeting, confusing, and tiring. Giving frees us from seeking, obtaining, owning, protecting, ensuring, and from the violence these activities can foster, allowing space for appreciation and gratitude. We find more lasting value and happiness in kindness, sharing, and understanding.
Perhaps we in the West have a special service to offer the buddhadhamma in these times. In America, Europe, Japan, and the other bastions of pervasive consumerism, we have more experience with modernity than those in emerging markets. We have been swimming in increasing complexity, commodification, and individualism for some time. On one hand, we may be more submerged in the fragmentation and dishonesty needed to sustain the illusion that consumer products bring happiness and meaning. On the other hand, these very dilemmas may situate us better to understand and mitigate them. Since dana and consumerism represent opposite values, we postmoderns will have a hard time with the simplicity of giving if we insist on hi-tech, fragmented complexity. Conversely, we can enjoy the benefits of dana if we simply relax the grip of buying, consuming, and owning. How we work our way through these challenges will profoundly influence the future of Buddhism in the West as well as in the Asian source countries that are bombarded with our consumerist culture whether they like it or not.
Dana for the Sake of Community
As understood in early Buddhist cultures, community naturally involved layers of dana. However, consumerism and other modern forces have made the old approach to community precarious. The Thai experience illustrates this well. Recovering sangha is one way that people have found to create nonconsumerist breathing space.
Traditional Buddhism in Thailand and elsewhere has had an agrarian village base. There, doing good or "making _boon_ " (from _punna_ , goodness) has been the central community value. Back when the lines between family, economics, community, politics, and religion were tenuous, _boon_ circulated as the main currency within the religious economy of Thai life. The most prominent practice of "doing good" consisted of giving food to the monks and making other donations to the wat (temple). Before capitalism took over, such dana was almost always in kind, there not being much actual cash in village economies. Dana supplied the material goods needed by the monks personally and for the daily running of the temple. Villagers gave what they had to give and considered "good" or worthy of giving: their best food, cloth, tools, labor, craft skills, and knowledge. As the wat served as community center, clinic, counseling center, news exchange, entertainment stage, and market, in addition to its religious and spiritual functions, support for the wat meant support for the entire community. In fact, until modernization, wats were communal property more than monastic property, sustained by generosity.
For their part, the monks were expected to live simply and unselfishly, to look after the wat and guard traditions. When somebody wanted to talk about a problem or the weather, the monks would listen. When someone needed a ritual, blessing, or chant, the monks would go. They were available 24-7, as we now say, as country doctors used to be in the United States. Actually, many of the monks _were_ country doctors. Being available and helpful was central to the life of village monks, including the itinerant meditators who would come and go. Most important, the participation of monks gave religious meaning to daily acts of generosity and kindness, elevating these from the realm of mutual obligations to spiritual significance.
_Boon_ circulated within fairly large loops connecting infants with grandparents, rich and poor, women and men, temple dwellers, ancestors, spirits, even honored water buffalo. The giving was seldom binary and tended to circulate widely as the blood of the community so long as its members understood goodness mutually. The money economy gradually changed most of that as capitalism shifted the operative principle away from goodness and onto money, from boon to baht (the Thai currency). Increasingly, donors gave baht, or food purchased with baht, rather than preparing food and other offerings themselves. Village skills and handicrafts suffered, partly because they were not volunteered and learned at the wat. Time spent in the fields working for cash crops increased, economic migration increased, and children saw less of their parents. Communal work and shared labor disappeared; even the wats had to start paying for labor. Things that did not earn money were devalued. Eventually Buddhism was expected to aid economic survival, magically if not concretely.
In many Thai towns today, monks queue up at dawn markets before stalls at which entrepreneurs sell ready-made food offerings. Donors queue up on the other side, pay their baht, pick up a tray, and turn to put the food in the bowls of waiting monks or buckets carried by temple boys. Then donors and donees go on their way. All very efficient, in the wonderful way of consumer capitalism, with donors putting less time and care into their offering and monks appreciating them less.
Rather than food offered as _boon_ in promise of better karmic fruits, baht is given in hope of more baht—successful business ventures, passing exams for career advancement, winning the lottery. The monks, too, are more money minded. Monastic titles and positions are linked to funds raised and spent on temple buildings. Stories are told of people getting rich after donating to a certain monk (for example, Luang Por Khoon) or wat (for example, the infamous Wat Phra Thammakai). Temple services such as the large funeral industry are treated as investments by temple committees, complete with outsourcing of flowers, coffins, and catering. City monks indirectly probe how much dana will be given before deciding which meal invitations to accept. Monks travel, study, and live in the same consumer economy as everyone else. As nothing is free anymore, they also need money. And they struggle, too, with the temptations of consumerism.
For Buddhists who see community as refuge and a priceless gem, anything that saps the lifeblood of community is threatening. The logic of consumerism includes increasing consumer "goods," maximizing market share, and eliminating inefficiencies. More consumers means more sales. Thus, sharing is out, individualism is in. Communal property is out, private property is in. Consumerism undercuts community by encouraging personal consumption patterns: focusing on what "I" want, how "I" want to look and feel. It's all about "me" and not much about "us." The word _community_ is now used loosely, often without any connection to shared physical place or face-to-face relationships.
Rejuvenating true dana means engaging in aspects of practice that take place off-cushion. Practicing dana within community can take many forms: bringing food to share with each other and the needy, offering skills and labor to community tasks, caring for teachers and guests, visiting the sick, helping with child rearing and elder care, mending cushions, endowing retreat scholarships, contributing to schools, attending peace rallies, building civil society—the possibilities are numberless. When Buddhist teachers and leaders depend on offerings and gifts, they accept a role that is more than professional. By connecting with students in this way, they promote the practice of generosity and gratitude, their own openness facilitating the sharing of dhamma.
Each time a gift is given, the nurturing bonds of community strengthen as gratitude for each other and the group deepens. The activity of physically handing something to another puts us in direct contact and relationship. Communal property balances private property and vibrant commons—parks, libraries, places of worship—which provide the space to do things together, gratis. When community is anchored in solid meditation practice and supported by such giving, emotional and relational needs can be taken care of more openly. For example, we notice somebody has missed a regular sitting a few times. We call up and find there's been a death in her family. Word is passed and offers appear to babysit, cook meals, and drive kids to school. Most of all, the expressions of friendship make a difficult time easier. The external support provides time for the bereaved member to meditate, which can help her accept her feelings of loss. The unhealthy need for "consumer therapies" such as eating, drinking, and shopping are mitigated by such sangha support.
Among the Six Dhammas for Harmonious Living Together, sharing resources has a central place. Sharing is an antidote to individualism and thus to consumer ego building. Gifts are the tangible signs of friendships that weave us into larger wholes. Unlike cash and plastic, direct dana makes us more concretely and consciously interdependent with others, which generally makes us more open to them. Circulating gifts keep this alive, which in turn nurtures all of us. The basic goodness of our giving nurtures us, as does the refuge of community.
Dana and Monasticism
Buddhism began as a mendicant movement, and monastic training has provided most of its teaching, scholarship, and leadership. In Asia, monasticism is now in a period of decline, owing to its own inability to adapt to rapid social change and because so much of the change is inimical to it. In the West, whose own monastic tradition was marginalized with the onset of modernity, various forces exclude monasticism. Consumerism is one of these. As a committed monastic myself for many years, I hope for Buddhist monasticism to find its proper role in modernity and expect that role to be a vital part of modern Buddhism's capacity to avoid the seductions of consumerism. This role will require monastics to adapt to modernity but not surrender to it, and to share leadership equally with other sincere practitioners.
Buddhist monasticism, as I understand it, is a lifestyle choice that gives primacy to dhamma study, practice, and service. Along with spiritual practice, monastic life recasts and purifies the ordinary work we perform each day through daily training based in simplicity, renunciation, and generosity. Buddhadasa Bhikkhu, with whom I lived for almost a decade, integrated the so-called spiritual and worldly by teaching that work is dhamma practice and dhamma practice is work. Dhamma practice is the inner spiritual work that transforms our lives, which is then integrated with the ordinary duties of daily life. While monastics are traditional exemplars of this, the principle applies to all Buddhists.
Work is Dhamma practice when we work for the sake of the work, out of compassion, to lessen our own selfishness. We lose the capacity for such spiritual work—work as service and letting go—when we debase its meaning to something done primarily in exchange for money to buy and consume. Professionalizing livelihood into careers further isolates vocation from other dimensions of life. The more we define ourselves through careers and material goods, the more we become _Homo consumerus_ without a clue how to live an integrated, spiritually grounded life. Such trends buffet everyone under consumerism, monastics included.
Nuns and monks, as human beings living in the same world as everyone else, are susceptible to modern temptations. As they conform to the cultural imperatives of consumerism, monasticism and teaching as vocations (in the old sense of the special lifework to which we are summoned) become professions (in the modern sense of occupations through which one earns a living). Consequently, they grow concerned with incomes and budgets, thinking certain bottom lines are needed to survive. When monastics succumb to pressures to build big, beautiful monasteries and centers, with all the modern amenities, their focus wanders from Dhamma. The spirit of dana leaks out and money-mindedness creeps in.
With shifting values, monastics and other spiritually committed people come to see themselves as needing to be relevant and productive. What do they have to offer people, they wonder? Are they "marketable?" As such thinking takes hold, the subtle qualities of Dhamma escape the productivity radar. Production compulsion pressures them to give up the old, simple, renunciate ways. No longer supported just because they live a noble life, they must now earn their keep, which is judged more by market standards than dhammic ones. If both monastics and the laity are colonized by consumerism, how can Buddhism flourish?
The monastic life as calling, not career, is a lifestyle honorable in itself, challenging us all to a way of life that supports dhamma practice more fully and deeply. Renouncing the means to generate income, monastics need dana to survive. Simple and upright, with clear basic needs, monasticism inspires support. Simultaneously, it is a vehicle for giving on successively more noble levels, thus embodying dana. The monastic way expresses life as gift both in receiving and offering. As a bonus, this lifestyle also produces art, architecture, poetry, historical records, social services, and community cohesion, all of which are free-flowing antidotes to consumerism.
As a further bonus, this lifestyle naturally produces teachers and teaching capable of questioning consumerism. Though most monastics need not be teachers, teachers arise as long as the integrity of the lifestyle is maintained. In India and traditional Buddhist cultures, householders have supported monasticism because they saw it as beneficial to themselves, their families, and society. As laity shared the fruits of their material production, monastics reciprocated with instruction. By facilitating householder participation in dhamma-centered life, monastics were known as a "field of goodness" ( _punnakheta_ ). When monastics give openly, they are like bees collecting pollen from flowers and producing honey. The rice of householders is then converted into _punna_ and dhamma. This is truly Dhammadana when monetary and economic considerations are absent.
With monasticism under assault by consumerism, the task today is to rejuvenate what remains of healthy monastic-lay relationships in Asia and adapt these creatively to modern realities. In the West we are growing Buddhist monasticism from scratch and must do so against the consumerist flow. As a former bhikkhu, I wonder how I can remain true to the alms mendicant lifestyle when there is little chance of collecting enough to eat through traditional methods (not to mention frostbite in winter). There seems to be little social space for noble begging and not much "windfall" to be gleaned when all lands have owners. If we keep to the traditional praxis of not accepting and using money, whatever the form, we must find lay people to provide everything we need. Or should we avoid troubling lay supporters by accepting the conveniences of credit cards and Internet shopping? The appearance of personal self-sufficiency facilitated by consumerism (within the limits of credit lines) comes at the cost of greatly reduced flow of dana, without which Buddhist monasticism cannot survive.
PRACTICING GENEROSITY
While consumerism preys on the alienated ego of modernity, generosity offers a way of loosening the grip of egoism on the heart. By practicing dana genuinely, we undermine the psychological structure of consumerism as we liberate ourselves from its selfishness. We will always be consumers, eaters, materially auto-producing "selves"; consumption is how biological life is recycled and therefore is not an evil in itself. Rather, it is the ideology of consumerism that is destructive because it destroys gift, generosity, decency, life, dhamma. In the Buddha's time, this would have been considered a form of _miccha-ditthi_ (wrong understanding). Buddhist practice requires integrating our physical needs and realities within a larger spiritual view that sees beyond ordinary ego needs, let alone the pettiness of consumerism. Honoring and practicing generosity can help us recover and stick to that way of wisdom, compassion, and liberation.
As I finish this piece, I'm halfway around the planet in Siam while the hot season awaits the collecting of the monsoons. Rains aren't daily yet, but enough have already come to scare away fears of El Niño dryness. The air is warm, thick, pungent here. The vegetation is lush, vibrant, full. Brilliant yellow butterflies flutter through the treetops in front of me. Below, the brown, turbid Pasak River winds around this cozy retreat past craggy limestone hills. The mango trees planted along the roads and pathways have dropped fruits too numerous for workers to harvest and guests to eat. Friends, colleagues, and students here also give kindness, food, support, and companionship in the study of life and Dhamma. Once again I am blessed by abundant natural and human generosity. Here the same sense of life, beauty, and gift flows through me and fills the heart just as a few months ago in Canada. Different seasons, different continents, different latitudes, yet life, nature, and Dhamma are everywhere. The Gift is beyond me as it embraces me. I surrender once more to all these gifts and great joy. May such surrender become as natural as breathing in and out.
15
Wash Your Bowls
Norman Fischer
THERE'S AN OLD ZEN STORY that I like very much. A monk comes to the monastery of the acclaimed Master Zhaozho. Diligent and serious, he asks for instruction, hoping for some esoteric teaching, some deep Buddhist wisdom, or, at the very least, a colorful response that will spur him on in his practice. Instead, the master asks him, "Have you had your breakfast yet?" The monk says that he has. "Then wash your bowls," the master replies, the only instruction he is willing to offer.
Although this story might seem merely to illustrate the gruff, odd, and cryptic style of the Zen master, it actually makes a fundamental point. Zhaozho wants to bring the monk down to the immediate present of his training. "Don't look for some profound Zen instructions here. That's too heady and abstract. Open your eyes!" he seems to be indicating. "Just be present with the actual stuff of your ordinary everyday life—in this case, bowls." A commentary to the story, as it appears in one of the koan collections, says, "When food comes, you open your mouth; when sleep comes, you close your eyes. As you wash your face you find your nose; when you take off your shoes, you feel your feet." Another commentary simply says, "It is so clear it is hard to see."
I have always appreciated the Zen emphasis on the material, practical aspects of our lives. Like the monk in the story, I came to San Francisco Zen Center years ago with huge metaphysical concerns. A student of literature, philosophy, and religion, and a product of the sixties drug and anti-Vietnam War culture, I was full of questions about what was real, what was right, what was enlightenment, what was consciousness. The world that I had inherited from my parents, in which so much was taken for granted, seemed no longer tenable. Everything was up for grabs; reality, apparently, needed to be reconstructed. I came to Zen Center propelled by this spirit, and I was willing to go to almost any length to meditate, read texts, practice austerities, listen to lectures—anything to answer my all-consuming questions.
But my questions weren't answered at all. They seemed to have very little to do with the Zen enterprise as it was presented to me. Instead of study and discussion (the only modes of truth discovery I knew at the time), I was taught how to mop the floor, wash the dishes, and tend the garden. Actually it was very good training for me. It was exactly what I needed. And out of the grounding that this training gave me, my metaphysical concerns began to be slowly and soulfully settled. As it turned out, the answers I was looking for were not propositional. Nor were they to be found in spiritual experiences, enlightenment flashes, or meditative states—although there were enough of these over the years to keep me going. Little by little, through tending to the daily life of the temple in the context of regular, disciplined meditation practice and just enough Buddhist instruction, I began to live my answers instead of talk them, to breathe and feel them bodily instead of intellectually.
Sometimes the Buddhist instruction I received had to do with the religious teachings of the tradition. I did hear a certain amount about impermanence, about emptiness, about nirvana. But more often I heard about being present, simply being present with body and mind fully engaged. Once, in the middle of a long silent retreat, I remember hearing my teacher begin speaking during a meal in a grave tone, as if he were about to explain the secrets of the universe. "When you eat the three-bowl meal during retreat," he intoned, "you should eat out of the first bowl first, and then eat some food from the second bowl, and then the third bowl, and then go back to the first bowl. This is the best way to eat."
This kind of instruction, this style of training, is quite in line with the classical Zen approach. Master Zhaozho was not unique. Over and over again throughout Zen literature you read of students approaching their masters with many complicated matters, only to be brought back down to earth directly. "What is Buddha?" a student asks. "The cypress tree in the courtyard!" the master replies. "What is the Way?" "A seven-pound shirt!" Like the teachers of old who saw that their students' existential concerns could best be met here on earth rather than high up in the clouds, my teachers grounded me and helped me keep my balance. "It's right here—in front of your nose, "they told me over and over again.
The word _zen_ means meditation, and meditation is certainly the most well-known of all Zen practices. But the meditation practice this tradition emphasizes is not exactly spiritual contemplation. In the Soto Zen that I practice, meditation is called _shikantaza_ , which means "just sitting." Soto Zen teachers continually stress the actual mechanics of sitting as sitting. When you receive meditation instruction, you are not given lofty objectives, mantras, or deep koans to meditate on. Instead the instructor will talk to you about many details of physical posture: the alignment of your ears and shoulders, the correct position of your hands and arms, the placement of hips and knees, and how to pay attention to your breathing. The instruction will be so physical, so concrete and specific, that you might well wonder when the "Zen" part begins. But this _is_ the Zen part: the meditation practice is in fact quite physical. To pay attention intensely to the body in all its details, to be present with the body in its physical immediacy— _this_ is the practice, and the depth of the practice derives from this.
In Soto Zen monasticism the emphasis on the physical as the fountainhead of the spiritual extends through and past the body to all aspects of monastic life. "Careful attention to detail," is the motto of the school. As Zhaozho instructs, monks are to be quite present with and careful of their bowls, their robes, their shoes. The temple work is considered not a necessary and unfortunate series of chores but rather an opportunity to realize the deepest truths of the tradition. Zen monastics take on the daily job of cleaning the temple inside and out, rushing up and down to wet-wipe the wood of the pillars and floors, raking leaves, cutting wood, drawing water. All these immediate physical tasks are seen as essential spiritual practices. The monks are continually taught that none of these physical maintenance jobs differ in any way from sutra chanting, text contemplation, or meditation itself. All is physical, all is immediate, all is the stuff of enlightenment. Meaning comes not so much from what you understand as simply through the way you do whatever it is you are doing.
Following a key text by Japanese Soto founder Dogen Kigen, called "Instructions to the Head Cook," Soto Zen temples, both in America and Japan, are especially devoted to kitchen work. Monks carefully wash, chop, and combine ingredients, clean pots and pans, mop floors, serve meals with dignity and beauty. Workers in Zen kitchens are instructed to approach their tasks, however menial or repetitive, with full religious attention, giving themselves fully to what they are doing. In Zen centers, "kitchen practice" is a revered undertaking with detailed procedures for the mindful care of food and tools. In our center, for instance, there is a "knife practice": knives are always washed immediately after use rather than being placed in a sink for washing later on (someone might be cut). There is also a "counter-cleaning practice" (wiping down with vinegar at the end of each work period), a "cutting-board practice" (different boards carefully stacked in different locations for fruit, onions, and other foods), and a "chopping practice" (specific ways of holding the knife and the food to be cut for various styles of chop). All of these teach the practitioner that the manner in which something is accomplished, its proper "dharma," as well as the way in which the cleaning up is done, is just as much a part of the work practice (if not much more!) as the result.
Careful attention to detail is not confined to kitchen work. The daily schedule usually calls for a period of mindful silent cleaning immediately following meditation. Even the maintenance shop has a Buddhist altar in it. Tools are to be handled with respect and put away in their proper places, not _after_ work is done but as an integral part of the work. Monks and laypeople ordained in the tradition sew their own Buddhist robes and are enjoined to care for them as sacred vestments. Bowls used for eating in the meditation hall are to be handled "as if they were Buddha's own head." Being present with and respectful of all material things, as if each and every one of them were a sacred object, is a primary practice and a primary value. The head monk in a monastic training period not only gives lectures and meets privately with students; he or she is also in charge of taking out the garbage and cleaning toilets. These traditional assignments are seen as holy tasks to be undertaken with full respect and honor (remembering an old koan: "What is Buddha?" "A shitstick!"). For students in training, the sight of the head monk diligently carrying garbage pails or wielding a toilet brush with full attention is as much a part of his or her teaching as the words uttered in the dharma hall.
In training period, too, Zhaozho's words about bowls are taken quite literally in the practice of _oryoki_ (formal Zen eating practice). Monastics take all of their meals with full formality in the meditation hall, eating out of a set of three bowls, which are wrapped ceremonially in a set of cloths, often hand sewn by the practitioner. The choreography of managing the cloths, laying out the chopsticks and spoons, receiving the formally served food, chanting, eating, and, yes, washing out the bowls with the hot water offered with bows and tender care is truly prodigious. It takes years to master and feel comfortable with the practice, but when you do, you find the movements enjoyable and beautiful. What at one point seemed fussy, complicated, and arbitrary, now having fully entered into the fingers and palms of the hands seems simply lovely in its quiet grace. Like playing the piano, which requires much clumsy exercise before fluency is achieved, the physical acuity of simply eating a meal is transformed through oryoki into a profound religious act. Such a practice of quiet physical carefulness—to the point where it becomes deep almost beyond speaking of it—has been extended from Zen into Japanese culture. Here the acts of making and drinking a cup of tea, arranging flowers, or writing a simple phrase with a brush on a piece of paper have become high forms of religious art.
Far from offering a path to transcend the material world, then, the process of Zen practice deepens and opens the material world, revealing its inner richness. This is accomplished not by making the physical world symbolic or filling it up with explanations or complications but simply by entering the physical world wholeheartedly, on its own terms. When you do that, you see that the material world is not just the material world, something flat and dumb, as we might have thought. The way we have always, unimaginatively, understood the material world to be is not in fact what it is. As the Zen masters show us, the material world is not superficial or mundane. What is superficial and mundane is our habitual view of the material world, which we have so long insisted on reducing to a single dimension. Dissatisfied with that, we look elsewhere for some relief, some depth. Zen master Yanguan knew this and tried to illustrate it for his attendant. "Bring me my rhinoceros fan," he said one day. "The fan is broken," the attendant said. "Then bring me the rhinoceros," Yanguan said.
To see the material world as it really is is to recognize its nondifference from the highest spiritual reality. For where is spiritual reality if it isn't right here in the middle of our lives in the material realm, bleeding through space and time at every point? Zen training is the effort to learn to enter the material world at such a depth and to appreciate it. As the story of Zhaozho indicates, the way to see the material world as it really is in its fullness is to be present with it and to take care of it. Thus, "Wash your bowls!"
All this is to say that Zen is quite a materialistic tradition. Far from proposing a spiritual alternative to materialistic life, Zen affirms the materialistic realm as nondifferent from the spiritual. In other words, Zen spirituality is not achieved through avoiding, bypassing, or transcending the material realm: it is achieved by entering the material realm in a mindful and thoroughgoing way.
Once many years ago, not long after I was ordained as a Zen priest, I visited my cousin in Miami. An oral surgeon, good at what he does and consequently rather wealthy, my cousin is quite enamored with cars. When he takes a fancy to a particular kind of car (once it was a Mercedes Benz sports convertible, later a Ford Bronco), he buys several versions of it, so that he typically has a small fleet of cars, all the same model, in different colors and with slightly different features. On this particular visit, he was quite taken with the Chevrolet Corvette. Quite tentatively he asked me whether I'd like to have a ride in one, and I said sure. He rolled the convertible top down, and we went out onto the highway, speeding along at a good clip and stirring a wonderful warm south Florida breeze as we went. I was impressed with the automobile's smooth handling and considerable power, and I enjoyed the ride thoroughly.
On our return I expressed my enthusiasm for the car. My cousin was surprised at my reaction. Clearly he'd expected that as a religious person I'd have disapproved of his conspicuous consumption. Maybe I did. But apart from any ideas I may have had about that, I could appreciate the actual experience of the automobile and enjoy it. He asked me how that was. "In experiencing the material world," I explained to him, with all the didactic authority of a newly ordained priest, "there are always two elements in play, the material object—in this case a car, the highway, the scenery going by—and the sense organs and mind that apprehend that object. You need both object and organ to have an experience of the material world. We all have bodies, we all eat food. So we are all materialists. So-called materialists emphasize the object; so-called nonmaterialists, or religious people, emphasize the sense organs and the mind. But we all always need both. The fact is, though, if the mind and the sense organs are acute enough, even a fairly humble object can bring a great deal of satisfaction. Think of how much money I save by practicing Zen! I can get a lot of good out of just one ride; I don't have to buy the car!" He saw my point. Just as he spent long hours working on teeth and jaws, and more hours studying the cars he wanted to purchase, I spent long hours on my meditation cushion cultivating my mind and perceptions, each of us working from his own angle on the question of being alive in this material world.
Honing the sense organs and mind (which includes the heart and spirit) does take cultivation. It takes mindfulness, the skill of quieting the mind so it can be present with what actually is, rather than with received, knee-jerk ideas about what is. The truth is, what we call "materialism" isn't really materialistic—it is idealistic. In other words, it is not the objects that we are after in our consuming—it is what those objects mean to us and to the people in our world. If you don't think this is true, just consider advertising. While advertising may once have had a mostly informative purpose, now its function is to create an aura of emotion and ideology around an object, so as to make it seem much more desirable than it actually is. A friend pointed this out to me in a magazine ad for a van. In the photo the van was parked on a gorgeous beach, with its doors wide open on both sides. On one side of the van was a man reclining. On the other side was a beautiful woman in a bathing suit, lying on the sand with her feet in the sea. A luminous, almost ethereal, shaft of sunlight shone down from the sky, right through the open doors of the van and onto the woman's sensuous face. The photo, digitally touched up with rich colors and smooth surfaces, suggested something delightful, which had nothing whatsoever to do with the actual van it was depicting.
This is a far cry from "wash your bowls," which emphasizes taking a very humble object and making it magnificent—not by applying images of desire but by simply and repeatedly taking care of it mindfully. Once, the twentieth-century Japanese Zen master Nakagawa Soen Roshi gave a retreat in America. The retreat took place in a rented school building, so there wasn't much kitchenware available for serving meals. The daily schedule included a tea service, and since there were no teacups, paper cups had to be used. On the first day of the retreat, after the initial serving of tea, the retreatants began to wad their cups to throw them away, but the Roshi stopped them. "No!" he scolded. "We need to use these same cups each day, so you have to save them." For seven days the retreatants used the same paper cups for tea. When the retreat was over, Soen Roshi said, "Okay, now we can throw away the paper cups." But the students wouldn't hear of it. "Throw them away?! These are our cups that we have used mindfully every day. How could we possibly throw them away? They are precious to us!"
My friends are always astonished when I tell them how much I enjoy shopping malls, especially at Christmastime when they are full of shoppers. I enjoy the feeling of joining together with other people who are out looking for gifts for their loved ones, anticipating a festive meal with them, happy to be spending lots of money in a celebration of life. I am, of course, aware of all the waste and misery that also accompanies the holiday season, but mostly that is not what I focus on. Yes, the parking lot is too crowded, and yes, the amount of merchandise in the stores is overwhelming. But I can't help it, I still enjoy myself.
The contemporary American shopping mall may seem like a recent blight on social life, but the truth is shopping malls are as old as human civilization. I have visited Jerusalem several times and walked through the narrow streets of the Old City. They are now, as they have been for millennia, crowded with shops overflowing with merchandise, jammed in cheek by jowl with each other, shopkeepers shouting at passers-by to get their attention. I have also spent many happy hours at the great Indian market in Oaxaca, Mexico, where you see women selling tamales, butchers displaying sides of beef, and all manner of clothing, jewelry, liquor, and food, including the Oaxacan specialty, peppered grasshoppers. Although I don't buy much at any of these places, I enjoy the spectacle. I especially enjoy the feeling of being with the people, shoppers and shopkeepers alike—all of us brought together in one teeming location by the simple human need for material goods that we hope will bring pleasure, comfort, and sustenance into our lives.
In the end, commerce is communication, a way of being together, transacting, each of us helping the other to fulfill our human needs. Thirteenth-century Japanese Zen master Dogen says in his essay "Bodhisattva's Four Methods of Guidance": "To launch a boat or build a bridge is an act of giving. . . . Making a living and producing things can be nothing other than giving." I know that it is possible for us to engage in commerce as an act of participation and compassion—to buy and sell in that spirit. Through the process of spiritual practice, we can cultivate a view of material things that appreciates them for what they are in themselves and recognizes in them an opportunity for meeting each other on the ground of our shared human needs.
When you do business with someone, you are cementing a relationship with that person. You could see the relationship as adversarial (who will get the best of whom?), but you could just as easily see it as mutual, each of you providing as fairly and as pleasantly as possible what the other needs. It is within the power of any of us to cultivate an attitude of mutuality in our economic transactions. In doing so, we come to see our customer, our supplier, our dealer, our banker, as friends, people who, like us, want to be happy, want to take care of their families and earn a living. To look at commercial life like this and to conduct ourselves as if it were so takes sensitivity and mindful awareness. This we need to develop over time, working with our thoughts and responses just as we work with our breath on the cushion. Part of that work is to be honest and realistic about our own greed, our own fear, our own confusion. But if we can do this with enough clarity and patience, then it may be possible for us to conduct our economic lives with some peacefulness and enjoyment.
For instance, we could pay attention to our thoughts and feelings as we engage in the acts of purchasing or selling to examine honestly our attitudes about money. To what extent is our feeling about money connected to our sense of self-worth—our sense of being powerful and important, or weak and unimportant? Clearly money, in and of itself, has very little to do with these feelings. Whatever feelings of high or low self-esteem we may have, they probably exist independently of money. We have only projected these feelings onto money and are very likely conducting our financial lives in a distorted or at the least an unconscious way. Perhaps our ingrained, habitual, and unexamined attitudes about money are just the playing out of childhood conditioning. Having grown up deprived we may be worried that there won't be enough; or, having grown up with plenty, we may feel guilty that there is too much or be constantly expecting more. Reflecting on this—not so much by thinking about it in the abstract as by observing in detail what we do, say, and feel as we deal with money—we can find a way to clarify how money actually functions in our private world. If its function is not reasonable or healthy for us, we can find, based on our honest investigations, the relief that always comes when something unconscious and dysfunctional comes to conscious awareness. Eventually we might be able to view money more clearly as a means of exchange between people, a convenient device for the distribution of the material things necessary for living. We might come to see money less as a source of worry, pride, or guilt and more as a way for us to share life together.
Contemporary commerce is characterized by its immense complexity. There is very little about it that is local. Goods we buy and sell involve unknown and unseen participants from all over the globe, many of whom may be exploited or exploiting others in the process of fulfilling our needs. To conduct our economic lives mindfully requires us not only to be mindful of our attitudes, the goods we buy, and our relationships to the people who supply us these goods but also to be as informed as we can be about the possible exploitation involved in our purchases, and to use our purchasing power to reinforce goodness and weaken greed and exploitation. When we know that a company or product is harmful to its workers, competitors, or the environment, we simply don't buy that product. When we know that a company or product is making a conscious effort to offer something useful in as harmless a way as possible, we go out of our way to buy it. When this is our consideration, price or convenience becomes less important than relationship. We want to give our business to people we can really support, and whose efforts we are interested in encouraging.
I suppose the effort to keep informed about companies we do business with (whose policies change constantly, and who seem these days to be bought and sold with alarming and tremendous frequency) could become crazy-making in the midst of the complicated lives we are all leading. Still, knowing that it is impossible to do it perfectly, we can nevertheless do it as perfectly as possible, trusting our intention more than our information. Information in the present age is powerful, but it goes out of date almost as soon as it's gathered. Intention, on the other hand, can remain firm and can help keep us on a wholesome course. While it is shortsighted to be uninformed, trusting to intention alone, intention's power to transform the world should never be underestimated.
It seems to me that the world is in need of a new economic theory to replace the one that is now in effect—unrestrained free-market capitalism. This system operates on the faith that an "unseen hand," as Adam Smith called it, will see to it that things don't go out of bounds. That free-market capitalism is, in this sense, fundamentally based on religious or mystical foundations has been more or less lost on us. There is, as we all know, plenty of greed, injustice, and gross manipulation in our economic system. Yet the world's capitalistic movers and shakers apparently believe in the mystical rightness of "the market," that somehow the market (which often seems to take on the proportions of a deity) will in the end serve us all as well as anything else could, and is less subject to corruption and disaster than other, more rational systems. In fact, the unseen hand has been relatively reliable. Although our world economy is in fairly terrible shape (especially when you consider its ecological costs), it is also miraculous that it is in as good a shape as it is (considering its complexity and the fact that it is ruled by people who are not as well-meaning as one would like). Many people starve, but more people are being fed every day. And little by little some of the more enlightened nations are joining together to cooperate for the collective good not only of each other but of the planet.
I don't know if Adam Smith ever proposed a definition of the "unseen hand," but here's mine: it is the sum total of human goodness, of our love for ourselves and each other, and of our hopes for a future that will be more humane than the present or the past. Perhaps we can trust the unseen hand to inspire us to more mindful consumption and production as time goes on, and to discover, eventually, some new organizing principles for our economic life. Until then—and long after!—we have our spiritual practice to guide our daily conduct as we go forth into the world, earning and spending as we must.
16
Green Power in Contemporary Japan
Duncan Ryuken Williams
SEVERAL YEARS AGO the Japanese Soto Zen environmental division produced a CD of songs encouraging sect members to avoid disposable chopsticks. The message was to carry around "my _ohashi_ " (chopsticks) as a way to save forests. Upset by this anticonsumerist message, the national chopstick manufacturer's association pressured sect headquarters to block the CD release. The project ground to a halt. In Japan, when competing interests of labor/industry and environment come to a head, Buddhist organizations almost always side with industry. Institutional Buddhism in Japan not only tends to support the establishment but is perhaps the most conservative pillar in contemporary Japanese society.
Buddhist temples have often served as stewards for much of the natural landscape of Japan since the early medieval period. But explicitly linking Buddhist doctrine with environmental protection is relatively recent. Historically the consumer rights movement in Japan has been driven by local citizens groups and environmental organizations born from the left and labor movements of the 1960s. However, beginning in the late 1970s, a number of Buddhist priests, temples, and lay associations dropped their traditional resistance to what had been perceived as a leftist cause, developing new forms of Buddhist environmentalism that resonated with a more conservative worldview.
This essay takes up Japanese Buddhist initiatives that have addressed two core consumer issues uniting people across the political spectrum: energy and waste. It is well known that postwar Japanese consumers have demanded efficiency, miniaturization, durability, and convenience from manufacturers of every conceivable consumer product from televisions and cell phones to automobiles. This postwar Japanese consumerism fits well with the newly emergent Buddhist environmentalism that focuses on _mottainai_ , "not wasting." Rather than being anticapitalist, this environmentalism might be called _hyper_ capitalist, since it demands ever more efficient and durable products for the consumer that reduce inefficiency and waste. Difficult questions about long-term nuclear waste have made consumption of nuclear energy problematic for many environmentalists. Given Japan's limited space and resources, waste of all kinds has been under discussion as the government is pressured by the market to develop a zero-emissions society based on recycling. This essay describes three ways Buddhists have become involved in rethinking Japanese consumer ethics through establishment-sect greening initiatives, through engaged Buddhist alternative energy models, and through temple-based recycling education.
THE SOTO ZEN "GREEN PLAN"
In the 1980s Shoei Sugawara, a forward-thinking abbot of the Soto Zen Senryuji Temple in Komae, proposed to his parishioners a way to make the temple more ecological. Even though Buddhism has traditionally advocated friendly relations between humans and nature, he felt the modern world had disrupted this relationship. One of the main characteristics of a Japanese Buddhist temple is the large roof on the main hall ( _hondo_ ), containing the primary image of worship ( _honzon_ ). Sugawara thought that if that broad space were used for solar panels, the temple could be energy self-sufficient. It would be many years before his idea for a "solar temple," using energy friendly to both nature and humans, would be actualized. He persisted in advocating for solar temples to other Soto Zen priests, and finally in the year 2000, a regional meeting of four hundred Soto Zen temples was held in Tokyo. The plenary speaker, Koichi Yasuda (abbot of Eisenji Temple), took up Sugawara's vision, laying out practical steps to install solar paneling at Buddhist temples.
When Senryuji's solar panels were finally hooked up, they produced more than enough energy for the electrical needs of the entire temple complex. Excess energy was sold to Tokyo Electric Power Company at its daytime peak rate, while the temple bought back energy when necessary (on cloudy days and at night) at the cheaper off-peak rates. This arrangement proved to be beneficial to the environment (no pollution), the temple (cheaper energy costs), and the power company (which was in power deficit during peak hours just when the solar panels were producing most energy). There was, however, one problem. Parishioners voiced strong resistance to solar technology because it interfered with the traditional architecture of their temple. Today the temple is working with an architectural firm to develop solar roof tiles made in the traditional Japanese Buddhist temple style. Sugawara sees the solution to this design problem as the key to Buddhist temples' adopting solar energy in the future.
While the energy advocacy of Sugawara stemmed from his personal interests, it was not out of line with his sect. Since 1995 the Soto Zen headquarters has maintained a nationwide campaign for the environment, taking up critical issues of consumer waste and energy use. The earliest of Japanese Buddhist sects to engage these concerns on a sect-wide basis, they developed a comprehensive "green plan" and promoted it to the more than fifteen thousand Japanese temples of Soto Zen Buddhism.
The Green Plan has been part of the official Soto Zen strategy to engage pressing contemporary issues under the slogan "Heiwa, Jinken, Kankyo" (Peace, Human Rights, and the Environment). Through pamphlets, books, and symposia, the sect has encouraged individual priests, temples, and sect organizations to take up the environmental cause as a part of their affiliation with the Soto Zen sect. Educational materials emphasize the teachings of Dogen and Keizan that promote sensitivity to the natural world (such as Dogen's view that grasses, trees, and forests are manifestations of buddha nature). They also point to conservation measures such as monastic rules on not wasting water and food. In the 1998 _Green Plan_ , the question is asked, "Why does a Buddhist sect like Sotoshu get involved with environmental issues?" In response, the official doctrine highlights eco-friendly teachings of Shakyamuni Buddha, Dogen, and Keizan that encourage increasing wisdom and decreasing desire (for example, Keizan's _heijoshin_ , "mind of equanimity").
The Plan also draws on teachings from the traditional lay-oriented manual _Shushogi_. Mimicking the traditional five-line verse ( _gokun_ ) used by monasteries before a meal, the sect advocates the following verses for reflecting on the environment:
_Green Plan_ gokun: _Save the Earth!_
_Five Verses to Living the Green Plan in Everyday Life_
_1) Let's Protect the Green Earth. The Great Earth Is the Home of All Life_.
_2) Let's Use Water Sparingly. Water Is the Source for All Life_.
_3) Let's Limit Our Use of Heat. Heat Is What Propels All Life_.
_4) Let's Maintain Clean Air. Clean Air Is the Open Space for All Life_.
_5) Let's Live in Harmony with Nature. Nature Is the Buddha in Form_.
The pragmatic character of these verses reflects a general tendency of the Green Plan to focus on everyday acts at the individual or temple level rather than doctrinal justification for its advocacy of green thinking. Green Plan pamphlets for sect households and temples include items such as checklists to monitor the use of TV and other electrical appliances (to meet a sectwide goal of reducing energy use by 1 percent), information on purchasing "eco-products," warnings on genetically modified foods, and detailed guides on how to properly separate recyclables. As a sign of the times, the sect manufactured and distributed to member households more than one and a half million cell phone straps with the slogan "Soto Zen Buddhism, Green is Life."
To chart progress on these initiatives, the sect established the Sotoshu Green Plan Kikin, or fund, to raise money for nonprofit environmental groups in Japan. To measure carbon emissions output, the sect headquarters distributed a chart to calculate the amount of carbon dioxide (CO2) each household produces per year. For each activity such as washing dishes, bath use, and aluminum can recycling, the household is encouraged to calculate the amount of CO2 reduced and to donate the equivalent savings to the Green Plan fund. Based on the Buddhist teachings of using less ( _chisoku_ ) and donating ( _fuse_ ), the fund has been a way to link Buddhist practice, environmental awareness, and fundraising. By focusing on carbon emissions reductions, the Soto Zen Green Plan supports the goals of the Kyoto Protocol, addressing consumption concerns related to global climate change.
ENGAGED BUDDHIST ALTERNATIVES
In contrast to sect-wide activities, a number of individual priests and their temples have developed alternatives outside the sectarian establishment and the mainstream economy. A good example is Okochi Hideto, a Jodo sect priest and leading figure in the Japanese engaged Buddhism movement. As abbot of Jukoin Temple, founded in 1617, with a current parish membership of 250 families, he could easily have settled for the life of a typical parish priest, performing funerary rites and organizing annual services around the temple calendar. But over the years, he has served in all kinds of social and environmental justice movements, including the JVC (Japan Volunteer Center), Kokusai Kodomodomo Kenri Center (JICRC, a children's rights group), and ARYUS (Bukkyo Kokusai Network), and has authored a number of books on small-scale development. Though some of the groups are Buddhist inspired, many are secular nongovernmental organizations working on social welfare issues in Japan and around the world.
The key to Okochi's engaged Buddhism is his interpretation of the Buddhist teaching of suffering. Over the years, he has made numerous trips to Southeast Asia, the Middle East, and Africa. From warfare in Rwanda to genocide in Cambodia, contact with the palpable suffering of people encouraged Okochi to reflect on the relative comfort of Japanese Buddhists. For him, Buddhism is based on feeling the teaching of suffering, not as an abstract concept, but as something in one's guts. In war-torn countries and poverty-stricken regions, Okochi experienced the type of conditions that inspired Honen, founder of the Jodo sect, to develop a Buddhist approach to suffering for the common people. At the time, Honen was responding to the severe socioeconomic conditions of medieval Japan, which left many people starving and impoverished.
Working with suffering, Okochi draws on Buddhist teachings such as the Four Noble Truths for inspiration. In an essay explaining his involvement with a local environmental group, he states:
When Shakyamuni Buddha (Siddhartha Gautama) gained enlightenment, his first teaching was the Four Noble Truths, that is, first, get a solid grasp of suffering (the problem), second, ascertain its causes and structure, third, form an image of the world to be aimed for, and fourth, act according to correct practices. Then, one gains a sense of the meaning of life in modern society as a citizen with responsibilities in the irreversible course of time. The suffering of the southern peoples and nature, from which we derive support for our lives even as we exploit it, has caused the Edogawa Citizens Network for Thinking about Global Warming to think, and therefore we have achieved concrete results. The problem is structural in nature, so by changing the system and creating measures for improvement, we achieve results.
Okochi interprets suffering as existing not only on a personal level but also at a deep structural level in the modern socioeconomic system. This brings him in line with the analysis of many engaged Buddhists such as Sulak Sivaraksa or A. T. Ariyaratne. For Okochi, Buddhism is a religion not simply for transforming oneself but also for transforming society. As he states, "the 'awakening' sought by the Buddha was an awakening to the entire universe. The Buddha is someone who lives responsibly based on this self-awareness of the universe, that is, as a 'citizen' of the world."
Okochi combines this emphasis on a return to the original teachings of the Buddha with Pure Land Buddhist rhetoric about making _this_ world the Pure Land. Many in the Jodo and Jodo Shin traditions interpret Amida's Pure Land to be a heavenly land where believers transfer after death. In contrast, Okochi believes that heavens and hells are manifest in this world and that this world is itself the locus for the development of the Pure Land. This notion is, of course, not original, but it is nevertheless a minority tradition within the Pure Land sects.
Another well-known advocate of this Pure Land approach is Keisuke Aoki, a Jodo Shin priest and the abbot of a temple in Himeji. Aoki was one of the first Buddhist priests to get involved in environmental issues. He has long advocated a Pure Land Buddhist theology in which hell ( _jigoku_ ) can be found in the human mind and in a society based on competition and oppression, while the Pure Land ( _jodo_ ) can be found where the web of life is celebrated and filled with infinite light ( _muryo komyo do_ ). In his 1997 book, _Edo to kokoro: Kankyo hakai kara jodo e_ (The Impure Land and One's Mind: From Environmental Destruction to the Creation of a Pure Land), he emphasizes human responsibility in "the destruction of the earth, which is the creation of hell." Well known locally for protecting the sea from overdevelopment, Aoki has energetically campaigned for many years against oil refineries and other industrial production that caused the "red-lake phenomenon" in Harima Bay, ruining the local fishing industry. According to his theology, this hell, which he describes more globally as a "shadow of a society centered on money," can be replaced by an "ecology of the Pure Land," where the Buddha, enlightenment, infinite light, and compassion permeate this world.
In his environmental work, Okochi linked this concept of building a Pure Land on earth with his critique of structural suffering. As an increasing number of Japanese became aware of global warming issues through the 1997 Kyoto conference, Okochi was mobilizing citizens in his locality in Tokyo. He helped establish the Edogawa Citizens Network for Thinking about Global Warming, an offshoot of an earlier organization, Group KIKI, which was dedicated to alternatives to nuclear power and other energy and waste issues. After a study tour to Sarawak, Malaysia, to document the destruction of the rain forest by Japanese multinationals, the group successfully pressured the local council to not use wood from tropical rain forests. The Citizens Network also raised funds for CFC-recovery equipment to donate to car demolition businesses in their local Edogawa Ward, a district responsible for 60 percent of CFC emissions in the twenty-three wards of Tokyo.
By far their most ambitious project was to establish an alternativeenergy power plant in the ward to end their neighborhood's dependence on Japanese fossil fuel and nuclear energy. In 1999 the Edogawa People's Power Plant No. 1 was constructed as a citizens' effort to withdraw from the energy companies and the financial institutions that fund them (which engaged in environmentally destructive investments). Its location: on the roof of Jukoin Temple.
The temple name, consisting of the Chinese characters _ju_ (life) and _ko_ (light), reflected the Jodo tradition's teachings that existence is unlimited life and light of the Buddha. In his rationale for the power plant project, Okochi proclaimed:
Human life as well as all life existing in nature is mutually interlinked and dependent on each other. This Buddhist concept aims at creating a global society of coexistence and co-prosperity. Juko-in, in solidarity not only with Buddhists but also with other citizens, NGOs and various other groups, is dedicated to ecological development and human rights issues.
This dedication meant that the four-hundred-year-old temple faced a radical rebuilding. After obtaining the understanding of the parishioners, the temple's architecture was completely modernized using eco-friendly concrete and wood building materials. The traditional roof tiles were replaced with two sets of fifteen large solar panels that would generate six thousand kilowatt-hours (kWh). This was enough to receive official recognition from the local government as the first of several planned People's Power Plants in Edogawa Ward.
The funding for this project—6 million yen—came from local environmental groups, individual donors, and loans from an independent bank that the group established: the Mirai Bank, or the Future Bank. Okochi adapted a temple fundraising strategy from the premodern period, when donors bought roof tiles for a new temple's construction for a sum above the actual cost. He asked locals to buy solar panels as a gift to the temple power plant. The _taiyo kawara_ , or "sun tiles," were sold at five thousand yen per panel and the funds deposited in the new bank.
The model for the Mirai Bank was based on medieval and early Buddhist mutual aid societies ( _ko_ ), with the modern goal of supporting environmental sustainability. Instead of giving their hard-earned money to the big national banks (which often use people's savings for environmentally destructive projects), the Edogawa citizens chose to invest ethically in building and protecting the future ( _mirai_ ). Inspired by microcredit banking in Third World countries, Mirai Bank not only criticized the existing capitalist system but offered an alternative economic model for a new kind of sustainable society in Japan. In addition to funding the power plant, the bank embarked on a consumer campaign to encourage the purchase of eco-products. Because 60 percent of energy in Japanese households is consumed by refrigerators, air conditioners, and lighting, the bank began by focusing on environmentally friendly refrigerators. The bank understood that average families take up new alternatives only if they don't have to sacrifice comfort or pay exorbitant fees. So, they provided interest-free loans to buy environmentally friendly refrigerators, which reduce energy consumption by four hundred kilowatt-hours per year. This is equivalent to nine thousand yen; thus a bank loan of fifty thousand yen could be paid off in five years.
The solar power plant generated not only alternative energy but also new small-scale economics. Excess energy beyond the temple's energy use was sold to Tokyo Electric Power Company with the income plowed back into paying off the initial investment. The Edogawa Citizens Network for Thinking about Global Warming decided to encourage local citizens to buy this excess energy at a premium with Green Power Certificates. By selling two hundred 30 kHh certificates for one thousand yen each, the power plant could return its initial investment in just nine years. To involve the local community and to build a more mutually dependent society, each Green Power investor also receives Edogawatt bills, a local currency that can be used to pay for babysitting, translation, and other services, "deepening interpersonal relationships and trust." Since solar energy has the lowest maintenance costs associated with energy production (almost zero), the idea is that each People's Power Plant can be profitable within a decade, generating clean, zero-emissions energy, and building a more intimate society at a time when modern Japanese society has grown increasingly impersonal.
Okochi's approach has been very practical and reflects his Jodo sect background and belief that ordinary Japanese citizens can participate in this type of engaged Buddhism without engaging in asceticism or sacrificing comfort. His ideal of "engaged citizenship," or the spirit of volunteerism in society, is active social reform.
A volunteer, according to Juko-in thinking, is not a person who provides his/her cheap labor to fill in cracks left by the administration, or a person looking for his/her own satisfaction. Volunteers look for the true nature of the problems and promote movements oriented towards social reforms. . . . They should take the side of the weaker (the people) and not the strong side of the system. They begin by experiencing problems of suffering. Then, they move to reflect on the structures and the mechanisms concerning those issues. . . . Those volunteers rich in work experiences with NGOs show us the face of the Buddha and famous Buddhist saints.
Thus Okochi aligns himself with ordinary citizens, disdaining what some might consider elitist asceticism. His approach differs from the Soto Zen establishment Buddhism because it is based in a critique of the current sociopolitical and capitalist system. With much of mainstream Japanese Buddhism aligned politically with the right and big business, Okochi's leftist rhetoric of siding with the poor and oppressed offers a marginal but important voice in the contemporary Japanese Buddhist landscape.
BUDDHIST CONSUMER EDUCATION
A third approach to reducing waste and changing consumption habits takes place in the context of traditional temple activities. Rinnoji Temple (a Soto Zen temple in Sendai, Miyagi prefecture), whose abbot has been active in volunteer efforts such as AIDS hospice and earthquake relief, is setting an example with its recycling and environmental education programs. Using the idea that the Buddhist spirit of attention to small things and "not wasting" starts at home, the temple looked to its own practices leading to waste and overuse of natural resources.
As a typical, though large, Japanese parish temple, the primary activity of the temple was not Zen meditation but the performance of funerary and memorial services for its parishioners. These services take place at death and in intervals over a period of thirty-three years. Parishioners also visit the temple with flowers and other offerings for the deceased during the annual summer ancestral festival of Obon. At this season the spirits of the deceased are thought to return to the temple graveyard or to the memorial tablet ( _ihai_ ) normally kept in the family altar ( _butsudan_ ). The abbot noticed that an enormous number of flowers were being donated at the temple graveyard—nearly five thousand flower bundles during the Obon season alone—and then were simply discarded into the landfill. The temple conceived of a plan to take these flowers and develop a high-quality composting system, creating fertilizer, which could be donated to local farmers. By 2000 the temple had expanded this recycling project to include the composting of leftover temple food. They also recycled into charcoal the bamboo offering stands used at grave sites.
Environmental education has also become a big part of the temple's activities since 2001. Each year the monks offer a presentation on recycling to the local middle school students using the temple recycling system as a model. In 2003 the temple produced a home video for its parishioners entitled _Kankyo no tame ni_ (For the Sake of the Environment) that gave instructions on home composting and how not to waste water used to clean rice. The video targets housewives, who are most responsible for cooking rice and monitoring home recycling. By working with housewives and young teens, the temple reinforced the message that environmental education must begin early and at home.
The Rinnoji example illustrates antiwaste activism that functions within the traditional boundaries of what some have termed "funerary Buddhism based on the parish system." This system, which characterizes mainstream Buddhism in contemporary Japan, tends to emphasize the continuity of tradition and customary/formalistic relationships between priests and parishioners. The fees paid for funerary and memorial services constitute a vast proportion of a temple's income. For the most part, any Buddhist consumer or environmental activities in Japan have had to operate within this system, which has been the mainstay of Japanese Buddhism since the beginning of the Tokugawa period (1603–1867). In contrast to Okochi's engaged Buddhism, temple composting is not a radical departure from social and political norms. However, even within these conservative institutions, Rinnoji Temple provides an example of efforts to raise consumer consciousness.
ETHICAL CONSUMERISM
Whether it be empowering consumers through temple education (Rinnoji), creating energy off the grid through solar roof panels (Jukoin), or making use of sect-wide organizations to promote "green Buddhism" (the Soto Zen Green Plan), Japanese Buddhists are beginning to make structural changes that directly impact consumption patterns. Precisely because establishment Buddhism is a pillar of mainstream Japanese society, even small actions at the more than one hundred thousand Buddhist temples have the potential to make dramatic changes not only at local temples but in the consumption patterns of the millions of lay Buddhist members of those temples.
Transformation of mass consumption patterns often starts with small-scale movements that set trends in the larger society. Buddhist temples in Japan have begun this process of reshaping Japanese society through creating new models of ethical consumerism. If Buddhism can have an impact on a hyperconsumerist culture such as Japan's, it is a testament to the role that Buddhism can play in the global marketplace.
Buddhist temples and centers in America, while still few in number, have a relatively high influence on trends in American popular culture. That influence can be mobilized to rethink consumption patterns and empower consumers to make ethical choices oriented to reduce suffering in the world. These small-scale acts may prove to have enormous impact on American society at large. When Buddhists can transcend borders in these ways—sharing ideas and strategies for a more sustainable society—this can be the beginning of a radical restructuring of the forces of the global economy.
17
Mutual Correction
Seeing the Pain of Others
David W. Chappell
_We must realize that when basic needs have been met, human development primarily is about being more, not having more_.
—Earth Charter, preamble
FROM THE BEGINNING of human history, human survival has depended on the capacity to consume as much as possible as quickly as possible. Whoever collected and consumed the most food, clothing, shelter, and weapons was the most able to survive. Over time this drive to achieve the utmost diversified and was expressed individually by who had the most cunning and skill, and socially by who had the best strategy and organization. These qualities became further developed through individual achievements in education, technology, sports, and the arts and were accompanied by parallel social achievements in governments, civil society organizations, and corporations.
Today this quest to achieve the utmost is facing new challenges as local cultures disappear into McWorld and as the planet's biological diversity diminishes daily. This challenge will only increase as population grows—from 6 billion to perhaps 9 billion people over the next forty years—and as consumption grows. If we wish excellence in developing the brightest and best, then seeking guidelines and practices that foster global excellence should be our first concern.
What can Buddhism offer to this challenge? What individual and social guidelines are relevant for today's consumerist world? Consumerism lies close to the heart of the Buddha's story, presenting conflicting messages. First there is the exemplary tale "from riches to rags" as Shakyamuni Buddha leaves his sumptuous royal palaces for a life of voluntary poverty. Yet soon after his enlightenment he visited kings and welcomed gifts of valuable parklands and treasures for his Buddhist community. Whereas the Buddha taught individuals to be free from greed and possessions, the early Buddhist social community amassed great wealth. A visit to the Emerald Buddha in Bangkok, or the golden spires of pagodas in Cambodia, demonstrates that in medieval Asia, Buddhist institutions were often the most vivid examples of conspicuous consumption. Religious paths in both East and West have often encouraged a form of "spiritual consumerism" by declaring that spiritual advancement could be won by donations to the religious community. Even today, Buddhism is not exempt from corporate greed.
Certainly in individual practice, Buddhist ethics do offer an antidote to excessive greed through practicing mindfulness, understanding impermanence, and observing the interrelatedness of all things. The peaceful balance and inclusiveness that emerge can support institutional practices that promote equity and harmony. But how to achieve this in our consumer culture? The challenge is to translate Buddhist methods of personal liberation into guidelines for the public sphere. To preserve biological and cultural diversity, liberate people from poverty and disease, and foster social harmony, much more needs to be done at the institutional level to protect the many cultures and forms of life from extinction. Here I suggest five proposals for a Buddhist ethic of consumption that can support institutional evolution in the direction of global excellence.
OPEN DISCLOSURE
In spite of the amazing achievements of modern consumerism, terrible tolls have been paid for its advance. It doesn't take a genius to recognize that our neighborhood shopping centers with their cozy comforts carry a false sense of reality. Not only have they not evolved organically as part of the local neighborhoods—where local dreams, transitions, and interdependence would be part of local observation and memory—but their sources are hidden. No advertisements proclaim who is profiting and by how much. Absent are the connections to the depletion of the earth and the suffering or pride of the workers who fuel the engines of production. There is no trail showing the path from impoverished sweatshop workers to the latest fashions, no pictures of the hands and faces that made the goods, no images in the glitter of jewelry shops of the trails through the forests and into the pits where children dig in the dark for gems.
The most popular form of Buddhism in East Asia is Amida devotionalism, which aims for salvation through rebirth in Amida's Pure Land. This is seen as the best place to hear the dharma and attain enlightenment. Today, however, the setting might seem to resemble an idealized shopping mall. This is how an Amida practitioner is instructed to visualize the Pure Land:
The rows upon rows of jeweled trees are evenly spaced, and the leaves are in orderly sequence. In between the leaves bloom exquisite flowers, and upon these flowers, fruits made of the seven kinds of jewels appear of their own accord. . . . This array of exquisite flowers . . . looks like revolving fire-wheels, gently spinning among the leaves. . . . There is a great ray of light which forms banners, flags, and countless canopies adorned with jewels. Within these jeweled canopies, all the works of the buddhas of the three-thousand-great-thousand worlds appear illuminated.
Doesn't this vision of Amida's Pure Land fulfill our wishes of consumption where all glitters with jewels and gold? Like the shopping mall, the Pure Land is completely available to all, but the currency is trust in the compassionate power of Amida Buddha. The Pure Land, however, is not the final destination but rather a necessary training station to cultivate enlightenment in preparation for returning to save others. While shopping malls actively cultivate attachment, yearning for the Pure Land is said to be neither addictive nor entrapping, safe as a fire built on ice that fizzles in the water created by its own heat. Thus the Pure Land is an enticement that in the end liberates self and benefits others.
Shopping malls, in contrast, deceive by not showing their past, by not showing the source of their goods, by not showing the effort and suffering and skill that produced their goods. They do not point beyond themselves to a higher and more noble purpose. They exist not to help us liberate others but as ends in themselves for consumers, and vehicles of wealth and exploitation for owners. Hardly a source of freedom, the goods of shopping malls become cages that imprison our minds, that conceal the stories of their creation, and that make us indebted to the financial system that generated them.
Buddhist compassion is based on a sense of connection and kinship, but this empathy is thwarted by the privacy walls that corporations construct to avoid responsibility. Nike, the largest garment seller in the world, was exposed for the obscene disparity between Michael Jordan's high endorsement fees and the enslaving wages paid to its Third World workers, usually women and sometimes children. Under enormous pressure, Nike provided the names and addresses of many of its subcontractors to enable human rights groups to investigate the working conditions of its producers. While Nike still remains the center of controversy, it has raised the bar for higher standards of transparency in corporate social responsibility. This may be less true for other firms such as Disney, which subcontracted with the military regime in Burma/Myanmar to produce some of its products.
Instead of privacy walls and concealed stories, Buddhist ethics demand greater mindfulness of corporate-consumer interconnections. More transparency not only is informative but also often transforms the behavior of those being watched, as Amnesty International has shown. Apparently people are less likely to harm others when they know that someone else is watching. From a Buddhist perspective, cultivating compassion depends on direct contact with suffering. Thus it is essential to work toward more _open disclosure_ of the sources of production, including the human and ecological costs and the character of the producers. This is my first proposal for a Buddhist ethics of consumption.
MUTUAL CORRECTION
In 1970 the Club of Rome report shook people from their infatuation with endless expansion by showing the limits of growth on our planet. Historically this was the first global-scale confrontation with the limits of the earth. After decades of rapid development, it was quite clear that unrestrained human activity was taking its toll. At Earth Day celebrations around the country, people raised concerns about too much waste, too much stuff, too much apathy. The question was up: Can we make a midcourse correction? Can we restrain human activity to protect the planet?
Buddhist teaching has always emphasized personal restraint in our lives with others. Monastic traditions guard against taking human life, animal life, and even insect life. This precept of _ahimsa_ (nonviolence) is concretely illustrated by the traditional monastic allowance of only four possessions: a bowl, a robe, a needle, and a strainer to remove insects from drinking water to protect the lives of these small beings. Monastic ethics are often considered the ideal, and they are elaborated in great detail in Buddhist scriptures. Even in the very early years, the Buddhist monastic community met twice a month on full moon and new moon days to recite together their rules of restraint in front of others. Mahayana rules for monks and laity require that in discrete ways, bodhisattvas must reprove those who are harming others. Even kings were to be modest and to seek guidance from the sangha. So social responsibility via mutual correction pervades Buddhist ethical practice.
Whereas Christians have emphasized that all people are sinners, Buddhists have taught that all of us are imperfect and biased because of our past karma. In both views, individuals are seen as flawed and in need of correction. And in both traditions, emphasis has been placed on ethics for individuals, not institutions. Though individual followers were urged to be nonattached, Buddhist monastic institutions accumulated great wealth. Buddhism has always been expansionistic in the name of altruism, and institutionally it has not developed norms to curb Buddhist growth. Only recently have a few modern Buddhist groups, such as the Tzu-chi Compassion Association of Taiwan, even practiced public bookkeeping. Most Buddhist groups have not. Instead, gifts of dana are slipped into the hands of abbots with no public accounting. Traditional Buddhist groups have been strangely silent on economic matters, suggesting a new age of accountability is needed within Buddhist groups as a method of providing checks and balances.
The Four Bodhisattva Vows offer another expression of mutual correction. First created by Tiantai Zhiyi (538–597), they are still recited daily by contemporary Zen Buddhists:
_Beings are infinite in number, I vow to save them all_.
_Compulsive desires are endless, I vow to end them all_.
_The teachings are innumerable, I vow to learn them all_.
_Buddhahood is supreme, I vow to embody it fully_.
The first vow, to save all beings, quickly reveals our shortcomings in fulfilling this impossible challenge. It might be called presumptuous, even paternalistic, but at its core, the first vow directs attention to the endless task of serving others. In turn, it is balanced by the second and third vows, which urge Buddhists to correct themselves by ending desire and to learn from others. This correction is needed for both Buddhists and Buddhist institutions to keep greed and consumerism in check at all levels. In fact, it may be those of us who are trying to be helpful to others who are in need of correction ourselves.
Today the money managers of lucrative pension plans and mutual funds are aggressive in monitoring giant corporations and in removing ineffective CEOs. Checks and balances are provided by exposure through media coverage, which can often work more quickly than government regulation. Rather than disparaging these actions as thwarting creativity, we can affirm the need for legal restraints over corporate excess as well as individual harmful behavior. This cultivation of checks and balances, or _mutual correction_ , for individuals and institutions is my second suggestion for a Buddhist ethic of consumption.
INCLUSIVE DECISION MAKING
Modern corporations have been given the legal status of persons, based on the 1886 court case of _Santa Clara County v. Southern Pacific Railroad Company_. This ruling invoked the rights of personhood by appealing to the Fourteenth Amendment, which extended constitutional rights to slaves freed after the U.S. Civil War. But corporations, in fact, are not persons. Single persons do not have access to the golden parachutes for corporate managers that permit escape and exploitation. They are not protected like corporations by the limited liability of stockholders. Furthermore, some research indicates that the courts never did give this status to corporations, a claim that will be tested when the _Kasky v. Nike_ case comes to the U.S. Supreme Court.
Though institutions are not biological persons, they impact people and communities in a variety of ways. There is a growing consensus that institutional decision making should follow international guidelines (some of which are not universally supported by Buddhists). The most famous is the Declaration of Human Rights (DHR) now in the process of national ratification. This document protects workers' rights and environmental safety for people impacted by resource exploitation. At their 1992 meeting, the Buddhist Churches of America voted not to support the DHR. Though some writers disagree about how Buddhist metaphysics relates to human rights concerns, Buddhist leaders on the front line, such as the Dalai Lama, Aung San Suu Kyi, and Sulak Sivaraksa, have not been shy about advocating for the DHR as a set of ethical guidelines for humanity in the age of globalization.
Mahayana Buddhist ethics and the Declaration of Human Rights share similar themes. The _Scripture of Brahma's Net_ (used by both monastics and laity) and the _Upasaka Sutra_ (used only by the laity) are the bestknown Mahayana precept texts, though, in fact, there are at least two hundred scriptures containing bodhisattva precepts. The great Japanese _vinaya_ scholar Gyonen (1240–1321) summarized Mahayana ethics in his _Risshu Koyo_ as: to prevent all evil, to cultivate all good, and to save all beings. Preventing evil includes dissolving false ideologies and attitudes that lead to harm and maintaining the basic five precepts. Cultivating good includes nurturing inner understanding and attitudes of kinship, compassion, and joy toward others. Saving all beings affirms the heroic goal of the bodhisattva—who is dedicated to helping others attain enlightenment; Mahayana texts assert that each and every person is called to be a bodhisattva. The Declaration of Human Rights likewise presents three parallel mandates: to prevent government infringement on the individual (articles 2–21), to affirm social responsibility for human development (articles 22–27), and to visualize and promote a global order of equity and well-being (articles 28–30).
The first of the Buddhist guidelines—preventing evil—is crucial to reducing global suffering related to consumerism. The Buddhist tradition recommends restraining personal behavior to avoid harming others through no killing, lying, stealing, or sexual misconduct. In parallel to this, the first section of the DHR focuses on behavior protecting the integrity of individual life. Whether or not individuals have inalienable legal rights, individuals can be harmed not just by other individuals but also by social organizations, especially the state. The DHR represents a milestone in the evolution of modern institutional ethics in the way it establishes government restraints on harming individuals, and likewise government restraints on corporations from harming individuals and the environment. This moral development in the DHR needs to be more fully embodied by Buddhists in order to make Buddhist ethics relevant to the difficult challenges of global consumerism.
A fundamental principle for consumers and institutions is to avoid harming individuals by being aware of those who will be most affected by their decisions. In meditation one may calmly review the many factors involved in our mental dispositions. Likewise, conscious consumers must also calmly and regularly review a wide range of information from a variety of sources. This principle of inclusive awareness to restrain excess harm applies equally to shoppers and to managers of religious institutions, universities, and nonprofit groups. While those who will bear the costs of decisions may not have the power to determine the decisions, it is important at least that their voices be heard, their advice solicited, and their vote included.
This principle of inclusive decision making—namely, to include in decision making those who are most affected by the decision—has been partially enacted by the World Bank in its projects for listening to the poor and in its World Faiths Development Dialogue. In contrast, the World Trade Organization only reluctantly gave up its efforts to institutionalize a "multilateral agreement on investment." This agreement would have allowed corporations to invest and withdraw themselves from projects anywhere in the world without any feedback from local constituencies or any penalty for local harm that they may have done.
I believe that inclusive decision making reflects the social ethics attributed to the Buddha. _The Mahaparinibbana Sutta_ ( _Digha Nikaya_ 16.1) records that the Buddha used seven criteria to evaluate the social strength of the Vajjian society. The first two are relevant here: holding regular and frequent assemblies, and meeting, dispersing, and conducting meetings in harmony. The Buddha's assumption was that everyone would somehow be involved. Restraining institutional harm by _including in decision making_ those who are most affected by the decisions is my third proposal for a Buddhist ethics of consumption.
GLOCALIZATION
A related principle to shared decision making is that "whatever decisions and activities can be undertaken locally should be." This principle is articulated by the International Forum on Globalization (IFG) and given the slogan "Protect the local, globally." The IFG calls this principle "subsidiarity," while others prefer the new term _glocalization_.
Michael Rothschild, president of the Bionomics Institute in San Francisco, has argued that biological systems are successful only when they can decentralize as many functions as possible. He feels that the collapse of centralized planning regimes like the USSR was inevitable because too many decisions were being made by authorities isolated from the work. In a similar way, corporations that favor centralized control by management and lack accountability to stockholders or local communities inevitably become parasites that he calls "corpocracies." Government regulations can encourage or prevent such accountability. The state of Delaware, for example, shields executives from liability by freeing management from accountability to stockholders. It is no surprise that this state alone attracts more than half of the Fortune 500 firms, many of which actively promote consumerism around the world.
Buddhist practice has traditionally been critical of giving false substantiality and heightened value to metaphysical generalizations and personal constructions such as atman and brahman. Applying this practice of critique to social structures can help balance the authority of cultural abstractions such as church, corporation, and nation-state, and the demand to sacrifice life for them. Conservation biologist Jared Diamond suggests that modern state authorities are now so reified that they have been enabled to extract taxes and monopolize violence in what he calls "kleptocracy." While this heightened view of the state has allowed the state to protect strangers and redistribute wealth to the weak and needy, it has also enabled rulers to exploit others and become heedlessly destructive. Economic globalization has fostered a similar aura of power in some corporate circles.
Today moral issues are being framed in economic terms, whether they deal with the environment, health care, or social equity. Increasingly governments are being held hostage to global economic institutions to the detriment of local cultures. In listing the 200 largest financial budgets in the world, Charles Gray found that only 39 were nations, whereas 161 were corporations. The Fortune 500 companies in 1999 consisted of companies that had budgets over U.S. $9 billion, but only 57 national governments had budgets as large as these five hundred corporations. As corporations increasingly "rule the world," citizens and local governments are called to find effective ways to engage these new economic powers.
Buddhist practice emphasizes the constancy of change. Giving special attention to the local need not mean that it should not change. Local traditions have always been in flux. To privilege one way of doing things locally because it is seen as a tradition may sacrifice a vibrant future because of nostalgia, laziness, or attachment. Rather, the values of the past and present, the individual and the collective, need to be explored in their rich potential in a search for more creative ways for life to flourish in the future.
Giving greater attention to the local is one form of critical evaluation of the abstract, whether institutional or intellectual. As such, it is part of traditional analytical practice for Buddhists. Seeing how things come to be in their local details, as well as come apart in their local details, not only informs the mind but also liberates the heart from bondage to limited structures. Calm and critical appraisal of abstractions—whether intellectual or corporate, whether cultural or personal—can uncover the specific and local realities of actual parts and processes. Glocalization—the regular deconstruction of the collective, the imagined, and the abstract in order to privilege the local wherever possible—is my fourth proposal for a Buddhist ethic of consumption.
REGARDING THE PAIN OF OTHERS
Buddhists often invoke "love and compassion" as their motives for action, but these are qualities that must be cultivated through daily practice to be effective. In the earliest Buddhist texts, the most common source of ethical behavior is the generic sympathy that all humans feel. Gautama Buddha told his followers to "go and travel around for the welfare of the multitudes, for the happiness of the multitudes, out of sympathy for the world."
For sympathy to be genuine, it needs to be explicit, to be embodied; it requires links to real people and places. The Dalai Lama explained this basic human response as he reflected on a visit to Auschwitz:
When I speak of basic human feeling, I am not only thinking of something fleeting and vague, however. I refer to the capacity we all have to empathize with one another, which, in Tibetan we call _shen dug ngal wa la mi so pa_. Translated literally, this means "the inability to bear the sight of another's suffering." Given that this is what enables us to enter into, and to some extent participate in, others' pain, it is one of our most significant characteristics. It is what causes us to start at the sound of a cry for help, to recoil at the sight of harm done to another, to suffer when confronted with others' suffering.
Common human sympathy as the "inability to bear the sight of another's suffering" requires direct contact with suffering. In our consumer society, our material goods often protect us from experiencing such suffering. Even our emotions are being commodified. Advertisers, theme-park operators, and television programmers have learned how to manipulate our emotions to keep our focus on endless desires. Our media-dominated world presents us with infinite imagined communities. In today's TV generation, much of our living and loving is imagined. To invoke sympathy, we must break through media images and make direct contact with living people and those in pain.
Writer Susan Sontag has reflected deeply on the impact of visual images that show the suffering of others. Observing Sebastiano Salgado's moving photographs _Migrations: Humanity in Transition_ , taken in thirty-nine countries, she points out that the powerless subjects go unnamed in the captions. While suffering shown on such a scale may prompt sympathy, such photographs can also inhibit action. "Making suffering loom larger, by globalizing it . . . invites them [the viewers] to feel that the sufferings and misfortunes are too vast, too irrevocable, too epic to be much changed by any local political intervention. With a subject conceived on this scale, compassion can only flounder." She goes on to observe that "in a world in which photography is brilliantly at the service of consumerist manipulations, no effect of a photograph of a doleful scene can be taken for granted."
Common human sympathy is the foundation of Buddhist ethics, but it is often manipulated by the media and politicians. Balanced information can help direct our sympathy to where the suffering really is. Herman Daly and John Cobb's Index of Sustainable Economic Welfare and the Genuine Progress Indicator offer more-inclusive gauges of economic impact on people and the environment and illustrate an "economics as if life mattered." We need to require more tools like these to be structured into our media and our social routines. As much as possible we need to know and to experience the impact that complex and distant economic decisions are having on living beings because economics affects the quality of life more than anything else today.
Although measuring the well-being of ecosystems is difficult, it would be helpful if our daily newspapers and weekly news magazines, such as _The Economist_ and _Business Week_ , provided indexes that measure not just economic growth but the health of the environment as well. Every day the Dow Jones and S&P 500 standings are reported, but only recently has the health of the planet been news. In addition to the growth or decline of the gross domestic product (GDP), we need reports on the growth or decline of vital natural resources, as well as the health and welfare of animals and humans. If there were an international mandate for these status reports, we could keep better track of how well we are caring for the earth, living sustainably, establishing justice, sharing equitably, practicing nonviolence, and so on.
Travel and tourism are another form of consumerism that carries hidden harm. Marveling at the wonders of the world is different from what Gautama Buddha intended when he said to "travel around for the welfare of the multitudes, for the happiness of the multitudes, out of sympathy for the world." While appreciating the wonders of the world, we must also ask on whose backs they were built. While the architecture in the center of Paris is striking, Sulak Sivaraksa reminds us that those impressive buildings were the result of colonization. Though it is good to appreciate beauty and cultural achievements, travel must constantly be balanced and informed by Sulak's advice to "go where the suffering is."
Touching those who live in pain shows us concretely how _harm must be reduced_ ; this is my fifth proposal for a Buddhist ethic of consumption.
In sum, a first response to consumerism should be to try to reestablish connections between consumers—individual, corporate, and government—and those who are most affected by consumption. And when the actions of consumers are destructive to people or to nature, the Buddhist goal would be to ensure that consumers do not hide from seeing the pain and devastation that their decisions are causing. My argument is not to restrain the "free" market but to enlighten it by increasing the visibility of its activities, its governance, and its costs. By working together in this more open and enlightening arena of checks and balances, I hope that we will naturally develop self-restraints and find a way to evolve a more balanced, humane, and green form of achieving our utmost. As stated in the Earth Charter preamble, "We must realize that when basic needs have been met, human development primarily is about _being_ more, not _having_ more" (italics added). And being more means finding ways to include the lives of others, in all their differences and pain, in our awareness and decision making.
Notes
Introduction
. John de Graaf, David Wann, and Thomas Naylor, _Affluenza: The All-Consuming Epidemic_ (San Francisco: Berrett-Koehler Publishers, 2001), p. 36.
. Michael Brower and Warren Leon, _The Consumer's Guide to Effective Environmental Choices_ (New York: Three Rivers Press, 1999).
. Brian Halweil and Lisa Mastny, eds., _State of the World 2004_ (New York: W. W. Norton, 2004).
. David Loy, "The Religion of the Market," _Journal of the American Academy of Religion_ 65, no. 2 (Summer 1997): 275–90.
. Quoted from Raymond Benton, Jr., in Neva Goodwin, "Overview Essay," in _The Consumer Society_ , eds. Neva R. Goodwin, Frank Ackerman, and David Kiron (Washington, DC: Island Press, 1997), p. 3.
. Jonathan Watts, "Concocted Death: A Buddhist Deconstruction of the Religion of Consumerism," in _Santi Pracha Dhamma_ (Bangkok: Santi Pracha Dhamma Institute, 2001), p. 126.
. Yiannis Gabriel and Tim Lang, _The Unmanageable Consumer_ (London: SAGE, 1995).
. Peter N. Stearns, _Consumerism in World History_ (New York: Routledge, 2001). See especially chapters 2 to 5.
. Alan Durning, _How Much Is Enough?_ (New York: W. W. Norton, 1992), p. 30.
. Eric Schlosser, _Fast Food Nation_ (Boston: Houghton Mifflin, 2001), p. 4.
. John C. Ryan and Alan Durning, _Stuff: The Secret Lives of Everyday Things_ (Seattle: Northwest Environment Watch, 1997).
. Hilary French and Brian Halweil, "Microbial Migrations," _Orion_ (January 2004).
. Durning, _How Much Is Enough?_ p. 51.
. Lester Brown et al., eds., _State of the World 1998_ (New York: W. W. Norton, 1998), p. 115.
. Halweil and Mastny, eds., _State of the World 2004_ , p. 28.
. Ibid., pp. 45, 120.
. Helena Norberg-Hodge, "Buddhism and the Global Economy," _Turning Wheel_ (Spring 1997): 13–17.
. Kalle Lasn, _Culture Jam_ (San Francisco: HarperCollins, 1999).
. Alan D. Kanner and Mary E. Gomes, "The All-Consuming Self," in _Ecopsychology_ , eds. Theodore Roszak, Mary E. Gomes, and Allen D. Kanner (San Francisco: Sierra Club Books, 1995).
. Bill McKibben, _The Age of Missing Information_ (New York: Random House, 1992).
. See for example, Roger Gottlieb, ed., _This Sacred Earth_ (New York: Routledge, 1996); J. Ronald Engel and Joan Gibb Engel, eds., _Ethics of Environment and Development_ (Tucson, AZ: University of Arizona Press, 1990); Mary Evelyn Tucker and John Grim, eds., _Worldviews and Ecology_ (Lewisburg, PA: Bucknell University Press, 1993); Richard Foltz, ed., _Worldviews, Religion, and the Environment_ , (Belmont, CA: Wordsworth, 2003). Regarding consumerism, see Paul Knitter and Chandra Muzaffar, eds., _Subverting Greed: Religious Perspectives on the Global Economy_ (Maryknoll, NY: Orbis, 2002).
. Gary Gardner et al., eds., _State of the World 2003_ (New York: W. W. Norton, 2003), pp. 152–75.
. Gabriel and Lang, _Unmanageable Consumer_. See chapter 9.
. Thich Nhat Hanh, _For a Future to Be Possible: Commentaries on the Five Wonderful Precepts_ (Berkeley: Parallax Press, 1993).
. Rita Gross, "Buddhist Resources for Issues of Population, Consumption, and the Environment," in _Buddhism and Ecology: The Interconnectedness of Dharma and Deeds_ , eds. Mary Evelyn Tucker and Duncan Ryuken Williams (Cambridge: Harvard University Press, 1997), pp. 291–312.
. P. A. Payutto, _Buddhist Economics: A Middle Way for the Marketplace_ , (Bangkok: Buddhadhamma Foundation, 1994); Sulak Sivaraksa, _Seeds of Peace_ (Berkeley: Parallax Press, 1992).
. See David Loy, "Pave the Planet or Wear Shoes? A Buddhist Perspective on Globalization," in _Subverting Greed_ , eds. Paul Knitter and Chandra Muzaffar (Maryknoll, NY: Orbis, 2002), pp. 58–76; David Loy and Jonathan Watts, "The Religion of Consumption," in _Mindfulness in the Marketplace_ , ed. Allan Hunt-Badiner (Berkeley: Parallax Press, 2002), pp. 93–104.
. Earlier collections include Allan Hunt-Badiner, ed., _Dharma Gaia_ (Berkeley: Parallax Press, 1990); Martine Batchelor and Kerry Brown, eds., _Buddhism and Ecology_ (London: Cassell Publishers, Ltd, 1992); Mary Evelyn Tucker and Duncan Ryuken Williams, eds., _Buddhism and Ecology_ (Cambridge: Harvard University Press, 1997); and Stephanie Kaza and Kenneth Kraft, eds., _Dharma Rain: Sources of Buddhist Environmentalism_ (Boston: Shambhala Publications, 2000).
Chapter 1: Desire, Delusion, and DVDs
. Buddhadasa Bhikkhu, _Heartwood of the Bodhi Tree_ (Boston: Wisdom Publications, 1994), p. 15.
Chapter 3: The Inner Pursuit of Happiness
. Lisabeth Cohen, _A Consumer's Republic: The Politics of Mass Consumption in Postwar America_ (New York: Alfred A. Knopf, 2003).
. Juliet Schor, _The Overspent American: Why We Want What We Don't Need_ (New York: HarperPerennial, 1998), p. 18.
. Juliet Schor, _The Overworked American: The Unexpected Decline of Leisure_ (New York: HarperCollins, 1992).
. Cohen, _Consumer's Republic_ , p. 403.
. Thomas Hine, _I Want That: How We All Became Shoppers_ (New York: Harper-Collins, 2002), p. 109.
. David Loy, _Lack and Transcendence: Existentialism, Buddhism, and Psychoanalysis_ (Berkeley: Asian Humanities Press, 1996).
. See Roger Rosenblatt, ed., _Consuming Desires: Consumption, Culture, and the Pursuit of Happiness_ (Washington, DC: Island Press, 1999).
. Manuel Castells, "The Informational Economy and the New International Division of Labor," in _The New Global Economy in the Information Age: Reflections on Our Changing World_ , Martin Carnoy et al. (University Park, PA: Pennsylvania State University Press, 1993), p. 19.
. Here I use the term _contemplation_ in a rather loose way as synonymous and interchangeable with the more widely used term _meditation_ , an English rendering of the Sanskrit term _dhyana_. Dhyana leads to and technically can be distinguished from an inner state of unitive awareness, called _samadhi_. The contemplative mode I am describing would include these two realms of dhyana and samadhi. I prefer _contemplation_ to _meditation_ , as the latter can be associated with use of the discursive intellect, as in Descartes's or Marcus Aurelius's _Meditations_. _To contemplate_ , on the other hand, is a Latin-based term that derives from the Greek _theorein_ , which means "to behold," or "to see," a state of awareness that more closely corresponds to what takes place in the Buddhist practice of sitting in silence.
. Dogen, "This Very Mind is Buddha" fascicle, _Shobogenzo_ (author's translation). For an alternate translation, see _The Eye and Treasury of the True Law_ , vol. 1, translated by Kosen Nishiyama and John Stevens (Tokyo: Nakayama Shobo, 1975), p. 19.
. This is also known as the _Sutra on Lovingkindness_. See Samuel Bercholz and Sherab Choedzin Koh, eds., _Entering the Stream: An Introduction to the Buddha and His Teachings_ (Boston: Shambala Publications, 1993), pp. 141–42.
. Cited in Alan Clements, _Instinct for Freedom: Finding Liberation through Living_ (Novato, CA: New World Library, 2002), pp. 91–92.
. Ibid., p. 108.
_Chapter 4: Young Buddhists in Shopping Shangri-la_
. James Silberstein, personal correspondence, February 9, 2003.
. Beliefnet.com, Teen Buddhist discussion board, May 17, 2003.
. Beliefnet.com, Teen Buddhist discussion board, May 16, 2003.
. Corey Flanders, personal correspondence, February 12, 2003.
. Dan Fisher, personal correspondence, February 20, 2003.
. Seunghee Ham, personal correspondence, February 20, 2003.
. "Convert Zen" is not a lineage but is a shorthand term for the style and culture of Zen that seems to be evolving among the predominantly Euro-American practice groups and centers.
. Jeff Wilson, personal correspondence, February 9, 2003.
. Beliefnet.com, Teen Buddhist discussion board, August 11, 2003.
. Connie Pham, personal correspondence, February 15, 2003.
. Flanders, personal correspondence, February 12, 2003.
. Wilson, personal correspondence, February 9, 2003.
. Beliefnet.com, Teen Buddhist discussion board, Summer 2003.
_Chapter 5: Marketing the Dharma_
. _Anguttara Nikaya_ , _Pathamalokadhamma Sutta_ (Sutta 5), _Metta Vagga_ (ch. 1), _Atthakanipaata_.
_Chapter 6: You Are What You Download_
. Thich Nhat Hanh, _For a Future to Be Possible: Commentaries on the Five Wonderful Precepts_ (Berkeley: Parallax Press, 1993).
_Chapter 7: Cultivating the Wisdom Gaze_
. Khenpo Karthar Rinpoche is the abbot of Karma Triyana Dharmacakra, Woodstock, New York. This quote is from a transcription of a talk given at his center in 2002.
. José Cabezón, "Singing Bowls and Power Beads: On the Commodification of Tibet" (unpublished paper presented at the symposium "Representing Tibet: A Symposium on the Representation of Tibetan Culture in the U.S.," University of Colorado, Boulder, CO, January 2000), p. 10.
. Quoted in ibid., p. 11.
. Chögyam Trungpa, _Cutting Through Spiritual Materialism_ (Boulder, CO: Shambhala Publications, 1973).
. _Materialism_ is a gloss of _kla-klo_ , which means "barbarian," especially a human being from an uncivilized area unreceptive to the compassionate and wise teachings of the Buddha.
. Chögyam Trungpa, _The Sadhana of Mahamudra, Which Quells the Mighty Warring of the Three Lords of Materialism and Brings Realization of the Ocean of Siddhas of the Practice Lineage_ (Halifax, NS: Nalanda Translation Committee, 1990), p. 6.
. Frances S. Adeney and Terry C. Muck, "Economic Growth vs. Human Well-Being: An Interview with John Cobb," _Buddhist-Christian Studies Journal_ 18 (1998): 77–88.
. John Cobb has devoted much of the last two decades to the untangling of these issues, and in his work with Herman Daly, former senior economist at the World Bank, has forged a penetrating critique of the economic theories that fuel the international economy. See Herman E. Daly and John B. Cobb Jr., _For the Common Good: Redirecting the Economy toward Community, the Environment, and a Sustainable Future_ (Boston: Beacon Press, 1994); and John B. Cobb Jr., _Sustaining the Common Good: A Christian Perspective on the Global Economy_ (Cleveland: Pilgrim Press, 1994).
. Kenneth Kraft, "Prospects of a Socially Engaged Buddhism," in _Inner Peace, World Peace: Essays on Buddhism and Nonviolence_ , ed. Kenneth Kraft (Albany: State University of New York Press, 1992), p. 12.
. Norberg-Hodge, "Buddhism and the Global Economy," _Turning Wheel_ (Spring 1997): p. 13.
. Jamgon Mipham, _Mkhas pa'i tshul la jug pa'i sgo zhes bya ba'i bstan bcos bzhugs so_ , published as _Gateway to Knowledge: The Treatise Entitled_ The Gate for Entering the Way of a Pandita _by Jamgon Mipham Rinpoche_ , vol. 1, trans. Erik Pema Kunsang (Hong Kong: Rangjung Yeshe Publications, 1997). This text is a digest of principal points of the compassionate and wise path of the bodhisattva drawn from the Indian and Tibetan traditions, presented in a systematic and highly condensed manner. My paper draws from the fourth chapter, "Dependent Origination," or _tendrel_ in Tibetan.
. Ibid., 4.1.
. Quoted in Norberg-Hodge, "Buddhism and the Global Economy," p. 13.
. Noam Chomsky, "Globalization: The New Face of Capitalism"(address at Boston College, Boston, MA, October 1999). See also Noam Chomsky, _Profit over People: Neoliberalism and Global Order_ (New York: Seven Stories Press, 1999).
. Chomsky, _Profit over People_ , pp. 13–15.
. Norberg-Hodge, "Buddhism and the Global Economy," pp. 13–14.
. Daly and Cobb, _For the Common Good_ , p. 89.
. Ibid., pt. 1, pp. 25–117.
. Chomsky, "Globalization" address, 1999. Derrick Jenson, "Driven by Desire: Why the Global Economy Won't Satisfy Us, an Interview with George Draffan," _The Sun_ (December 2001): 8.
. Chomsky, "Globalization" address, 1999.
. In _Santa Clara County v. Southern Pacific Railroad Company_ , the U.S. Supreme Court took it upon itself to rewrite the Constitution, granting to a corporation the rights guaranteed a person of equal protection under the law. A two-sentence assertion by a single judge elevated corporations in this way, laying the foundation for special protections of corporations that have formed the basis of the global economy, changing the course of history. David Korten, _The Post-Corporate World: Life after Capitalism_ (Bloomfield, CT: Kumarian Press, 1998), pp. 184–86.
. Ibid., p. 186.
. Mipham, _Gateway to Knowledge_ , 4.2, 4.7–19.
. Ju Mipham's text ( _Gateway to Knowledge_ , 4.2) uses an analysis of the twelve nidanas only for the inner analysis, saying that the outer analysis more appropriately looks at patterns of cause as in the sprouting of a seed or the interaction of the six elements or other cooperating conditions.
. Ibid., 4.14.
. Daly and Cobb, _For the Common Good_ , p. 88. They use the example of Pimples Carson, John Steinbeck's character in _The Wayward Bus_ , who spent half his income on treatments for acne and the other half on candy bars and sweets whose advertisements told him that a working man needed them for quick energy.
. Mipham, _Gateway to Knowledge_ , 4.8.
. Quoted in Judith Simmer-Brown, "Speaking Truth to Power: The Buddhist Peace Fellowship," in _Engaged Buddhism in the West_ , ed. Christopher Queen (Boston: Wisdom Publications, 1999), pp. 80–81.
. Mipham, _Gateway to Knowledge_ , 4.27.
. Ibid.
. The term is _anunayadrstikaruna_ , or "compassion based on emotionally-tinged views." Robert Thurman, trans., _The Holy Teaching of Vimalakirti_ (University Park: Pennsylvania State University Press, 1976), p. 46.
. Donald Rothberg, "Responding to the Cries of the World: Socially Engaged Buddhism in North America," in _The Faces of American Buddhism_ , Charles S. Prebish and Kenneth K. Tanaka, eds. (Los Angeles: University of California Press, 1999), pp. 282–83.
. Mipham, _Gateway to Knowledge_ , 4.43: "The one who perceives dependent origination with the eyes of discriminating knowledge will come to see the _dharmas_ possessing the natures of the eightfold noble path, and with the wisdom gaze which comprehends all objects of knowledge will perceive the _dharmakaya_ of buddhahood."
_Chapter 8: No River Bigger than_ Tanha
. Buddhadasa Bhikkhu, _Paramadhama_ , vol. 1 (Bangkok: Dhammadana Foundation, 1982), pp. 173–74 (translated from the Thai).
. We choose to use the old name Siam for the country now known as Thailand because the name Thailand implies authoritarianism, chauvinism, and irredentism. The country was called Siam until 1939, when the name was changed to Thailand. Then it reverted to the original name again in 1946. However, the country has officially been called Thailand ever since the military coup d'état in 1947. This new name signifies the crisis of traditional Siamese Buddhist values. Removing the name the country has carried for all its history has been an important step in the psychic dehumanization of its citizens, especially since the original name was replaced by a hybrid, anglicized word.
. Helena Norberg-Hodge, _Ancient Futures: Learning from Ladakh_ (San Francisco: Sierra Club Books, 1999).
. P. A. Payutto, _A Dictionary of Buddhism_ (Bangkok: Saha Dhammic Co., Ltd.: 2001), p. 211.
. Sulak Sivaraksa, www.sulak-sivaraksa.org.
. Buddhadasa Bhikkhu, _Dhammic Socialism_ , ed. Donald Swearer, 2nd ed. (Bangkok: Thai Inter-religious Commission for Development), 1993.
. Ibid.
. Buddhadasa, "A Notion of Buddhist Ecology," trans. G. Olsan, _Seeds of Peace_ (Bangkok) 3, no.2 (May 2530 [1987]).
. Sulak Sivaraksa, _Seeds of Peace, a Buddhist Vision for Renewing Society_ (Berkeley: Parallax Press, 1992), p. 102.
. Sivaraksa, www.sulak-sivaraksa.org.
. Payutto, _Dictionary of Buddhism_. These principles include: to hold regular and frequent meetings; to meet together in harmony, disperse in harmony, do business duties in harmony; not to break the agreed principles; to honor and respect the wise elders; to respect and treat women well; to perform proper rituals and spiritual practice; and to support those who practice for enlightenment.
. For a more detailed story of this monk, see Yano Sherry, "Phra Krusupajariyawat—Finding the Middle Path between Modern and Traditional," in _Socially Engaged Buddhism for the New Millennium_ , ed. Sulak Sivaraksa (Bangkok: Foundation for Children: 1999), pp. 148–93.
. Other such organizations are Bandang Tuburan in the Philippines and the Rural Reconstruction Alumni and Friends Association (RRAFA) in Thailand.
_Chapter 9: Taming the "I Want" Mind_
. There are six realms of unenlightened existence: devas, humans, and titans in the upper realms, animals, pretas (hungry ghosts), and hells in the lower realms.
. Translation of the Three Treasures that is used in the lineage of Roshi Philip Kapleau.
. Zenno Ishigami, ed., _Disciples of the Buddha_ (Tokyo: Kosei Publishing, 1989), p. 19.
. Bassui, _Mud and Water, a Collection of Talks by the Zen Master Bassui_ , trans. Arthur Braverman (San Francisco: North Point Press, 1989), p. 22.
. The Ten Cardinal Precepts, as phrased in the Harada-Yasutani lineage, are
1. Not to kill but to cherish all life
2. Not to take what is not given but to respect the things of others
3. Not to misuse sexuality but to be caring and responsible
4. Not to lie but to speak the truth
5. Not to cause others to use substances that confuse the mind or do so oneself but to keep the mind clear
6. Not to speak of the misdeeds of others but to be understanding and sympathetic
7. Not to praise oneself nor disparage others but to overcome one's own shortcomings
8. Not to withhold spiritual or material aid but to give them freely where needed
9. Not to indulge in anger but to exercise control
10. Not to revile the Three Treasures (the Buddha, the Dharma, and the Sangha) but to cherish and uphold them
. Cited in Francis Dojun Cook, _How to Raise an Ox_ (Los Angeles: Center Publications, 1978), p. 168.
. Layman P'ang, _The Recorded Sayings of Layman P'ang_ , trans. Ruth Fuller Sasaki, Yoshitake Iriya, and Dana R. Fraser (New York: Weatherhill, 1971), p. 19.
. Cook, _How to Raise an Ox_ , p. 192.
_Chapter 10: Penetrating the Tangle_
. Yiannis Gabriel and Tim Lang, _The Unmanageable Consumer_ (London: SAGE, 1995), chapter 9.
. Michael Schudson, "Delectable Materialism: Second Thoughts on Consumer Culture," in _The Ethics of Consumption_ , ed. David Crocker and Toby Linden (Lanham, MD: Rowman and Littlefield, 1998), pp. 249–68.
. Ibid, p. 258.
. Brian Halweil and Lisa Mastny, eds., _State of the World 2004_ , (New York: W. W. Norton), p. 18.
. Ibid.
. This paper draws on work developed earlier for the 2003 Buddhism and Ecology conference (Berkeley, CA) hosted by Ryukoku University of Kyoto and the Institute for Buddhist Studies, Berkeley, California.
. Christopher Chapple, quoted in Hammalawa Saddhatissa, _Buddhist Ethics_ (London: Wisdom Books, 1987), p. 75.
. See Andrew Cockburn, "21st Century Slaves," _National Geographic_ 204, no. 3: pp. 2–25.
. For a detailed review of the four types of clinging, see Watts, "Concocted Death: A Buddhist Deconstruction of the Religion of Consumerism in _Santi Pracha Dhamma_ ," (Bangkok: Santi Pracha Dhamma Institute, 2001), pp. 126–47.
. Kazuaki Tanahashi, ed., _Moon in a Dewdrop: Writings of Zen Master Dogen_ (San Francisco: North Point Press, 1985), p. 70.
. Shohaku Okumura, "To Study the Self," in _The Art of Just Sitting_ , ed. John Daido Loori (Boston: Wisdom Publications, 2002), p. 105.
. Ibid., p. 107.
. Ibid., p. 110.
. Hammalawa Saddhatissa, _Buddhist Ethics_ (London: Wisdom Books, 1987), pp. 73–74.
. For analysis of the issues facing Buddhists and vegetarian eating, see Kate Lawrence, "Nourishing Ourselves, Nourishing Others: How Mindful Food Choices Reduce Suffering," in _Mindfulness in the Marketplace_ , ed. Allan Hunt-Badiner, (Berkeley: Parallax Press, 2002).
. Quoted in Saddhatissa, _Buddhist Ethics_ , p. 77.
. For an introduction and compilation of the causation texts in the Nidanasamyutta, see Bhikkhu Bodhi, _The Connected Discourses of the Buddha_ , vol. 1 (Boston: Wisdom Publications, 2000), pp. 515–661.
. See Naomi Klein, _No Logo: No Space, No Choice, No Jobs_ (Toronto: Knopf Canada, 2000); and Alissa Quart, _Branded: The Buying and Selling of Teenagers_ (Cambridge, MA: Perseus, 2003).
. Green consumers are described as "LOHAS," people who lead Lifestyles of Health and Sustainability. According to _The State of the World 2004_ , this group now includes nearly one-third of adult Americans and in the year 2000 accounted for $230 billion in consumer purchases.
_Chapter 11: Form and Elegance with Just Enough_
. Shambhala Training is a meditation program that offers training in basic meditation intended for people of all religions or no religion. It is devoid of any specifically religious content so that people who have negative reactions to ritual or religious teachings can experience the benefits of meditation.
. The Venerable Khandro Rinpoche is one of very few women gurus recognized by the traditional Tibetan religious establishment and perhaps the only such woman teacher who teaches in English and travels internationally. She is considered to be one in the sequence of rebirths of a lineage of important women teachers including Yeshe Tsogyel. She was born in India as the daughter of Mindrolling Trichen Rinpoche, an important Nyingma lineage holder, and was recognized at an early age and trained in the traditional manner for high lamas.
. Stupas are found universally throughout the Buddhist world, including the so-called "pagodas" of East Asian Buddhism. They began in ancient Buddhist India as reliquary mounds, where the ashes or relics of great teachers were placed. They became places of pilgrimage, and religious institutions often grew up around them. The largest stupa in North America is the Great Stupa of Dharmakaya Which Liberates Upon Seeing at Shambhala Mountain Center in northern Colorado, which enshrines some of the relics of Chögyam Trungpa Rinpoche. For more information, see Adrian Snodgrass, _The Symbolism of the Stupa_ (Ithaca, NY: Southeast Asia Program, 1985).
. David Loy, "The Religion of the Marketplace," in _Visions of a New Earth: Religious Perspectives on Population, Consumption, and Ecology_ , eds. Harold Coward and Daniel C. Maguire (Albany: State University of New York Press, 2000), pp. 15–28.
. I have used this argument in discussing ways to encourage population control. See Rita Gross, "Toward a Buddhist Environmental Ethic," in Coward and Maguire, eds., _Visions of a New Earth_ , pp. 147–60.
. As used in Shambhala Buddhism (and Tibetan Buddhism in general), this stage is called Hinayana, a term that has a precise technical meaning referring to the first stage of the path, understood as a long journey eventually including the Mahayana and perhaps the Vajrayana stage of practice. While the Hinayana teachings of Tibetan Vajrayana Buddhism are similar to those of contemporary Theravada Buddhism, the term is not used to refer to those Buddhist schools.
. From the daily chant book for Shambhala Buddhism (unpublished source).
. The Shambhala teachings of Shambhala International refer to the teachings as "the sacred path of the warrior." Many of the teachings draw on the shamanic heritage of Tibet as well as the heritage of Gesar of Ling, the hero of Tibet's national epic. "Warriorship here does not refer to making war on others. Aggression is the source of our problems, not the solution. Here the word 'warrior' is taken from the Tibetan _pawo_ , which literally means 'one who is brave.'" Chögyam Trungpa, _Shambhala: The Sacred Path of the Warrior_ (Boston: Shambhala Publications, 1988), p. 28.
. Ju Gampopa, _Gems of Dharma: Jewels of Liberation_ , trans. Ken Holmes and Katia Holmes (Forres, Scotland: Altea, 1995), pp. 169–74.
. Vajrayana Buddhism includes recognition of and practices relating to many beings called protectors. The function of protectors in Vajrayana Buddhism is literally to protect and serve the dharma and dharma practitioners. Some of the protectors are considered to be wrathful manifestations of great buddhas and bodhisattvas. Others are local spirits who obstructed the spread of Buddhism in Tibet but were tamed and converted to become dharma protectors by great teachers such as Padmasambhava. Their appearance is always wrathful and conventionally frightening. Daily practices regarding the protectors include a simple offering, usually of tea and grains, and a series of chants.
. Shambhala Buddhism daily chant book (unpublished source).
_Chapter 12: Consuming Time_
. Joe Robinson, "Four Weeks' Vacation," _Utne Reader_ (September–October 2000).
. Robert Levine, _A Geography of Time_ (New York: Basic Books, 1997), p. 107.
. Perhaps it is no coincidence that Ende later became interested in Buddhism. He visited Japan several times, and his first visit in 1977 included a discussion with a Zen priest.
. _Samyutta Nikaya_ 1.10.
. Nagarjuna, _Sunyatasaptati_ , v. 58 (my version of this famous verse).
. Nagarjuna, _Mulamadhyamikakarika_ 13:5, in Candrakirti, _Lucid Exposition of the Middle Way_ , trans. Mervyn Sprung (Boulder, CO: Prajna Press, 1979).
. Dogen, quoted in Reiho Matsunaga, _The Soto Approach to Zen_ (Tokyo: Layman Buddhist Society Press, 1958), p. 68.
. Dogen, quoted in Kazuaki Tanahashi, ed., _Moon in a Dewdrop: Writings of Zen Master Dogen_ (San Francisco: North Point Press, 1985) excerpts from pp. 76–80; trans. altered.
. Ibid., pp. 70–71.
. E. E. Evans-Pritchard, _The Nuer_ (New York: Oxford University Press, 1969), p. 103.
. Anthony Aveni, _Empires of Time_ (New York: Kodansha, 1995), p. 135.
. Ibid., p. 331.
. Damian Thompson, _The End of Time_ (London: Minerva, 1996), p. 325.
. Ibid., p. 332.
. Developed in depth in David Loy, _Lack and Transcendence: The Problem of Death and Life in Psychotherapy, Existentialism and Buddhism_ (New York: Humanities Press, 1996) and David Loy, _A Buddhist History of the West: Studies in Lack_ (Albany: State University Press of New York, 2002).
. Quoted in Levine, _Geography of Time_ , pp. 204–5.
. See a summary of this talk at <http://www3.plala.or.jp/mig/talk-uk.html>, section IV.
_Chapter 13: Three Robes Is Enough_
. _Majjhima Nikaya_ 2.13–16, "The Discourse on All the Outflows."
. _Vinaya_ Nis. Pac.1.
. _Sutta Nipata_ 2.4, _Mangala Sutta_ , "The Highest Blessings."
. Ibid., 1.8, _Metta Sutta_ , "The Buddha's Words on Loving-Kindness."
. P. A. Payutto, _Buddhist Economics: A Middle Way for the Marketplace_ (Bangkok: Saha Dhammic Co., Ltd., 1994), pp. 69–70.
. _Dhammapada_ 183–85.
. A number of Ajahn Buddhadasa's teachings on this topic can be found in his book _Dhammic Socialism_ and also in Santikaro Bhikkhu, "Buddhadasa Bhikkhu: Life and Society through the Natural Eyes of Voidness," in _Engaged Buddhism: Buddhist Liberation Movements in Asia_ , eds. Christopher Queen and Sallie B. King (Albany: State University of New York Press, 1996), pp. 147–94.
. _Anguttara Nikaya_ 8.41, _Uposatha Sutta_.
. Ibid., 8.53, "The Dhamma in Brief."
. _Digha Nikaya_ 16.1.11, "The Discourse on the Buddha's Last Days."
. Payutto, _Buddhist Economics_.
. _Jataka_ V 382.
. Ibid., 393–411.
. _Anguttara Nikaya_ 5.41, abbrev.
. Ibid., 4.62, abbrev.
. _Samyutta Nikaya_ 3.19.
. _Cullavagga_ 11.13–14.
. _Anguttara Nikaya_ 8.54, "A Layperson's Welfare."
_Chapter 14: Practicing Generosity in a Consumer World_
. This essay was begun in a cabin in Ontario, Canada, provided by Arrow River Forest Hermitage. At the time of writing, I was still a practicing monk. While there, along with daily meditation and translation work, I pondered Lewis Hyde's _The Gift: Imagination and the Erotic Life of Property_ (New York: Vintage, 1979). As my country banged its war drums in preparation for another invasion of Iraq, it was a gift to dwell for a few weeks in a country more known for its peacekeeping efforts than for making and dropping bombs. All of these inform and move this consideration of dana.
. Throughout this article, I understand _sangha_ in the inclusive sense that includes women and householders, which I believe is in line with the original emphasis— _supatipanno_ , those who practice well. As refuge it refers to the "noble ones," those who practice on the highest level and have realized the fruitions of the path. Cf. next note.
. Sagathavagga, Sakkasmayutta (11), no.15, verses 916–17, in _The Connected Discourses_ , trans. Bhikkhu Bodhi (Boston: Wisdom Publications, 2000), p. 333. Here, "Sangha" refers to the four kinds of noble ones, the exemplars of dhammic life and the leaders of the community of the Buddha's disciples.
. Visuddhimagga ix, 124, Trans. Bhikkhu Nanamoli (Kandy, Sri Lanka: Buddhist Publication Society, 1991), pp. 352–53.
. Adapted from a haiku proposed by David Loy, Think Sangha colleague and profound elucidator of the lack running through our lives. See David Loy, _A Buddhist History of the West: Studies in Lack_ (Albany: State University Press of New York, 2002).
. See the well-known analysis of violence found in the _Mahanidana Sutta_ (D.ii.58–59).
. The following discussion owes much to the work of Phra Phaisan Visalo, a close friend and colleague whose many excellent writings have yet to be translated into English.
. Translating _punna_ as "merit" tends to distort its meaning, I believe, and may betray a pecuniary spirit that has crept in along with the growing role of money. "Goodness" better conveys the original meaning of _boon_.
. Kamala Tiyavanich's _The Buddha in the Jungle_ (Chiang Mai, Thailand: Silkworm, 2003) provides abundant examples.
. Such mass produced and poor quality food contributes to the poor health common among monks today.
. Luang Por Khoon became famous during the 1990s economic boom when rumors spread of people (including royalty) getting rich after making donations to him. Wat Phra Thammakai has unabashedly embraced capitalism, often distorting the Buddha's teaching to win followers among the merchant and professional classes. In a still unresolved scandal concerning misuse of temple funds, the abbot personally invested in gold mines, which he justified as more efficient in producing devotional objects "marketed" (their own terminology) to devotees.
. See the _Parinibbana Sutta_ (D.ii.80; numerous translations available) and _Kosambiya Sutta_ (M.i.322).
. _Career_ originally meant "a course on which horses race" and then "rapid and continuous course of action," especially one involving professional advancement.
_Chapter 15: Wash Your Bowls_
. Shoyoroku, _The Book of Serenity_ , case 39, trans. Thomas Cleary (Hudson, NY: Lindesfarne Press, 1990), p. 173.
. Mumonkan, _The Gateless Barrier_ , case 7, trans. Robert Aitken (San Francisco: North Point Press, 1990), p. 54.
. Dogen, "Instructions for the Tenzo," in Kazuaki Tanahashi, ed., _Moon in a Dewdrop: Writings of Zen Master Dogen_ (San Francisco: North Point Press, 1985), pp. 53–66.
. This phrase is used in the priest ordination ceremony at San Francisco Zen Center.
. Shoyoroku, _Book of Serenity_ , case 25, p. 108.
. Dogen, "Bodhisattva's Four Methods of Guidance," in Tanahashi, ed., _Moon in a Dewdrop_ , p. 45.
_Chapter 16: Green Power in Contemporary Japan_
. An extensive survey of the origins and development of Japanese consumer and environmental organizations since the 1960s can be found in Margaret A. McKean, _Environmental Protest and Citizen Politics in Japan_ (Berkeley: University of California Press, 1981). These organizations include labor unions, consumer buying clubs, associations of housewives, and consumer health organizations.
. This paper draws on work developed earlier for the 2003 Buddhism and Ecology conference (Berkeley, CA) hosted by Ryukoku University of Kyoto and the Institute for Buddhist Studies, Berkeley, California.
. The discussion of the Senryuji Temple case comes from an interview with its abbot, Shoei Sugawara, at Senryuji Temple, August 8, 2003.
. See Sotoshu Shumucho, ed., _Jinken, heiwa, kankyo "Green Plan" no susume_ [Human Rights, Peace, and the Environment: Promoting the "Green Plan"] (Tokyo: Sotoshu shumucho, 1996). The pamphlet highlights Dogen's appreciation of nature.
. See Sotoshu Shumucho, ed., _Green Plan: Kodo no tame no Q &A_ [The Green Plan: Q&A for Action] (Tokyo: Sotoshu shumucho, 1998), questions 3–4, 6–14, 30. These verses can be found on most pamphlets, including Sotoshu Shumucho, ed., _Chikyu o sukue!: Seikatsu ni ikasu Green Plan gokun_ (Tokyo: Sotoshu shumucho, n.d.).
. See editorial, "Idenshi kumikae shokuhin no hyoji gimu settei," _Kyara_ 44 (2001): 29–33.
. See Sotoshu, _Green Plan_ , questions 15–30.
. The biographical data on Okochi comes from his article, "NGO to jiin no tachiba kara," _Bukkyo Times_ (May 14, 1998): 7, as well as from interviews I conducted with him in July and August 2003 at Jukoin temple.
. See the Jukoin Temple Web page <http://oa145309.awmi2.jp/page-262.html>, "The Citizen's Strategy for Creating a New World," p. 2.
. Ibid.
. On Aoki's work protecting Harima Bay, see Keisuke Aoki, _Edo to kokoro: Kankyo hakai kara jodo e_ [The Impure Land and One's Mind: From Environmental Destruction to the Creation of a Pure Land] (Tokyo: Fujiwara shobo, 1997), pp. 59, 73.
. Ibid., in a subsection of chap. 2.
. Ibid., pp. 146, 229.
. See the Jukoin Temple Web page <http://oa145309.awmi2.jp/page-261.html>, p. 1.
. Many of the details on the solar panel power plant project can be found in Okochi Hideto, "Shimin ga tsukuru taiyoko hatsudensho: Shiminritsu Edogawa daiichi hatsudensho, tada ima kensetsuchu," _Shigen kankyo taisaku_ 35, no. 3 (1999): 44–46.
. See Jukoin Temple Web page <http://oa145309.awmi2.jp/page-262.html>, "The Citizen's Strategy for Creating a New World," p. 3.
. See <http://oa145309.awmi2.jp/page-261.html>, p. 2.
. See Rinnoji, ed., _Kankyo no tame ni_ [For the Sake of the Environment], video (Sendai, Japan: Rinnoji, 2003), and their Web site, <http://www.rinno-ji.or.jp>.
_Chapter 17: Mutual Correction_
. For an accessible overview of the current challenges, see Edward O. Wilson, _The Future of Life_ (New York: Alfred A. Knopf, 2002).
. See Jacques Gernet, _Buddhism in Chinese Society: An Economic History from the Fifth to the Tenth Centuries_ , translated and updated by Franciscus Verellen (New York: Columbia University Press, 1998).
. Ryukoku University Translation Center, trans., _The Sutra of Contemplation on the Buddha of Immeasurable Life as Expounded by Sakyamuni Buddha_ (Kyoto: Ryukoku University, 1984), p. 37. Cf. Luis Gomez, trans., _The Land of Bliss: The Paradise of the Buddha of Measureless Light_ (Honolulu: University of Hawaii Press, 1996).
. On May 12, 1998, Nike CEO Philip Knight reported to the National Press Club a plan to improve labor conditions among his company's six hundred subcontractors. While acknowledging Nike's past, which was "synonymous with slave wages, forced overtime and arbitrary abuses," he proposed reforms in health and safety, child labor, workers' education, and independent monitoring. Even though critics remain, such as Naomi Klein in her book _No Logo_ , others, such as the consumer watch group Global Alliance, have praised Nike for its efforts.
. Gernet, _Buddhism in Chinese Society_ , trans. and updated by Franciscus Verellen (New York: Columbia University Press, 1998).
. In his book _Unequal Protection: The Rise of Corporate Dominance and the Theft of Human Rights_ (Emmaus, PA: Rodale, 2002), Thom Hartmann found that the claim that corporations were fictive persons did not exist in the ruling made by the judge in the 1886 case but was only a heading that was given to the case by the court reporter.
. Ironically, this decision was made fifty years to the day after Franklin D. Roosevelt signed Executive Order no. 9066 on February 19, 1942, which led to the detention in prison camps of 35,327 Buddhist Americans of Japanese ancestry. This information was given to me by Alfred Bloom, who participated in the 1992 meeting.
. See Dameon Keown, Charles Prebish, and Wayne Husted, eds., _Buddhism and Human Rights_ (Surrey, UK: Curzon, 1998).
. See, for example, Aung San Suu Kyi, "In Quest for Democracy," in _Freedom from Fear_ , Aung San Suu Kyi et al. (New York: Penguin, 1995), pp. 174–75.
. See a recent translation of "The Scripture of Brahma's Net" by Hubert Nearman, in _Buddhist Writings on Meditation and Daily Practice_ (Mount Shasta, CA: Shasta Abbey, 1994), pp. 49–188.
. See the English translation of the _Upasaka Sutra_ by Heng-ching Shih, _The Sutra on the Upasaka Precepts_ (Berkeley: Bukkyo Dendo Kyokai, 1991). Buddhist ethics are designed for two kinds of people: monastics and lay society. Since Buddhism has been dominated by the monastic community more than any other religion, principles of behavior for society are underdeveloped and have tended to urge laity to mimic monastics or to enter the monastery. A very different approach is taken by this important early Mahayana treatise for lay Buddhists, which elevates the life of the laity above the monastic community, since the laity can give food, medicine, and practical help, whereas the monks can give only words. See also Ono Hodo, _Daijo kaikyo no kenkyu_ [Studies on Mahayana Ethics] (Tokyo: Risosha, 1954).
. The move to include a multilateral agreement on investment (MAI) clause into the charter for the World Trade Organization in the late 1990s was finally withdrawn in the face of opposition, especially by the Council of Canadians and the International Forum on Globalization (IFG), and as demonstrated in the battle in Seattle in 1999.
. International Forum on Globalization, _Alternatives to Economic Globalization: A Better World is Possible_ (San Francisco: Berrett-Koehler, 2002), pp. 60–61;William Lim, "Glocalizing Traditions," in _Socially Engaged Spirituality_ , ed. David Chappell (Bangkok: Sathirakoses-Nagapradipa Foundation, 2003), pp. 564–66.
. Michael Rothschild, _Bionomics: Economy as Ecosystem_ (New York: Henry Holt, 1990), p. 303.
. See the chapter "From Egalitarianism to Kleptocracy," in Jared Diamond, _Guns, Germs and Steel_ , (New York: Norton, 1999), pp. 265–92.
. The decline of democracy because of the global economy is analyzed by Benjamin R. Barber, _Jihad vs. McWorld_ (New York: Ballantine, 1996).
. Charles Gray, "Corporate Goliaths: Sizing Up Corporations and Governments," _Multinational Monitor_ (June 1999): 26–27.
. See the brilliant and timely work by David C. Korten, _When Corporations Rule the World_ (San Francisco: Berrett-Koehler, 1995).
. Harvey B. Aronson, _Love and Sympathy in Theravada Buddhism_ (Delhi: Motilal Banarsidass, 1980), chap. 2.
. Dalai Lama, _Ethics for the New Millennium_ (New York: Riverhead, 1999), pp. 63–65.
. Susan Sontag, _Regarding the Pain of Others_ (New York: Farrar, Straus and Giroux, 2002), pp. 78–80.
. Herman E. Daly and John B. Cobb Jr., _For the Common Good: Redirecting the Economy toward Community, the Environment, and a Sustainable Future_ (Boston: Beacon Press, 1994), pp. 443–507.
. For full Earth Charter text and materials, see www.earthcharterusa.org.
Contributors
**Ajahn Amaro** studied meditation under Ajahn Chah in Thailand and ordained as a bhikkhu in 1979. After residing for many years at Amaravati Buddhist Centre near London, he helped establish Abhayagiri Monastery in California and is now the co-abbot. His books include _Silent Rain_ and _The Pilgrim Kamanita_.
**David W. Chappell** is Professor of Comparative Religion at Soka University of America and Professor Emeritus, University of Hawaii. He was founding editor (1981–1995) of the _Journal of Buddhist-Christian Studies_ and has published many books on Buddhism and its relation to society.
**Pema Chödrön** is a fully ordained nun and the resident teacher at Gampo Abbey in Cape Breton, Nova Scotia. She is the author of _The Wisdom of No Escape_ , _Start Where You Are_ , _When Things Fall Apart_ , and _The Places That Scare You_. Her most recent book is _Comfortable with Uncertainty_.
**Thubten Chödrön** studied with Ven. Lama Yeshe and Ven. Zopa Rinpoche, receiving full ordination in 1986 in Taiwan. After teaching in Seattle with Dharma Friendship Foundation (DFF) for nine years, she founded Sravasti Abbey in Idaho. Her books include _Open Heart, Clear Mind_ ; _Buddhism for Beginners_ ; _Working with Anger_ ; and _Taming the Monkey Mind_.
**Norman Fischer** is a Zen priest and poet. He is a former abbot of the San Francisco Zen Center and the founder of and teacher at the Everyday Zen Foundation. He is the author of _Taking Our Places: The Buddhist Path to Truly Growing Up_ ; his latest book of verse is _Slowly but Dearly_.
**Joseph Goldstein** is a cofounder of the Insight Meditation Society, the Forest Refuge, and the Barre Center for Buddhist Studies. He is the author of _One Dharma: The Emerging Western Buddhism_ , _Insight Meditation: The Practice of Freedom_ , and _The Experience of Insight_. He has been teaching insight and lovingkindness meditation retreats worldwide since 1974.
**Linda Goodhew** is an associate professor in the Department of English Literature and Language, Gakushuin University, Tokyo. A different version of the article on Momo and Dogen is included in the book _Fantastic Dharma: New Buddhist Myth in Modern Fantasy_ , forthcoming from Wisdom Publications.
**Sunyana Graef** , a sanctioned heir of Roshi Philip Kapleau, established the Vermont Zen Center in 1988 and is the head teacher there. She also teaches at the Toronto Zen Center and at the Casa Zen in Costa Rica. She is married, has two grown daughters, and lives in Shelburne, Vermont.
**Rita M. Gross** is internationally known for her work on Buddhism and gender, including her book _Buddhism after Patriarchy: A Feminist History, Analysis and Reconstruction of Buddhism_. She has also written widely on Buddhism and contemporary social issues and is a senior teacher of Shambhala Buddhism, a network of meditation centers founded by Chögyam Trungpa.
**Ruben L. F. Habito** was born and raised in the Philippines and lived in Japan for twenty years before coming to the United States in 1989. Author of _Living Zen, Loving God and Healing Breath: Zen Spirituality for a Wounded Earth_ , he is resident teacher at Maria Kannon Zen Center in Dallas, Texas, and also teaches at Perkins School of Theology, Southern Methodist University.
**Pracha Hutanuwatr** is Deputy Director of Santi Pracha Dhamma Institute and Program Director of the Grassroots Leadership Training project in Bangkok, Thailand. He has written a biography of Buddhadasa in Thai and worked closely with Sulak Sivaraksa on many initiatives, including the Spirit in Education Movement and the International Network of Engaged Buddhists.
**Stephanie Kaza** is Associate Professor of Environmental Studies at the University of Vermont, where she teaches religion and ecology, ecofeminism, and unlearning consumerism. She is a long-time Zen student and the author of _The Attentive Heart_ and coeditor (with Kenneth Kraft) of _Dharma Rain: Sources of Buddhist Environmentalism_.
**Sumi Loundon** is Assistant Director at the Barre Center for Buddhist Studies and editor of _Blue Jean Buddha: Voices of Young Buddhists_. Sumi received a master's degree from Harvard Divinity School, with training in Buddhist studies and Sanskrit. She lives with her husband in Barre, Massachusetts.
**David Loy** is a professor in the Faculty of International Studies, Bunkyo University, Chigasaki, Japan, and a longtime Zen student. He has written numerous articles on socially-engaged Buddhism in the modern context. His books include _A Buddhist History of the West: Studies in Lack_ and _The Great Awakening: A Buddhist Social Theory_.
**Jane Rasbash** lives in Scotland and works in the field of sustainable development and engaged Buddhism, with extensive involvement in Southeast Asia with the Spirit in Education Movement. She has also served as codirector of the Grassroots Leadship Training program in Burma and as executive secretary to the Alternatives to Consumerism conferences in Thailand.
**Santikaro** ordained as a Theravada bhikkhu in 1985 to study under Buddhadasa Bhikkhu in Thailand. He lived at Suan Mokkh Temple until 1999 and spent nineteen years as a bhikkhu. Since disrobing, he continues his work developing Liberation Park, a Dhamma study center in Oak Park, Illinois.
**Judith Simmer-Brown** is a senior teacher of the lineage of Chögyam Trungpa and professor of Religious Studies at Naropa University in Boulder, Colorado. Her books include _Dakini's Warm Breath: The Feminine Principle in Tibetan Buddhism_ and the coedited volume _Benedict's Dharma: Buddhists Reflect on the Rule of Saint Benedict_.
**Duncan Ryuken Williams** is Assistant Professor of East Asian Buddhism at the University of California–Irvine and an ordained Soto Zen priest. He is the author of a monograph entitled _The Other Side of Zen: A Social History of Soto Zen Buddhism in Tokugawa Japan_ and coeditor of _American Buddhism_ and _Buddhism and Ecology_.
**Diana Winston** is a writer, activist, teacher, and the founder of the Buddhist Alliance for Social Engagement (BASE) program. She is the author of _Wide Awake: A Buddhist Guide for Teens_. She served as Associate Director of Buddhist Peace Fellowship though 2002 and is now training as a vipassana teacher with Jack Kornfield.
Sign up to learn more about our books and receive special offers from Shambhala Publications.
Or visit us online to sign up at shambhala.com/eshambhala.
| {
"redpajama_set_name": "RedPajamaBook"
} | 4,246 |
{"url":"https:\/\/www.mail-archive.com\/git@vger.kernel.org\/msg41518.html","text":"Re: [PATCH] Fix safe_create_leading_directories() for Windows\n\nSebastian Schuberth <sschube...@gmail.com> writes:\n\n> On 02.01.2014 20:55, Junio C Hamano wrote:\n>\n>> Thanks; the conclusion is correct --- you need a good commit\n>> message in the recorded history. That does not have anything to do\n>> with integrating with pulling from subsystem maintainers, which we\n>> regularly do.\n>\n> I'll send a v2 which adds a proper commits message inline.\n>\n>> Perhaps with s|Linux|POSIX|, but more importantly, was there a\n>> specific error scenario that triggered this change?\n>\n> Yes, cloning to a non-existent directory with Windows paths fails like:\n>\n> fatal: could not create work tree dir 'c:\\foo\\bar'.: No such file or directory\n\nOK. That was why I wanted to see (and Dscho correctly guessed) a\ngood description in the proposed log message to see what problem the\nchange is trying to address, so that we can judge if the change is\ntackling the right problem.\n\n> Seems like the path to clone to is taken as-is from argv in\n> cmd_clone(). So maybe another solution would be to replace all\n> backslashes with forward slashes already there?\n\nThat sounds like a workable alternative, and it might even be a\npreferable solution but if and only if clone's use of the function\nto create paths that lead to a new working tree location is the only\n(ab)use of the function. That was what I meant when I said \"it may\nbe that it is a bug in the specific caller\". AFAIK, the function\nwas meant to be used only on paths we internally generate, and the\npaths we internally generate all are slash separated, in line with\nhow paths are stored in the index.\n\nIf we are going to change the meaning of the function so that it can\nnow take any random path in platform-specific convention that may be\nincompatible with the internal notion of paths Git has (i.e. what is\npassed to safe_create_leading_directories() may have to be massaged\ninto a slash-separated form before it can be used in the index and\nparsed to be stuffed into trees), it is fine to do so as long as all\nthe codepaths understands the new world order, but my earlier \"git\ngrep\" hits did not tell me that such a change is warranted.\n\nThanks.\n--\nTo unsubscribe from this list: send the line \"unsubscribe git\" in\nthe body of a message to majord...@vger.kernel.org\nMore majordomo info at http:\/\/vger.kernel.org\/majordomo-info.html","date":"2016-10-24 13:26:08","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6811123490333557, \"perplexity\": 4142.660107130295}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2016-44\/segments\/1476988719566.74\/warc\/CC-MAIN-20161020183839-00042-ip-10-171-6-4.ec2.internal.warc.gz\"}"} | null | null |
@implementation KKBaseTransition
#pragma mark - 初始化
- (instancetype)init
{
return [self initWithDuration:0.5 options:0];
}
- (instancetype)initWithDuration:(NSTimeInterval)duration options:(UIViewAnimationOptions)options
{
if (self = [super init]) {
self.duration = duration;
self.options = options;
}
return self;
}
#pragma mark - 实现动画代理
// 动画执行时间
- (NSTimeInterval)transitionDuration:(id<UIViewControllerContextTransitioning>)transitionContext
{
return self.duration;
}
- (void)animateTransition:(id<UIViewControllerContextTransitioning>)transitionContext
{
// 子类实现
}
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,954 |
package org.keycloak.crypto;
public enum KeyUse {
SIG("sig"),
ENC("enc");
private String specName;
KeyUse(String specName) {
this.specName = specName;
}
public String getSpecName() {
return specName;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,875 |
module RDL::Type
class SingletonType < Type
attr_accessor :val
attr_reader :nominal
@@cache = {}
@@cache.compare_by_identity
class << self
alias :__new__ :new
end
def self.new(val)
t = @@cache[val]
return t if t
t = self.__new__ val
return (@@cache[val] = t) # assignment evaluates to t
end
def initialize(val)
@val = val
@nominal = NominalType.new(val.class)
end
def ==(other)
return false if other.nil?
other = other.canonical
return (other.instance_of? self.class) && (other.val.equal? @val)
end
alias eql? ==
def match(other)
other = other.canonical
other = other.type if other.instance_of? AnnotatedArgType
return true if other.instance_of? WildQuery
return self == other
end
def hash # :nodoc:
return @val.hash
end
def to_s
if @val.instance_of? Symbol
":#{@val}"
elsif @val.nil?
"nil"
else
@val.to_s
# "Singleton(#{@val.to_s})"
end
end
def <=(other)
return Type.leq(self, other)
end
def member?(obj, *args)
t = RDL::Util.rdl_type obj
return t <= self if t
return true if obj.nil?
obj.equal?(@val)
end
def instantiate(inst)
return self
end
def widen
return self
end
def copy
return self
end
def satisfies?
yield(val)
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,264 |
Dillinja "Feel My Pain" … You can get the full playlist on our Vibes Promotion Blog.
This entry was posted on Monday, September 26th, 2011 at 5:40 pm and is filed under Podcast. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,592 |
Building on Pennsylvania's commitment to combatting the state's growing heroin epidemic, Senator Wayne Langerholc, Jr. (R-35) will be introducing legislation that will establish a pilot program to help individuals in recovery obtain meaningful employment opportunities.
Langerholc's legislation will create the "Recovery to Work Pilot Program" to connect individuals in recovery with high-priority occupations through local workforce development boards.
Langerholc said the pilot program will be spearheaded by the Department of Labor and Industry with the assistance of the departments of Health, Community and Economic Development, and Drug and Alcohol Programs, as well as the Pennsylvania Commission on Crime and Delinquency.
These departments will develop a plan for the local workforce development boards to work with the treatment and recovery community as well as local employers and training providers to offer job training and employment opportunities to individuals in recovery.
Langerholc added that Pennsylvania is heading in the right direction with its continued attention to this serious epidemic, including the governor's recent declaration of the crisis as a public health emergency. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,452 |
Free US shipping $45+ || Free int'l shipping $75+
Eyeshadow Palettes Menu
Take Me To... Istanbul
Take Me To... Santorini
Take Me To... Paris
Take Me To... Los Angeles
Take Me To... Stockholm
Take Me To... Tokyo
Take Me To... Hong Kong
Hustle & Bustle #1
Bundle 1: All 8 Eyeshadow Palettes
Bundle 2: All 6 "Take Me To..." Palettes
Bundle 3: All 2 "Hustle & Bustle" Palettes
Mascara Menu
Hidden Talent Mascara
Cheeks Menu
Blushes Menu
Take The Risk Or Lose The Chance
Bundle: All 4 "The Motto" Blushes
Lipsticks Menu
Bundle: All 8 "Power Charms" Lipsticks
Take Me To... Menu
Eye Am Unique
Eye Am Unique Menu
Hustle & Bustle
Hustle & Bustle Menu
The Motto
The Motto Menu
Power Charms
Power Charms Menu
Call Me Mavie.
Variety Bundle: The Daily Trio
Variety Bundle: Eye Travel
Variety Bundle: Eye Hustle
Variety Bundle: Eye Love Me
Variety Bundles
Variety Bundles Menu
Variety Bundle: Call Me Mavie
2019 Holiday Giveaway Official Rules
NO PURCHASE IS NECESSARY TO ENTER OR WIN.
The "2019 Holiday Giveaway" (the "Campaign") on @maviecosmetics is sponsored by Mavie. LLC. ("Sponsor") and governed by these rules ("Official Rules").
By participating in the sweepstakes, the entrant agrees to abide by these Official Rules, including by meeting all eligibility requirements, and understands that the results of the sweepstakes, as determined by Sponsor and its agents, are final in all respects. The Campaign is subject to all federal, state and local laws and regulations and is void where prohibited by law.
This promotion is in no way sponsored, endorsed or administered by, or associated with, Facebook, Instagram, or Twitter. Any questions, comments or complaints regarding the promotion should be directed to Sponsor, not Facebook, Instagram, or Twitter.
1. Eligibility: The Campaign is open to legal residents of the United States, who are eighteen (18) years of age or older at the time of entry. Employees of Mavie. LLC, its affiliates, subsidiaries, advertising and promotion agencies, and suppliers (collectively the "Employees"), and immediate family members and/or those living in the same household of Employees are not eligible to participate in the Campaign.
2. Campaign Period: Entries will be accepted online starting on December 19, 2019, at 10:00 AM Pacific Time and ending on December 25, 2019, at 12:00 AM Pacific Time. Entries must be received by December 25, 2019, at 12:00 AM Pacific Time.
3. How to Enter: The Campaign must be entered by following the rules on the designated Instagram post. Entries that are incomplete may be disqualified at the sole discretion of Mavie. LLC. You may enter more than once. If you use fraudulent methods or otherwise attempt to circumvent the rules, your submission may be removed from eligibility at the sole discretion of Mavie. LLC.
4. Prize: There will be two (2) winners only: One (1) winner on @maviecosmetics and one (1) winner on @nurseluxe on Instagram. Each of the winners (the "Winner") will receive one (1) "Take Me To... Santorini" eyeshadow palette; one (1) "Take Me To... Tokyo" eyeshadow palette; one (1) "Take Me To... Hong Kong" eyeshadow palette; one (1) NurseLuxe November 2019 Box. The prizes are non-transferable, and no cash equivalent is permitted. Any and all prize-related expenses, including without limitation any and all federal, state, and/or local taxes, shall be the sole responsibility of Winner.
5. Winner Selection and Notification: All eligible entries received during the Campaign Period will gathered into a database. Two (2) winners - one (1) on @maviecosmetics and one (1) on @nurseluxe - will be chosen at random. The odds of winning depend on the number of eligible entries received. The winner on @maviecosmetics will be notified via Instagram Direct Message sent to the Instagram account used for their entries on the designated Instagram post within five (5) days following selection of Winner on @maviecosmetics. Mavie. LLC shall have no liability for Winner's failure to receive notices due to spam, junk e-mail or other security settings or for Winner's provision of incorrect or otherwise non-functioning contact information. If Winner fails to claim the prize within seven (7) days from the time the award notification was sent, the prize will be forfeited. Mavie. LLC reserves the right to re-select a new winner at random shall the previous winner fail to claim the prize in compliance with the official rules. Upon the request of the Sponsor, the potential winners may be required to execute and return a Prize Acceptance, Affidavit of Eligibility, and Release Form and IRS W-9 form. If Sponsor's request is declined or otherwise not complied with, the potential winner will be disqualified.
6. Rights Granted: By entering this Campaign, you understand and agree that Sponsor, as well as its agents, employees, affiliates, licensees, successors, and assigns, shall have the right, to the extent permitted by law, to print, publish, broadcast, distribute, and use in any media now known or hereafter developed, in perpetuity and throughout the World, without limitation, your entry, name, portrait, picture, voice, likeness, image, and statements about the Campaign for publicity, trade, advertising, public relations, and promotional purposes, without additional compensation, notice, review, or consent.
7. Limitation of Liability: By entering this Campaign, you agree to release and hold harmless Sponsor and its agents, employees, affiliates, licensees, successors, and assigns subsidiaries, and affiliates from any liability, illness, injury, death, loss, litigation, claim, or damage that may occur, directly or indirectly, whether caused by negligence or not, from: (i) your participation in the Campaign and/or your acceptance, possession, use, or misuse of any prize or any portion thereof; (ii) technical failures of any kind, including but not limited to the malfunction of any computer, cable, network, hardware, or software, or other mechanical equipment; (iii) the unavailability or inaccessibility of any transmissions, telephone, or Internet service; (iv) unauthorized human intervention in any part of the entry process or the Campaign; (v) electronic or human error in the administration of the Campaign or the processing of entries.
8. Disputes: As a condition of participating in this campaign, entrant agrees that any and all disputes that cannot be resolved between the parties, and causes of action arising out of or connected with this Campaign, shall be resolved individually, without resort to any form of class action, exclusively before a court located in California having jurisdiction. Further, in any such dispute, entrant hereby waives all rights to, punitive, incidental, or consequential damages, including reasonable attorney's fees, other than participant's actual out-of-pocket expenses (i.e., costs associated with entering this Campaign).
9. Privacy Policy: Information submitted with an entry is subject to Sponsor's Privacy Policy, which is available at https://callmemavie.com/pages/privacy-policy.
10. Questions: Any questions regarding this Sweepstakes on @maviecosmetics should be directed to info@callmemavie.com with the subject line: 2019 Holiday Giveaway.
Stay in touch👇 And get $5 off your next order.
© 2021, Mavie. Cosmetics Powered by Shopify | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,781 |
Pro Pinball – seria czterech gier komputerowych typu pinball stworzonych przez brytyjskie studio Cunning Developments (wewnętrzne studio Empire funkcjonujące w latach 1994 - 2002 r) i wyprodukowanych przez Empire Interactive. Wydane zostały one pomiędzy rokiem 1995 a 1999. Gry z serii to: The Web (1995), Timeshock! (1997), Big Race USA (1998) oraz Fantastic Journey (1999). W 2001 roku gry Big Race USA, Fantastic Journey i Timeshock zostały wydane w zestawie na konsolę Sega Dreamcast pod tytułem Pro Pinball Trilogy. Członkowie Cunning Developments pracują obecnie dla Silverball Studios, które przy aprobacie twórcy serii, Adriana Barritta, planuje ją wznowić po ewentualnym dofinansowaniu przez serwis Kickstarter.
Przypisy
Linki zewnętrzne
Oficjalna strona internetowa gry
Oficjalny profil Adriana Barritta na portalu LinkedIn
Serie gier komputerowych
Komputerowe pinballe | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,732 |
If you are a vegan or you are just trying to lose some weight, then choosing what you eat carefully is important. You don't want a situation where beef and chicken obstruct your weight loss efforts. Nowadays, you will find many people opting for supplements and training to build lean muscles and shake off extra pounds. Here, you will find many articles that will give you valuable advice on stress-free options concerning vegetarian foods that will help lose weight and get that perfect body.
Top of the list is this amazing meal. It takes a short time to prepare as many of the ingredients used lose their nutrient value when overcooked. You will love the delicate balance between sweetness and bitterness with a final lime touch that smooths everything down your throat. It features fried Tofu with Zucchini that is then simmered with red pepper for that delicious sour taste. It is finalized with some coconut curry sauce and chopped fresh basil.
If you have been wishing for the best Savannah Mushrooms, then this Portobello dish is just what you need. The mushrooms are usually capped and marinated giving it a saucy and tasty touch that makes many fall in love with it. You can serve them with steaks as ordered or as hamburger buns.
Finally, there is this tasty version of the classic Chinese vegetarian dish. Top chefs delicately prepare it to a level that you can no longer realize the chicken in it. It is seen as a green way to enjoy all that comes with fried chicken that is considered unhealthy. It is made from wheat gluten giving it low fat content, but its high protein level. You will love trying out this Vegetarian meal for weight loss purposes. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,207 |
Bank of America overdraft service fees dropped 90% over the last two months
Fees aren't completely going away, but they're getting much more manageable
Photo (c) Iryna Drozd - Getty Images
The overdraft fee bonanza may be coming to an end for U.S. banks. When the Consumer Financial Protection Bureau (CFPB) raised its voice about fees earlier this year, the message was apparently heard loud and clear. On Thursday, Bank of America demonstrated proof of the agency's action.
The company announced that it has made a sizable, customer-favoring shift for its 35 million consumer checking account holders. The bank said fees related to overdraft services declined by 90% in June and July when compared to the same period in 2021. June and July were the first two months after sweeping changes related to these services were implemented.
That comparison is hefty, too. According to ConsumerAffairs' research, Bank of America's overdraft fees accounted for 1% of its revenue in 2021. One percent may seem insignificant, but it comes out to close to $320 million. Now, for the second quarter of 2022, consumer client overdraft fees made up less than 0.4% of the company's total revenue.
Things will likely get even better if we're to take Bank of America at its word. In making its announcement, the company said new solutions and enhanced programs introduced over the last decade will reduce consumer overdraft fees by 97% from 2009 levels by next year.
"For more than a decade, Bank of America has invested heavily in supporting our clients' financial health through industry-leading solutions and ongoing enhancements to our overdraft services," said Holly O'Neill, President of Retail Banking, Bank of America. "Our scale, client focus and technology investments have allowed us to adopt policies and innovate in ways that help clients manage their everyday finances and liquidity needs on their own terms, while also delivering for our shareholders."
Fees aren't going completely away
Bank of America customers should note that the company is not completely eliminating overdraft fees; it's just reducing the amount that consumers have to pay. As part of its recent actions, customers now only pay $10 for overdraft fees instead of $35.
However, customers can get around those reduced fees through Bank of America's SafeBalance checking account. The program costs $4.95 each month, with exceptions for students, people under age 18, or customers who are enrolled in the bank's Preferred Rewards program.
Take a Financial Relief Quiz. Get matched with an Authorized Partner.
You need $1,400 to meet today's emergency expense, report finds
Favorite food prices too high? Here are some cheaper alternatives
The cost of raising a child is over $300,000
CFPB continues efforts to reduce overdraft and insufficient fund fees
Capital One to completely eliminate overdraft fees
Ally Bank is eliminating overdraft fees. Could your bank be next?
TD Bank to pay $122 million to settle charges related to overdraft fees | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,059 |
First appearing in the 1490s in illuminated manuscripts, the use of complex spatial composition and certain 'classical' decorative motifs continues to develop in the arts until the 1530s. Priority is given to new decorative ideas which come from the Loire Valley or are observed on imported Italian works.
In parallel, an idealized but also expressive representation of the human figure imposes itself, especially in sculpture which takes the form of portrait medallions, reliquary busts and eloquent statues.
While itinerant masters continue to exercise their profession, such as the sculptor Jean Bauduy (Prophets and Sibyls), Toulousain artists distinguish themselves in the mastery of these new styles which they spread widely. Such is the case of goldworkers like Antoine Favier or painters in the mould of Antoine Olivier, the latter a talented master who goes unrecognized for many years. Among the elites, who assert their rank through the arts, flourishes an ideal view of Toulouse and its prestigious Roman past.
As early as the 1530s and 1540s artists and artisans begin searching for models of harmony and rules of composition within the classical canon. This trend towards the classical takes physical form in 1550 in the lines of Jean Rancy's statue Dame Tholose, intended as an embodiment of municipal glory. Nicolas Bachelier and his peers in sculpture, architecture and painting, such as Dominique Bertin and Bernard Nalot, have recourse to vrayes antiques ('true classics'), basing their endeavours on Roman models and artistic literature. Their talents for design and drawing are exploited even in engineering. This erudite enthusiasm goes hand in hand with a flourishing humanism supported by the world of publishing. At the same time, references to royal castles and their decors abound through direct adaptations or interpretations of engravings. Thus an art derived from sophisticated sources develops, elegantly combining regularity and exuberance.
© "Feeding the Multitude", 1556, anonymous from the Languedoc. Narbonne Cathedral. Photo Right holder unknown. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,767 |
"The Vet"
An aerial view of Veterans Stadium in 2002. Construction work on Citizens Bank Park can be seen to its east.
3501 South Broad Street
City of Philadelphia
Philadelphia Department of Recreation
Baseball: 61,831
Football: 65,352
Baseball:
Left field — 330 feet (100 metres)
Left center field — 371 feet (113 metres)
Center field — 408 feet (124 metres)
Right center field — 371 feet (113 metres)
Right field — 330 feet (100 metres)
Backstop — 54 feet (16 metres) (2003)
AstroTurf (1969–2000)
NexTurf (2001–2003)
Broke ground
April 10, 1969 (pre-opening)
April 10, 1971 (official opening)
Demolished
($367 million in 2016 dollars[1])
Hugh Stubbins & Associates
George M. Ewing Co.
Stonorov & Haws
McCormick Taylor & Associates, Inc.
McCloskey & Co.[2]
Philadelphia Phillies (MLB) (1971–2003)
Philadelphia Eagles (NFL) (1971–2003)
Philadelphia Atoms (NASL) (1973–1975)
Philadelphia Fury (NASL) (1978–1980)
Philadelphia Stars (USFL) (1983–1984)
Temple University (NCAA) (1978–2002)
Pennsylvania Historical Marker
September 28, 2005[3]
Veterans Stadium was a multi-purpose stadium located at the northeast corner of Broad Street and Pattison Avenue, in Philadelphia, Pennsylvania, as part of the South Philadelphia Sports Complex. The listed seating capacities in 1971 were 65,358 seats for football, and 56,371 for baseball.
It hosted the NFL's Philadelphia Eagles from 1971 to January 2003 and the National League's Philadelphia Phillies baseball team from 1971 to 2003. The 1976 and 1996 Major League Baseball All-Star Games were held at the venue. The Vet also hosted the annual Army-Navy football game seventeen times: first in 1980, and last in 2001.
In addition to professional baseball and football, the stadium hosted other amateur and professional sports, large entertainment events, and other civic affairs. With the construction of the adjacent Citizens Bank Park, Veterans Stadium was demolished in March 2004, and a parking lot now sits on its former site.
Inception, design and construction 1.1
First game 1.2
Final games 1.3
Demolition and commemoration 1.4
Baseball 2.1
Stadium features 3
700 Level 3.1
Playing surface 4
Notable games and incidents 6
Other events at Veterans Stadium 7
Amateur baseball 7.1
Minor League baseball 7.2
Soccer 7.3
High School football 7.4
Professional wrestling 7.5
Concerts 7.6
Other events 7.7
Further reading 11
Inception, design and construction
Exterior of Veterans Stadium.
As early as 1959, Phillies owner Bob Carpenter proposed building a new ballpark for the Phillies on 72 acres (290,000 m2) adjacent to the Garden State Park Racetrack in Cherry Hill, New Jersey. The Phillies' then-home, Connie Mack Stadium, was starting to show its age (it had been built in 1909), had inadequate parking, and was located in a declining neighborhood. Furthermore, in 1959 alcohol sales at sporting events were banned in Pennsylvania but were legal in New Jersey. The proposed ballpark would have seated 45,000 fans, been expandable to 60,000 and would have had 15,000 parking spaces.[4]
The American League's Philadelphia Athletics had moved to Kansas City, Missouri after the 1954 season and Philadelphians weren't about to lose another professional sports franchise. In 1964, Philadelphia voters approved a $25-million-bond issue for a new stadium to serve as the home of both the Eagles (who played at the University of Pennsylvania's Franklin Field) and the Phillies. Because of cost overruns, the voters had to go to the polls again in 1967 to approve another $13 million. At a total cost of $60 million, it was one of the most-expensive ballparks to date.[5]
The stadium was named by the Philadelphia City Council, in 1968, for the veterans of all wars. As early as December 1969, the Phillies expected that they would play the first month of the 1970 season at Connie Mack Stadium before moving to the new venue.[6] However, the opening was delayed a year because of a combination of bad weather and cost overruns.
The stadium's design was nearly circular, and was known as an "octorad" design, which attempted to facilitate both football and baseball. Qualcomm Stadium in San Diego had been similarly designed. As was the case with other cities where this dual approach was tried (other examples include RFK Stadium in Washington, D.C.; Shea Stadium in New York City, the Astrodome in Houston; Atlanta-Fulton County Stadium in Atlanta; Busch Memorial Stadium in St. Louis; Riverfront Stadium in Cincinnati; and Three Rivers Stadium in Pittsburgh), the fundamentally different sizes and shapes of the playing fields made the stadium inadequate to the needs of either sport.
Sculptor Joe Brown's statue "Batter" as it stood outside Veterans Stadium.
The Phillies played their first game at the stadium on Saturday, April 10, 1971, beating the Montreal Expos, 4–1, before an audience of 55,352. Jim Bunning (named to the Baseball Hall of Fame in 1996) was the winning pitcher while Bill Stoneman took the loss. Entertainer Mike Douglas, whose daily talk show was taped in Philadelphia, sang The Star-Spangled Banner before the game. The emcee for the opening ceremonies was newly arrived Harry Kalas. Boots Day opened the game by grounding out to Bunning. Larry Bowa had the stadium's first hit and Don Money slugged the first home run.[7]
The Phillies' final game at the Vet; September 28, 2003.
As the stadium aged, its condition deteriorated. A hole in the wall allowed visiting teams' players to peep into the Eagles Cheerleaders dressing room. So many mice infested the stadium that the security force employed cats as mousers.[8] The final football game played at the Vet was the Eagles' 27–10 loss to the Tampa Bay Buccaneers in the NFC Championship Game on January 19, 2003. The Eagles moved into Lincoln Financial Field in August 2003.[9]
The final game ever played at the stadium was the afternoon of September 28, 2003, a 5-2 Phillies loss to the Atlanta Braves.[10] Unlike other final games at the stadium, "America the Beautiful" was sung instead of the National Anthem at the pregame ceremonies.[11](The final National Anthem rendition had been sung by Lauren Hart, daughter of Gene Hart, the night before, prior to the final night game in Stadium history. Hart also sang the final God Bless America performance at the seventh-inning stretch in the stadium's final game.) The final win was recorded by Greg Maddux of the Braves, the final loss by the Phils' Kevin Millwood. The final Phillies run was scored by Marlon Byrd at the top of the 3rd inning, and the final run altogether by the Braves' Andruw Jones on a double by Robert Fick (who also had the last hit at Tiger Stadium as a Detroit Tiger 4 years earlier) at the top of the 5th. The final hit at the Vet was a single by the Phills' Pat Burrell at the bottom of the 9th. The next batter, Chase Utley, grounded into a double play to end the game and the Vet. However, the ceremony that followed pulled at the heartstrings of the sellout crowd. Both Paul Owens, a former general manager, and Tug McGraw, a former pitcher, made their final public appearances at the park that day; later that winter both men died.[12][13] The last publicly broadcast words uttered in the park were by Harry Kalas — a veteran announcer who helped open the facility on April 10, 1971 — who paraphrased his trademark home run call: "And now, Veterans Stadium is like a 3-1 pitch to Jim Thome or Mike Schmidt. It's on a looooooong drive...IT'S OUTTA HERE!!!" The team moved into Citizens Bank Park in 2004, with the first game being played there on April 12, 2004.
Demolition and commemoration
On March 21, 2004, the 32-year-old stadium was imploded in 62 seconds. Frank Bardonaro, President of Philadelphia-based AmQuip Crane Rental Company pressed the "charge" button and then he and Nick Peetros, Project Manager for Driscoll/Hunt Construction Company simultaneously pressed the "fire" button to trigger the implosion[14] while Greg Luzinski and the Phillie Phanatic, the Phillies' mascot, pressed a ceremonial plunger for the fans.[15] A parking lot for the current sporting facilities was constructed in 2004 and 2005 at the site.
On June 6, 2005, the anniversary of World War II's D-Day, a plaque and monument to commemorate the spot where the stadium stood and a memorial for all veterans was dedicated by the Phillies before their game against the Arizona Diamondbacks. On September 28, 2005, the second anniversary of the stadium's final game, a historical marker commemorating where the ballpark once stood was dedicated. In April 2006, granite spaces marking the former locations of home plate, the pitcher's mound, and the three bases for baseball, as well as the goalpost placements for football, were added in Western Parking Lot U.
56,371 (1971–1972)
Stadium features
Veterans Stadium on Phillies Opening Night, 1986.
The stadium was a complicated structure with its seating layered in seven separate levels. The lowest, or "100 Level", extended only part way around the structure, between roughly the 25-yard lines for football games and near the two dugouts for baseball. The "200 Level" comprised field-level boxes, and the "300 Level" housed what were labeled "Terrace Boxes". These three levels collectively made up the "Lower Stands". The "400 Level" was reserved for the press and dignitaries; the upper level began with "500 Level" (or "loge boxes"), the "600 Level" (upper reserved, or individual seats), and finally, the 700 Level (general admission for baseball). Originally, the seats were in shades of brown, terra cotta, orange and yellow, to look like an autumn day, but in 1995 and 1996, blue seats replaced the fall-hued ones.
At one time, the stadium could seat over 71,000 people for football, but restructuring in the late 1980s brought capacity down to around 66,000.
The stadium was harshly criticized by baseball purists. Even by multi-purpose-stadium standards, the upper deck was exceptionally high, and many of the seats in that area were so far from the field that it was difficult to see the game without binoculars. Like most of its contemporaries, foul territory was quite roomy. Approximately 70% of the seats were in foul territory, adding to the stadium's cavernous feel. There was no dirt in the infield except for sliding pits around the bases. In the autumn, the football markings were clearly visible in the spacious outfield area. Although the stadium's size enabled the Phillies to shatter previous attendance records, during the years the Phillies were not doing as well even crowds of 35,000 looked sparse.
The stadium had been known for providing both the Eagles and the Phillies with great home-field advantage. In particular, the acoustics greatly enhanced the crowd noise on the field, making it nearly impossible for opposing teams to hear one another.
The "700 Level" was well known for being home to the rowdiest fans at Philadelphia Eagles games, and to a lesser extent, Philadelphia Phillies games. In his book If Football's a Religion, Why Don't We Have a Prayer?,[16] Jereé Longman described the 700 Level as having a reputation for "hostile taunting, fighting, public urination and general strangeness." Due to an improvement in facilities, there is no equivalent in either Lincoln Financial Field or Citizens Bank Park. The name has also been the inspiration for websites relating to Philadelphia sports, as well as a weekly "Letters to the Editor" section in the Sunday Sports pages of The Philadelphia Inquirer.
Veterans Stadium during the 1980 NFC Championship Game against the Dallas Cowboys, January 11, 1981.
The field's surface, originally composed of AstroTurf, contained many gaps and uneven patches. In several places, seams were clearly visible, giving it the nickname "Field of Seams". It perennially drew the ranking of the "NFL's worst field" in player surveys conducted by the NFL Players Association, and visiting players often fell prey to the treacherous conditions resulting in numerous injuries.[17] The NFLPA reportedly threatened to sue the city for the poor conditions, and many sports agents told the Eagles not to even consider signing or drafting their clients. The Eagles, for their part, complained to the city on numerous occasions about the conditions at the stadium. Baseball players also complained about the surface. It was much harder than other AstroTurf surfaces, and the shock of running on it often caused back pain.
Two of the most-publicized injuries blamed on the playing surface occurred exactly six years apart. On October 10, 1993, Chicago Bears receiver Wendell Davis had his cleat get caught in a seam while running a simple pass route. He tore both of his patella tendons, ending his career.[18] On October 10, 1999, Dallas Cowboys wide receiver Michael Irvin suffered a neck injury that led to his premature retirement. (The previously winless Eagles rallied from a 10–0 deficit and won 13–10.)
In 2001, the original AstroTurf was eventually replaced by a new surface, NexTurf. It was far softer, and reportedly much easier on the knees.[19] However, the city crew that installed the new turf reportedly did not install it properly, resulting in seams being visible in several places.
The first football game on the new turf was scheduled to take place on August 13, 2001, when the Eagles were to play the Baltimore Ravens in a preseason game. However, Ravens coach Brian Billick refused to let the Ravens take the field for warm-ups when he discovered a trench around an area where third base was covered up by a NexTurf cutout. City crews unsuccessfully tried to fix the problem, forcing the game to be canceled. Later, players from both teams reported that they sank into the turf in locations near the infield cutouts. Team president Joe Banner was irate after the game, calling the stadium's conditions "absolutely unacceptable" and "an embarrassment to the city of Philadelphia."[20] City officials, however, promised that the stadium would be suitable for play when the regular season started.
The problem was caused by heavy rain over the weekend prior to the game, which made the dirt in the sliding pits and pitcher's mound so soft that the cutouts covering them in the football configuration became mushy and uneven. Even when new dirt was shoveled on top, it quickly became just as saturated as the old dirt. The problem was solved by using asphalt hot mix, which allowed for a solid, level playing surface, but required a jackhammer for removal whenever the stadium was converted from football back to baseball (between August and October of each year).
Virginia Tech and Temple meet at The Vet in 2001.
Fans who attended games in the stadium for a football game gained a reputation of being among the most vociferous in sports, especially those in the notorious 700 Level, the highest seating level in the stadium prior to the construction of luxury skyboxes behind that seating area. The stadium became famous for the rowdiness of Eagles fans, although it was not the site of the incident in which fans booed Santa Claus during a halftime show. (The Santa Claus incident occurred on December 15, 1968, at Franklin Field, the Eagles' home stadium at the time.[21])
One of the more well-known examples of the fans' behavior was during the 1989 season at a follow-up game to what many called the "Bounty Bowl". On Thanksgiving Day, November 23, 1989, the Eagles had defeated the Dallas Cowboys at Texas Stadium, 27-0.[22] In that game, Cowboys placekicker Luis Zendejas suffered a concussion during a rough block by linebacker Jessie Small after a kickoff. After the game, Cowboys rookie head coach Jimmy Johnson commented that Eagles coach Buddy Ryan instituted a bounty on Zendejas and Cowboys quarterback Troy Aikman. Two weeks later, on December 10, they played the rematch dubbed "Bounty Bowl II" at the stadium which the Eagles won 20-10.[23] The stadium seats were covered with snow in the stands. The volatile mix of beer, the "bounty" and the intense hatred for "America's Team" (who were 1–15 that season) led to fans throwing snowballs at Dallas players and coaches.[24] Beer sales were banned after that incident for two games. A similar incident in 1995 at Giants Stadium during a nationally telecast San Diego Chargers–New York Giants game[25] led the NFL to rule that seating areas must be cleared of snow within a certain time period before kickoff.
The Eagles fans' behavior during a Monday Night Football loss[26] to the San Francisco 49ers in 1997 and a 34-0 loss to Dallas a year later[27] was such that the City of Philadelphia assigned a Municipal Court Judge, Seamus McCaffrey, to the stadium on game days to deal with fans removed from the stands in what was referred to as "Eagles Court".[8] Two years later, fans threw D-Cell batteries at St. Louis Cardinals outfielder J.D. Drew after he spurned the Phillies' offer to play with them, and wound up going back into the draft and picked by the Cardinals.[28]
Notable games and incidents
Veterans Stadium before and during one of U2's Zoo TV Tour shows in 1992
On June 25, 1971, Willie Stargell hit the longest home run in stadium history in a 14–4 Pirates win.[29] The spot where the ball landed was marked with a yellow star with a black "S" inside a white circle until Stargell's 2001 death, when the white circle was painted black.[30][31] The star remained until the stadium's 2004 demolition.
One of the most notable events in the stadium's history was Game 6 of the 1980 World Series on October 21. In that game, the Phillies clinched their first world championship with a 4–1 victory over the Kansas City Royals in front of 65,838 fans. Tug McGraw's series-ending strikeout of the Royals' Willie Wilson was instrumental in their win.
A very notable football game played at the stadium took place less than three months after the Phillies' title: the Eagles' 20–7 victory over the Dallas Cowboys in the 1980 NFC Championship Game, played on January 11, 1981, in front of 70,696 fans.[32] As a psychological ploy, the Eagles chose to wear their white jerseys for their home game in order to force the Cowboys into their "unlucky" blue jerseys. At the end of the game, Philadelphia police circled the field with horses and dogs as they had done for the Phillies World Series victory; despite the police presence, Eagles fans successfully rushed the field.[33]
Veterans Stadium was host to the latest-finishing game in baseball history, a twi-night double-header between the Phillies and the Padres that started on July 2, 1993, at 5:05 PM and ended at 4:40 AM the following morning. The two games were interrupted multiple times by rain showers. The Padres won the first game,[34] and led in the second, but lost in a come-from-behind victory for the Phillies in the tenth inning on an RBI single by Phillies closing pitcher Mitch Williams.[34] The second game ended with an estimated 6,000 fans at the ballpark.[15]
The Phillies clinched the National League Championship Series at the stadium twice: the first in 1983 over area-born Tommy Lasorda and the Los Angeles Dodgers, and the second in the 1993 National League Championship Series over future divisional rivals the Atlanta Braves. The 1993 season was the last LCS with a two-division League format.
The 1994 Army–Navy Game at Veterans Stadium
The Phillies pitched two no-hit games at the stadium, the only nine-inning no-hitters in stadium history. Both were against the San Francisco Giants. Terry Mulholland pitched the first[35] on August 15, 1990, in a 6–0[36] Phillies win.[37] Kevin Millwood pitched the second on April 27, 2003, and beat the Giants 1–0,[38] upstaging the Phillie Phanatic's birthday promotion that afternoon. The Montréal Expos' Pascual Pérez pitched a five-inning[39] no-hitter shortened by rain on September 24, 1988. MLB changed its rules in 1991 to require that fully recognized no-hitters – past, present and future – be complete games of at least nine innings.[40]
Another game that is well-remembered by Eagles fans was known as "The Body Bag Game", which took place on November 12, 1990, when the Washington Redskins visited the stadium for a Monday Night Football game. The Eagles' head coach at that time, Buddy Ryan, was quoted as saying that the Redskins' offense would "have to be carted off in body bags." The Eagles' number-one defense scored two touchdowns in a 28–14 win[41] and knocked nine Redskin players out of the game, including both of their quarterbacks.[42] The Redskins were forced to finish the game using running back/returner Brian Mitchell (who would become an Eagles player over a decade later) at quarterback.[43]
During the 1998 Army–Navy Game, a serious accident occurred when a support rail collapsed and eight West Point cadets were injured. That led to the call for new stadiums for football and baseball for the main stadium tenants.[44]
Other events at Veterans Stadium
The Liberty Bell Classic, Philadelphia Division I college baseball tournament, was played at the stadium from its inception in 1992 through 2003. The original eight schools were:
University of Pennsylvania (the Quakers)
University of Delaware (the Fightin' Blue Hens)
Saint Joseph's University (the Hawks)
Drexel University (the Dragons)
Villanova University (the Wildcats)
Temple University (the Owls)
West Chester University of Pennsylvania (the Golden Rams)
La Salle University (the Explorers)
In the first championship game in 1992, Delaware defeated Villanova 6-2.[45]
The stadium hosted the 1998 Atlantic 10 Conference Baseball Tournament, won by Fordham.[46]
In November 1987, the new owners of the Phillies AAA franchise, the Maine Guides, considered playing the 1988 season at the Vet because Lackawanna County Stadium would not be ready until the 1989 season. The team would have had to play 12:35pm day games when the Phillies had night games scheduled at the Vet.[47] Ownership elected to remain in Old Orchard Beach for 1988, renamed the club the 'Maine Phillies', and moved to Moosic, PA in 1989 as the Scranton/Wilkes-Barre Red Barons.
The Eastern League Trenton Thunder played two home games at the stadium in April 1994. The Thunder beat the Canton-Akron Indians, 10 to 9, in front of 483 fans on April 20, 1994, and won 9 to 3 on April 21. Future Phillies broadcaster Tom McCarthy was in the booth for the Thunder during these two games.[48]
The stadium was the home field for the Philadelphia Atoms and the Philadelphia Fury, both North American Soccer League teams. The Fury drew 18,191 fans for their April 1, 1978, opener at the stadium which they lost 3-0 to the Washington Diplomats. The Fury averaged 8,279 per-match in 1978 NASL, 5,624 per-match in 1979 NASL, and 4,778 in the 1980 NASL seasons. The club was moved to Montreal in 1981 NASL season.[49]
The stadium hosted an exhibition match on August 2, 1991, between the U.S. National Team and English professional soccer club Sheffield Wednesday. John Harkes played for Wednesday, the first American to play in the English Premier League. 44,261 fans saw the U.S. score two second-half goals to defeat Sheffield Wednesday 2-0.[50]
Philadelphia established a bid committee to host matches for the 1994 World Cup which was to be played in the United States. Phillies president Bill Giles was on the Philadelphia bid committee and hoped to use Veterans Stadium for games. In addition to the challenge of installing a natural grass field for the games, FIFA would have required the Phillies to vacate the stadium for a month to allow for sufficient preparation time prior to the matches. Giles could only offer 17-days.[51] Of the nine venues eventually chosen to host matches, not one was home to a professional baseball club.
Veterans Stadium hosted Philadelphia's City Title high-school football championship game from 1973 to 1977 and in 1979. The series was suspended in 1980.[52] With the entry of the Philadelphia Catholic League into what is now PIAA District XII (which was formed when the Public League joined the PIAA in 2002), the "City Title Game" was restored in 2008.
The only professional wrestling event held in Veterans Stadium was National Wrestling Alliance/Jim Crockett Promotions "Great American Bash" on July 1, 1986, with an attendance of 10,900. The event was the start of a 14-city summer tour.
The stadium has hosted many stadium concerts, by famous artists of many different genres.
The venue also played host to religious events including annual Jehovah's Witnesses conventions, which was open to the public each year it took place. It also played host to a Billy Graham crusade in 1992.
Home plate at Veterans Stadium, home to the Philadelphia Phillies for thirty-three seasons, is remembered with this granite and bronze marker in the parking lot near Citizens Bank Park. (2006)
Veterans Stadium's goalpost, used by the Philadelphia Eagles for thirty-two seasons, is marked in the same parking lot. (2011)
Veterans Stadium's pitching mound is marked. (2011)
A brief history of how the stadium was named and a tribute to veterans of all wars is on display outside where the stadium stood. (2006)
The historic marker shows the stadium's major moments. (2007)
Dedication plaque that once was attached to The Vet. (2007)
^ Consumer Price Index (estimate) 1800–2014. Federal Reserve Bank of Minneapolis. Retrieved February 27, 2014.
^ "Index". Ballparks.com. Retrieved May 9, 2014.
^ "PHMC Historical Markers Search" (Searchable database). Pennsylvania Historical and Museum Commission. Commonwealth of Pennsylvania. Retrieved 2015-09-28.
^ Bernstein, Ralph (March 1, 1959). "Philadelphia On Verge of Losing Phils". The Milwaukee Sentinel. Associated Press. p. 2C.
^ "Stadium Facts". Lincoln Financial Field. Retrieved May 9, 2014.
^ "Phillies Card 28 Spring Exhibitions".
^ "April 10, 1971 Montreal Expos at Philadelphia Phillies Box Score and Play by Play".
^ a b Anderson, Dave (October 29, 2002). "Sports of The Times; To Eagles, Shockey Is Public Enemy No. 1".
^ Associated Press (January 19, 2003). "Bucs Stop McNabb to Earn First Super Bowl Berth".
^ "September 28, 2003 Atlanta Braves at Philadelphia Phillies Box Score and Play by Play".
^ Last Phillies Game at Veterans Stadium at youtube.com
^ Roberts, Kevin (December 26, 2003). "Former Phillies GM Owens Dies at 79".
^ "Former Relief Pitcher Tug McGraw Dead at 59".
^ Guts and Bolts: The Implosion of Veterans Stadium.
^ a b Westcott, Rich;
^ Longman, Jeré (2006). If Football's a Religion, Why Don't We Have a Prayer?. New York: HarperCollins Publishers.
^ Hooper, Ernest (December 28, 2009). "They Say the Vet Stadium Turf Is Hard as Concrete — Maybe That's Why Last Week It Was Treated Like Piece of Philly Highway".
^ Mitchell, Fred (October 10, 1993). "Bears—Yes, Bears—Gain First-Place Tie".
^ Williams, Pete (January 15, 2001). "Versatility Wins Southwest Rec's Nexturf a Gig at Veterans Stadium".
^ "N.F.L.: ROUNDUP; Eagles' Turf Unsafe For Ravens' Game".
^ Polaneczky, Ronnie (December 15, 2008). "This is Philly: After 40 Years, We'll Still Boo a Bad Santa".
^ "Philadelphia Eagles at Dallas Cowboys - November 23rd, 1989".
^ "Dallas Cowboys at Philadelphia Eagles - December 10th, 1989".
^ Eskenazi, Gerald (December 11, 1989). "Eagles Top Cowboys in an Emotional Contest".
^ Sandomir, Richard (December 31, 1995). "DECEMBER 24-30;Icy Reception".
^ "San Francisco 49ers at Philadelphia Eagles - November 10th, 1997".
^ "Dallas Cowboys at Philadelphia Eagles - November 2nd, 1998".
^ "June 25, 1971 Pittsburgh Pirates at Philadelphia Phillies Box Score and Play by Play".
^ Mandel, Ken (June 25, 2003). "Stargell's Star a Lasting Tribute; Blast is Marking Point for All Hitters".
^ Fitzpatrick, Frank (June 30, 2003). "Blast From the Past; Stargell's Upper-Deck Home Run at Veterans Stadium in '71 Still Has Plenty of Clout".
^ "Dallas Cowboys at Philadelphia Eagles - January 11, 1981".
^ Wulf, Steve (January 19, 1981). "Eagles That Didn't Need Wings".
^ a b "July 2, 1993 San Diego Padres at Philadelphia Phillies Box Score and Play by Play".
^ Gennaria, Mike (August 19, 2003). "Mulholland Recalls Vet No-Hitter".
^ "August 15, 1990 San Francisco Giants at Philadelphia Phillies Box Score and Play by Play".
^ "April 27, 2003 San Francisco Giants at Philadelphia Phillies Box Score and Play by Play".
^ "September 24, 1988 Montreal Expos at Philadelphia Phillies Box Score and Play by Play".
^ Chass, Murray (September 5, 1991). "BASEBALL; Maris's Feat Finally Recognized 30 Years After Hitting 61 Homers".
^ "Washington Redskins at Philadelphia Eagles - November 12th, 1990".
^ Didinger, Ray; Lyons, Robert S. (2005). The Eagles Encyclopedia. Philadelphia:
^ Berger, Ken (December 7, 1998). "Nine Injured in Fall When Railing Breaks at Veterans Stadium".
^ "At Bat in Our Community: Liberty Bell Classic".
^ "Atlantic 10 Conference Baseball Record Book". Atlantic 10 Conference. p. 15. Archived from the original (PDF) on February 16, 2012. Retrieved February 16, 2012.
^ "Park Delay May Force Guides back".
^ Edwards, Christopher T. (1997). Filling in the Seams: The Story of Trenton Thunder Baseball. B B& A Publishers. pp. 62–65.
^ Holroyd, Steve. "Remembering the "Pseudo-Atoms" — The Philadelphia Fury, 1978-1980".
^ "This May Be the Kick American Soccer Needs".
^ Jensen, Mike (June 5, 1991). "World Cup Bid Might Fall Short; Sites Needed for One Month".
^ "FB City Title Recaps". Ted Sillary. Retrieved April 23, 2009.
Philadelphia Phillies: "Veterans Stadium: Field of Memories"
Birker, Paul Arthur (2005). Veterans Stadium; Field of Memories. Philadelphia:
Westcott, Rich (2005). Veterans Stadium: Dismantled.
Events and tenants
Franklin Field Home of the Philadelphia Eagles
Connie Mack Stadium Home of the Philadelphia Phillies
Milwaukee County Stadium
The Ballpark in Arlington Host of the All-Star Game
1996 Succeeded by
Jacobs Field
Tampa Stadium
Edward Jones Dome Host of NFC Championship Game
Candlestick Park
Based in Philadelphia, Pennsylvania
Baker Bowl
Philadelphia Municipal Stadium
Franklin Field
Curse of Billy Penn
Philadelphia Sports Hall of Fame
Matt Guokas, Sr.
Dan Baker
The Garbage Picking Field Goal Kicking Philadelphia Phenomenon
Frankford Yellow Jackets
Pennsylvania Keystoners
Steagles
"Happy Hundred"
Miracle at the Meadowlands
Bounty Bowl series
Body Bag Game
4th and 26
Miracle at the New Meadowlands
Division championships (13)
League championships (3)
NFL championship appearances (4)
1980 (XV)
2004 (XXXIX)
WTEL
WIP-FM
Merrill Reese
Mike Quick
Division: East Division
Formerly the Philadelphia Quakers
Owners and executives
Opening Day starting pitchers
First-round picks
No-hitters
Award winners and league leaders
Shibe Park
Coffee Pot Park
Cooke Field
McKechnie Field
Wilmington Park
Flamingo Field
Clearwater Athletic Field
Jack Russell Memorial Stadium
Carpenter Complex / Bright House Field
Phillie Phanatic
Hot Pants Patrol
Wheeze Kids
Baseball Wall of Fame
Philadelphia Phillies (NFL)
Jim Bunning's perfect game
Phold
Franchise awards
"Team to Beat"
Roy Halladay's perfect game
Philadelphia Athletics (City Series)
Important figures
Grover Cleveland Alexander
Gavvy Cravath
Darren Daulton
Granny Hamner
Willie Jones
Mike Lieberthal
Garry Maddox
Sherry Magee
Cy Williams
record holders
Bill Duggleby
George McQuillan
José Mesa
Lefty O'Doul
Kent Tekulve
Owner: Limited partnership (John S. Middleton, Jim & Pete Buck, David Montgomery, & Pat Gillick)
President: Andy MacPhail
General Manager: Matt Klentak
Manager: Pete Mackanin
championships (2)
NL pennants (7)
championships (11)
Lehigh Valley IronPigs
Reading Fightin Phils
Clearwater Threshers:
Lakewood BlueClaws:
Williamsport Crosscutters
Gulf Coast League Phillies:
VSL Phillies:
DSL Phillies
Comcast SportsNet Philadelphia
WCAU
The Comcast Network
WPHT
WDAS
Phillies radio network affiliates
Broadcasters:
Scott Franzke
Larry Andersen
Philadelphia Atoms
Philadelphia Atoms (1973–1976)
Thomas McCloskey
Chris Bahr
Chris Dunleavy
Jim Fryatt
Andy Provan
Bob Rigby
Manfred Schellscheidt
NASL Championship (1)
1973 (Champions)
NASL Division titles (1)
1973 (Eastern Division)
Indoor (1975–84)
Temple Owls football
Vernon Park (?–1927)
Temple Stadium (1928–1977)
Veterans Stadium (1978–2002)
Lincoln Financial Field (2003–present)
Franklin Field (alternate, 1978–2002)
Bowls & rivalries
Villanova (Mayor's Cup)
Culture & lore
Hooter T. Owl
"T For Temple U"
NFL draftees
Multi-purpose baseball parks (open air)
Anaheim Stadium (Angels; Anaheim, California)
Cleveland Municipal Stadium (Indians; Cleveland, Ohio)
Canadian National Exhibition Stadium (Blue Jays; Toronto, Ontario)
Memorial Stadium (Orioles; Baltimore, Maryland)
O.co Coliseum (Athletics; Oakland, California)
Robert F. Kennedy Memorial Stadium (Senators and Nationals; Washington, D.C.)
Rogers Centre (Blue Jays; Toronto, Ontario)
Kansas City Municipal Stadium (Athletics and Royals; Kansas City, Missouri)
Atlanta–Fulton County Stadium (Braves; Atlanta, Georgia)
Busch Memorial Stadium (Cardinals; St. Louis, Missouri)
Candlestick Park (Giants; San Francisco, California)
Mile High Stadium (Rockies; Denver, Colorado)
Qualcomm Stadium (Padres; San Diego, California)
Riverfront Stadium (Reds; Cincinnati, Ohio)
Shea Stadium (Mets and Yankees; Queens, New York City)
Sun Life Stadium (Marlins; Miami Gardens, Florida)
Three Rivers Stadium (Pirates; Pittsburgh, Pennsylvania)
Philadelphia Veterans Stadium (Phillies; Philadelphia, Pennsylvania)
Articles which use infobox templates with no data rows
WorldHeritage articles needing clarification from November 2009
Articles with dead external links from December 2010
Defunct multi-purpose stadiums in the United States
Army–Navy Game
Defunct Major League Baseball venues
Defunct National Football League venues
Defunct college football venues
Defunct soccer venues in the United States
Defunct sports venues in Philadelphia, Pennsylvania
Demolished sports venues in Pennsylvania
United States Football League venues
Philadelphia Eagles stadiums
Philadelphia Phillies stadiums
Philadelphia Atoms sports facilities
Temple Owls football venues
Baseball stadiums in Pennsylvania
Sports venues completed in 1971
Sports venues demolished in 2004
1971 establishments in Pennsylvania
2004 disestablishments in Pennsylvania
Philadelphia Fury
North American Soccer League (1968–84) stadiums
South Philadelphia
Culture of Philadelphia, Pennsylvania
Pennsylvania, National Football League, Pittsburgh Steelers, Philadelphia, Frankford Yellow Jackets
Association football, Dallas Tornado, Bobby Smith (soccer), Al Miller (soccer), Philadelphia Fury (1978–80)
Philadelphia Eagles, Philadelphia Union, Philadelphia, Temple Owls football, Pennsylvania | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 971 |
You are invited to celebrate an evening of Black Brazilian Cinema this Friday night at 7:00pm at auditorium 404 at 66 West 12th Street.
The event is hosted by Peter Lucas of GPIA, three seminal films made by Black Brazilian directors will showcase the tradition and the ongoing innovation of Black Brazilians.
Traditional Brazilian refreshments will be served. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,279 |
Tutti pazzi per Moose è una serie televisiva di animazione.
Trama
La serie segue avventure di Jack Jumble, dodicenne scatenato che ha fatto amicizia con Moose, un alce parlante.
Episodi | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,768 |
Q: How to structure a folder with Java libraries and their source/documentation for IDEA Using IDEA 9/10, I don't want to use MVN2 anymore (reasons mostly similar to http://kent.spillner.org/blog/work/2009/11/14/java-build-tools.html), but I enjoy some of the things that it provides. The most important point is having my library management include code and documentation automatically.
Jars are not the problem, because I can just throw a folder at IDEA and tell it that my "jars are there". Is there a way to place docs and source relative to that folder so that javadoc and source get detected by IDEA automatically?
(I don't want to check in ipr/iml any more, that just led to constant merge conflicts for us.)
A: There is no such feature at the moment, you always have to attach sources and documentation manually if your project is not managed by Maven.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,282 |
Церковь Святой Богородицы Катогике () — небольшая средневековая церковь в городе Ереван, столице Армении. Расположена в районе Кентрон на пересечении проспекта Саят-Новы и улицы Абовяна.
История
Самые старые надписи, высеченные на одной из стен церкви Катогике, датированы 1264 годом.
После землетрясения 1679 года, между 1693 и 1695 годами, к западной части церкви была пристроена большая базилика Святой Богородицы. Новый храм был построен из традиционного армянского туфа и не имел купола. Это была трёхнефная базилика, построенная в стиле армянской церковной архитектуры. Площадь молельного зала составляла 14,0×19,3 м, а внешнего периметра — 16,4×28,4 м, это была одна из самых из самых вместительных церквей Еревана. Церковь имела входы с южной и западной стороны.
В 1936 году базилика Святой Богородицы была снесена, чтобы освободить место для жилых зданий и лингвистического института на проспекте Саят-Нова. Во время сноса была обнаружена старинная церковь Катогике, заключённая в структуре большой базилики. После протестов со стороны археологов церковь была сохранена. В стенах разрушенной церкви было найдено множество старых хачкаров XV—XVII веков.
Нынешняя церковь Святой Богородицы, которая продолжает носить имя Катогике, имеет относительно небольшие размеры (5,4×7,5 м). В связи с очень ограниченным пространством, она используется только в качестве часовни-молельни.
Церковь Святой Анны
К северу от старинной церкви был построен новый религиозный комплекс. Он включает в себя большую церковь Святой Анны, а также здание ереванской резиденции Католикоса.
Галерея
Примечания
См. также
История Еревана
Храмы Еревана
Культовые сооружения по алфавиту
Церкви Армении
Армянские храмы XIII века | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,884 |
Cedar Creek is a ghost town in Box Elder County, Utah, United States. Founded in the 1860s, Cedar Creek was a farming town. Businesses included a school, an inn, and a store. The interstate highway system built through Cedar Creek and the nearby communities of Snowville and Park Valley. Cedar Creek was abandoned when weather conditions made farming difficult.
History
Cedar Creek was established in the 1860s as a farming community and was named after a creek that ran north of the town. By the early 20th century, about 20 families lived in Cedar Creek. A school that also served as a church was constructed in town, as was an inn, a service station, and a store. Some activities, including dances, theater performances, and talent shows, were held in the school. The town's mail was delivered to a home rather than to a post office. When the interstate highway system was developed, it ran from Snowville to Cedar Creek, then to nearby Park Valley. Native Americans were often seen near town, collecting nuts and hunting rabbits. The town's school teacher was considered one of the smartest people in town, and the residents of Cedar Creek often came to her for farming advice. In the 1920s, dry summers and cold winters made farming difficult. People then left town, and by the end of the decade, Cedar Creek was abandoned. Only a few buildings remain today.
See also
List of ghost towns in Utah
References
Ghost towns in Box Elder County, Utah
Ghost towns in Utah | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,215 |
{% highlight html %}
<section class="applications-section" id="maps-and-data">
<div class="inner">
<h2 class="section-title">Maps + data</h2>
<div class="row">
<div class="col">
<div class="card">
<header>
<h2>GFW Interactive map</h2>
<div class="icon"><svg><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#shape-map"></use></svg></div>
</header>
<div class="content">
<p>View and analyze data on the GFW Interactive Map.</p>
</div>
<footer>
<a href="/map" class="btn green medium">Open map</a>
</footer>
</div>
</div>
<div class="col">
<div class="card">
<header>
<h2>Country profiles & rankings</h2>
<div class="icon"><svg><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#shape-country"></use></svg></div>
</header>
<div class="content">
<p>View country-specific data, analyze forest change within a country or subnational jurisdiction, or view country rankings based on forest statistics.</p>
</div>
<footer>
<a href="/countries" class="btn green medium">View countries</a>
</footer>
</div>
</div>
<div class="col">
<div class="card">
<header>
<h2>Download data</h2>
<div class="icon"><svg><use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#shape-download"></use></svg></div>
</header>
<div class="content">
<p>Browse, learn more about, and download the data displayed on Global Forest Watch.</p>
</div>
<footer>
<a href="http://data.globalforestwatch.org" class="mobile-friendly btn green medium">Browse data</a>
</footer>
</div>
</div>
</div>
</div>
</section>
{% endhighlight %}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,029 |
Q: Changing class attributes by reference I'm relatively new to Python and have problems with immutable variables.
I'm trying to change the value of a class attribute (e.g. car.color). The difficulty is, that I can not use the namespace of car for doing this.
Up to now I did not find a satisvying answer to my questions. In the code below I tried to summarize the possible solutions (workarrounds) I found and their disadvantages:
class Car:
def __init__(self):
self.color = "green"
self.color_list = ["green"]
self.color_attrib = "green"
self.name = "VW Golf"
"""
and many more attributes...
"""
def makesetter(self, attribute):
def set_value(value):
attribute=value
return set_value
def set_color(self, value):
"in this function I directly have access to car.color and can change its value: "
self.color = value
def set_attrib(self, attribute_string, value):
setattr(self,attribute_string,value)
def change_attribute(attribute, value):
"In this function I can not access car.color directly"
attribute=value
def change_attribute_list(attribute, value):
"In this function I can not access car.color directly"
attribute[0] = value
if __name__ == "__main__":
car1 = Car()
change_attribute(car1.color, "red")
print(car1.color) # Color does not change because car1.color is immutable
g = car1.makesetter(car1.color)
g("red")
print(car1.color) # Color does not change because car1.color is immutable
change_attribute_list(car1.color_list, "red")
print(car1.color_list) # Color changes but seems like a workarround
# Disadvantage: in the namespace of car1, the user has to use a list to access a string value "car1.color_list[0]"
car1.set_color("red")
print(car1.color) # Color changes but seems like a workarround
# Disadvantage: Car needs a setter function for each attribute
car1.set_attrib("color_attrib","red")
print(car1.color_attrib) # Color changes but seems like a workarround
# Disadvantage: Attribute has to be passed as string & no auto completion while coding
Actually the function setattr() is internally exactly doing what I want. But it works with a string argument.
I tried to look into this function but it seems to be written in C++.
So do I have to use C++ to solve this problem without a workarround?
Or is there a Pythionic way of doing this?
A: The problem is you are trying to redefine the value of an instance from outside of the class. Since in __init__ you are defining your variables with self, they are only available for that instance. This is the point of a class - it's what makes them extensible and reusable.
Ideally, you would make a method within the class that would update those attributes, however, if you really need to update the class from an external function, you will have to define it as a class level variable. For instance:
class Car:
def __init__(self):
Car.color = "green"
can now be updated using:
def change_attribute(attribute, value):
"In this function I can not access car.color directly"
Car.color=value
outside of the class because you have not assigned it to one specific instance. Doing this presents a problem, however. Since we don't have a separate instance variable, if we try to re-instantiate the class, we are stuck with what was previously changed, i.e.
if name == "main":
car1 = Car()
car2 = Car()
change_attribute(car1.color, "red")
print(car1.color) # Prints red
print(car2.color) # Prints red
change_attribute(car2.color, "blue")
print(car1.color) # Prints blue
print(car2.color) # Prints blue
This is why classes themselves should be self contained and are meant to be immutable - the instance itself should be changed.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 88 |
\section{Introduction}
One of the powerful tools for code comprehension research is investigating the names that are given to functions, variables, and data structures.
Names bear witness to what the developer thought about the role of each part of code in the whole program \cite{salviulo14}.
There has therefore been substantial research on names and their meanings \cite{alsuhaibani21,aman21,avidan17,beniamini17,binkley15,butler15b,fakhoury20,gellenbeck91,lawrie07,newman20,schankin18}.
As part of this body of work, it has been shown that different developers often given different names to the same objects \cite{feitelson22}.
And renaming, where a maintainer changes a previously given name, is a common form of refactoring \cite{arnaoudova14,peruma18}.
Additional research has considered how easy it is to remember names \cite{binkley09c,etgar22}, and whether similar names may cause confusion \cite{tashima18,aman21b}.
In all these contexts it is important to be able to compare names to each other.
However, so far this has been done using general string-matching approaches, such as the edit distance.
Even worse, using Python's default Sequence Matcher is susceptible to giving results that depend on the order of the inputs.
To advance the research on variable naming we suggest a library of comparison functions that are specifically designed for comparing names in code.
These functions include features like
focusing on matching words rather than disconnected letters,
dealing with reordering,
and considering semantic similarities.
Importantly, they attempt to promote a metric of similarity that matches human perception, at the possible expense of lexical matching.
Thus they are not as mathematically crisp as the longest common subsequence or edit distance metrics, but may be better tuned for research involving humans and names.
\hide{
confusing names with low edit distance \cite{tashima18}.
similarity of names: \cite{aman21b}.
Aman et al.\ conjecture that similar names may be confusing, especially when dealing with long compound names composed of multiple words.
They therefore study the similarity of 31.8 million name-pairs from 684 Java projects.
Importantly, they distinguish between two types of similarity: string similarity and semantic similarity.
}
\section{Existing Algorithms for String Comparison}
The most common algorithms for comparing two strings (or variable names) are the Longest Common Subsequence algorithm, the Edit Distance calculation, and Python's Sequence Matcher.
\subsection{Longest Common Subsequence}
The Longest Common Subsequence algorithm (LCS) finds the longest sequence of characters that appear in the same order in both strings.
The length of this sequence divided by the length of the shorter (or longer) input string can then be used as a metric for the degree of similarity between the strings.
For example, if the input strings are ``a string is born'' and ``strong is better'', the longest common subsequence is ``strng is br'':
\begin{center}
\includegraphics[scale=0.8]{lcs.eps}
\end{center}
Thus 11 of 16 characters match, implying that the strings are quite similar to each other.
Note that the letters in the common subsequence need not be consecutive to each other.
When the \emph{are} consecutive we call it a sub\emph{string}.
\subsection{Edit Distance}
The Edit Distance (also known as the Levenshtein Distance \cite{levenshtein66}) counts the minimum number of edit operations required to transform one string into the other.
This has been used in naming research by Tashima et al.\ \cite{tashima18}.
There are several variants depending on which operations are allowed.
The most commonly allowed operations are the insertion, deletion, or substitution of a single character;
a possible fourth is the transposition of adjacent characters \cite{damerau64}.
Using the above two strings as an example again, turning the first into the second requires the following edit operations:
delete 2 characters `a' and ` ';
substitute `i' with `o';
substitute `o' with `e';
add 3 characters `t', `t', and `e';
and delete the character `n':
\begin{center}
\includegraphics[scale=0.8]{edit.eps}
\end{center}
The total number of character operations which divide the strings is therefore 8.
This can again be turned into a score by dividing by the length of longer input string \cite{aman21b}.
(It is important to normalize relative to the longer string, because the edit distance can be larger than the length of the shorter one but is limited by the length of the longer one.)
Note, however, that this score reflects the divergence between the strings, not their similarity.
To turn it into a similarity score, subtract it from 1.
\subsection{Sequence Matcher}
\label{sect:pyseqmat}
The above algorithms sometimes produce counter-intuitive results.
For example, if we use LCS to compare ``my string has mysterious chars'' with ``mystery match'', the longest common subsequence has 10 letters, but does not include a match of ``mysterious'' with ``mystery''.
This is counter-intuitive to humans, who see this as the most prominent match between these two strings.
\begin{center}
\includegraphics[scale=0.8]{mystery.eps}
\end{center}
The Python Sequence Matcher algorithm, which is part of the \code{difflib} library, is intended to better match human intuitions, and has been used in naming research by Etgar et al.\ \cite{etgar22}.
Interestingly, it has also been claimed to be advantageous for comparing sketch-based passwords \cite{amarnadh21}.
It is based on the Ratcliff-Obershelp algorithm, which was designed in the context of educational software to be ``forgiving and understanding of simple typing mistakes, and allow intelligent responses to erroneous input'' \cite{ratcliff88}.
The idea is to prefer matching \emph{contiguous substrings} over matching subsequences of disjoint letters.
Specifically, the algorithm starts by finding the longest contiguous substring of the two input strings, and then continues recursively on both sides of this substring.
Using the above example again, the longest common substring is ``myster'', and the recursive calls will find nothing on the left but a space and ``ch'' on the right, for a total of 9 matching letters.
\begin{center}
\includegraphics[scale=0.8]{mystery-py.eps}
\end{center}
The final score is the relative length of the resulting subsequence of identical letters, in this case 9/21.5 (the divisor is the average length of the two input strings).
\subsection{Shortcomings of Existing Algorithms}
While all the above algorithms provide reasonable measures for the similarity or difference between strings, they also have shortcomings.
Some of these are especially troublesome in the context of code comprehension studies involving variable names.
One problem, shared by the LCS and Edit Distance algorithms, is the possible fragmentation of the matched subsequences.
For example, if we compare the input string ``stop rampant germs at church'' with the other string ``strange match'', we will find that the shorter string is perfectly matched in the longer one!
But human beings reading these two strings will find this match artificial, because the two strings are composed of words that have no relation to each other.
Another problem is that these algorithms do not deal with changes in order.
As humans we can see that ``first second'' is closely related to ``second first''.
But LCS will just identify the longer repeated part and ignore the other, while calculating the edit distance will double-charge by suggesting a deletion from one place and an insertion in another.
The Python Sequence Matcher algorithm was designed to solve the problem of fragmentation.
However, it too suffers from some drawbacks.
The major one is that it is not symmetric, meaning that comparing string \code{a} with string \code{b} may lead to a different result than comparing \code{b} to \code{a}.
The reason for this unfortunate ``feature'' is that there can be more than one substring with the same maximal length.
The result then depends on which is found first and used as the root of the recursion, and this may depend on the order of the input strings%
\footnote{See \code{\footnotesize https://stackoverflow.com/questions/35517353/how-does-pythons-sequencematcher-work}.}.
For example, if our input strings are ``FirstLightAFire'' and ``LightTheFireFirst'' in this order, we will find that ``First'' is the longest common substring.
But using this as the basis for matching the input strings leads to an empty remainder to the left in the first one, and an empty remainder to the right in the second.
Therefore the recursive calls will not find any additional matches.
However, if we reverse the order of the inputs, ``Light'' becomes the first longest common substring.
In this case the recursive call with the remainders to the right will find an additional match, ``Fire''.
In the context of variable names (and actually also any other text), another issue is concerned with structure.
Humans do not consider names and strings as sequences of letters --- they parse them into words.
So it may be beneficial to actually compare the words in strings and names, rather than just looking for uninterrupted sequences of letters as done by Python's Sequence Matcher.
In addition, acknowledging the role of words opens the door to also consider the use of synonyms, which may be composed of completely different letters, but convey the same meaning.
\section{The New Library}
Our name matching library is based on the following decisions:
\begin{enumerate}
\item To prefer long \emph{contiguous substrings} over long disjoint subsequences, as in Python's Sequence Matcher.
As the example above indicates (matching 10 letters with LCS but only 9 with Python's Sequence Matcher), this may lead to \emph{sub-optimal} matchings.
But it is supposed to be more in line with how humans look at strings.
\item To be \emph{symmetric}, thus avoiding the main problem with Python's Sequence Matcher.
This is achieved by basing the match on the longest substring that maximizes the score rather than on the first one that is found.
\item To support a focus on \emph{words} rather than letters.
This is achieved by creating two versions of all the functions, one based on comparing letters and the other based on comparing words.
It gives users the choice of whether to work at the level of letters or words.
The difference is that respecting word boundaries better reflects the semantics of the names, and avoids situations such as that shown above where ``mystery'' was matched to ``my string''.
In addition, when comparing words long and short words receive the same weight.
\item To take possible \emph{reorderings} into consideration.
This is achieved by creating functions that allow reordering in addition to the original functions which only match in the same order.
It is important in the case of variable names to acknowledge that variable names like \code{countItems} and \code{itemsCount} are actually the same.
Users can use the difference between the score of the ordered and unordered functions to see the effect of word reordering.
\item To support the option of \emph{semantic matching} based on synonyms.
This is achieved by adding functions that use a dictionary of synonyms when comparing words.
It is again important for variable name research, for example to recognize that \code{itemsNumber} and \code{itemsCount} are actually more or less the same.
In addition, words forming singular-plural pairs or abbreviation-expansion pairs are also matched.
\end{enumerate}
\subsection{Provided Functionality}
Based on the above, we wrote a set of functions for finding matches between strings (or variable names).
Almost all of these functions use the concepts of Python's Sequence Matcher --- first finding the longest matching substring, and then matching both sides of the original match.
The difference is that they seek the optimal matches, so the algorithm is necessarily symmetrical.
Specific functions also enable matching between synonyms and singular/plural words, with a configurable ``cost'' for these cases vs.\ identical words.
In addition, we developed another set of functions that also perform ``cross matches'', i.e.\ matches between the left side of the match in one string to the right side of the other string.
For these functions we had to build a new scoring formula, because using the Sequence Matcher formula will give the same score to matches in any order, while clearly the preservation of order should lead to a higher score.
With all these variations, our library provides six main functions for comparing names:
\begin{enumerate}
\item \textbf{Ordered Match}: A function that operates on \emph{letters}, which improves upon Python's Sequence Matcher algorithm by being symmetric and finding the matches that maximize the score.
\item \textbf{Ordered Words Match}: A similar function that operates on \emph{words}.
As a result, each element match is not binary (match or mismatch) as in letters, but can also have intermediate values when words are similar but not identical.
This naturally affects the scoring.
\item \textbf{Ordered Semantic Match}: A function like the previous one, that uses a database of English synonyms and plural words to score semantically similar words.
\item \textbf{Unordered Match}: A function that operates on \emph{letters}, which enables cross matches (from different sides of the previous match).
Note that this is different from just taking the maximum of running the original functions on both orders of the input \cite{etgar22}, because this needs to be done at all levels of the recursion.
\item \textbf{Unordered Words Match}: A function that operates on \emph{words}, that enables cross matches.
\item \textbf{Unordered Semantic Match}: A function like the previous one, that scores on semantically similar words.
\end{enumerate}
Some of these functions accept parameters which define nuances and variations in the matching, for example the threshold value for considering similar words to be a match.
Full details are given below.
All of these functions return detailed information about the found matches, and specifically:
\begin{enumerate}
\item The ``normalized'' version of the input names (with all letters converted to lowercase and with word separators removed), and the list of words extracted from each one (when the function works on words).
\item The locations of all matches that were found, and, when the function works on words, the score of each individual word match.
\item The final score for the similarity between the two names, in the range $[0,1]$.
\end{enumerate}
In addition to the above functions we also have a function that divides a multi-word name to its constituent words, either based on underscores (or some other separator character provided by the user) or on camelCase notation.
This is used to normalize names and allow for valid comparisons that reflect content and not style.
\subsection{The Scoring formula}
\subsubsection{Scoring Rules}
Before committing to a scoring formula, we developed ten desirable rules that the scoring formula should respect.
These rules can then be used as guidelines when we weigh alternative formulas.
The first three are preliminary requirements reflecting basic principles:
\newcounter{myitem}
\begin{enumerate}
\item \textbf{Style neutrality}:
the result of comparing names should not depend on style.
Therefore changes in capitalization should be ignored, and the \_ should be ignored in snake\_case names.
\item \textbf{Non-optimality}:
giving a higher score to the biggest match is not a requirement.
Of course we want to promote good matches, but counting matching letters is not the only and most important yardstick.
\item \textbf{Normalization}:
Matches are not absolute but relative to the length of the names.
If the compared names have different lengths, this should be reflected by lowering the match score.
\setcounter{myitem}{\value{enumi}}
\end{enumerate}
The next two rules are defined by equalities:
\begin{enumerate}
\setcounter{enumi}{\value{myitem}}
\item \textbf{Symmetry}:
the result should be the same regardless of the order of the inputs.
Thus for any matching function
\[ \mbox{func}( str1, str2 ) = \mbox{func}( str2, str1 ) \]
\item \textbf{Consistency}:
different functions should produce the same result in simple cases.
The definition of ``simple'' cases is cases that are not handled by special versions of the functions.
As we have special functions to handle multiple words, reordering, and semantic matching, the simple cases are names composed of a single word, with no reordering, and no semantic equivalences.
For such cases and all matching functions
\[ \mbox{func1}( str1, str2 ) = \mbox{func2}( str1, str2 ) \]
\setcounter{myitem}{\value{enumi}}
\end{enumerate}
The other five rules are inequalities, which reflect different possible levels of matching:
\begin{enumerate}
\setcounter{enumi}{\value{myitem}}
\item \textbf{Focus}:
adding extra baggage reduces the matching score.
Thus for any matching function
\[ \mbox{func}( \mbox{"match"}, \mbox{"match"} )
> \mbox{func}( \mbox{"match"}, \mbox{"match.and.more"} ) \]
\item \textbf{Continuity}:
preserving the continuity of adjacent items should always receive a higher score than when they are separated.
Thus for all functions
\[ \mbox{func}( \mbox{"begin.end.aaaaaa"}, \mbox{"begin.end.zzzzzz"} ) > \mbox{func}( \mbox{"begin.end.aaaaaa"}, \mbox{"begin.middle.end"} ) \]
\item \textbf{Order preservation}:
matching in the same order should always receive a higher score than when words or letters are reordered.
And for functions that support reordering, matching with reordering should score higher than matching of unrelated strings.
Thus for all functions
\[ \mbox{func}( \mbox{"begin.end"}, \mbox{"begin.end"} )
> \mbox{func}( \mbox{"begin.end"}, \mbox{"end.begin"} ) \]
and for reordering functions
\[ \mbox{unordered}( \mbox{"begin.end"}, \mbox{"end.begin"} )
> \mbox{unordered}( \mbox{"begin.xyz"}, \mbox{"wuv.begin"} ) \]
\item \textbf{Words weight equality}:
when names are divided into words, long and short words have the same weight.
Thus letter-matching achieves a higher score than word-matching on long words, and a lower score on short words:
\[ \mbox{words}( \mbox{"gargantuan\_small"}, \mbox{"gargantuan\_little"} )
< \mbox{letters}( \mbox{"gargantuan\_small"}, \mbox{"gargantuan\_little"} ) \]
and
\[ \mbox{words}( \mbox{"gargantuan\_small"}, \mbox{"humongous\_small"} )
> \mbox{letters}( \mbox{"gargantuan\_small"}, \mbox{"humongous\_small"} ) \]
\item \textbf{Semantics count}:
exact matches should always score higher than those based on semantics.
But for functions that support semantic matching, this should score higher than matching of unrelated words.
Thus for all functions
\[ \mbox{func}( \mbox{"little"}, \mbox{"little"} )
> \mbox{func}( \mbox{"little"}, \mbox{"small"} ) \]
and for semantic functions
\[ \mbox{semantic}( \mbox{"little"}, \mbox{"small"} )
> \mbox{semantic}( \mbox{"little"}, \mbox{"smell"} ) \]
\end{enumerate}
\subsubsection{Crafting a Formula}
It is impossible to reduce all the above rules to practice in a single formula applicable to all the special cases.
We therefore made some compromises.
We start with the scoring formula used in Python's Sequence Matcher, called the \code{ratio}, and use it for scoring the similarity between sequences of letters.
This formula works as follows:
given two strings \code{a} and \code{b}, and letting \code{m} stand for all the matches between them, the similarity score between those two strings is
\[
ratio = \frac{2|\code{m}|}{|\code{a}|+|\code{b}|}
\]
(where the $|$~$|$ refers to the number of letters in each string).
This score is just the ratio between all the matching letters and the average length of both strings.
It provides normalization, symmetry, and focus from the list of desired rules.
In functions which handle words we depart from the above formula.
On one hand, we want to distinguish close-but-not-identical words.
For example, the score when comparing ``similar'' to itself should be higher than when comparing it to ``similarity''.
But at some point we need to recognize that the words are probably just different, e.g.\ when comparing ``similar'' with ``smaller''.
Our compromise is to use the same ratio formula from above also when comparing words, but to define a minimal required threshold.
If the threshold is not reached the similarity score between the words is set to 0.
Note that for dissimilar words this breaks the requirement for consistency.
The default threshold value is 2/3 (but it can be changed by a parameter).
Using $ratio$ to denote the basic similarity between two words, the word similarity is then
\[
word\_ratio = \left\{
\begin{array}{l@{\hspace{10mm}}l}
ratio & \mbox{if } ratio \ge 2/3 \\
0 & \mbox{otherwise}
\end{array}
\right.
\]
when the compared names are composed of multiple words, the scores for the different words need to be combined.
This is done using a simple generalization of the basic formula.
Denoting the two inputs by \code{a} and \code{b}, and using \code{m} to denote the set of matching words (that is, words that score above the threshold), the formula is
\[
multi\_word\_ratio = \frac{\displaystyle 2 \sum_{w \in \code{m}} word\_ratio(w)}
{||\code{a}||+||\code{b}||}
\]
where $||$~$||$ denotes the number of words in each name.
This gives the same weight to each word.
When using semantic search, we need to decide on the value to assign to two dissimilar words which are found to be synonyms.
We decided to use the threshold value used to identify matching words.
In other words, in the functions that support the matching of synonyms and the such, these matches will be given a score of 2/3 --- at the bottom of the range of scores for matching words.
If the threshold is changed, so is the score for semantic matches.
To score for continuity we consider a string of $n$ elements (letters or words) as if it was composed of $2n-1$ elements.
These elements are the original $n$ elements, and an additional $n\!-\!1$ ``glue'' elements binding neighboring letters or words.
For example, the string ``ab'' will be considered as being composed of ``a'', ``a\&b'', and ``b''.
When comparing it with another string ``cab'' all three will match.
But if the other string is ``acb'', only the ``a'' and ``b'' elements will match, and the ``a\&b'' glue element will not, leading to a lower total score.
The appropriate relative weight of glue elements is debatable.
It could be any arbitrary configurable value, but this would be hard to justify.
We therefore chose to use the highest possible value that respects a preference for longer matching over continuity.
This means that we want $n$ matching elements with no continuity to score higher than $n\!-\!1$ matching elements that are all continuous.
To achieve this, the default score for all the glue elements together should be equal to the score for matching one basic element.
So, when comparing names with $n$ words each, each matching word adds $\frac{1}{n+1}$ to the score, and each matching glue adds $\frac{1}{(n-1)(n+1)}$ to the score.
Importantly, this leads to a perfect score of 1 when the inputs are indeed identical.
If the inputs have different numbers of elements, $n$ is set to the average number, as in the basic matching formula above.
Finally, we need to consider the distinction between ``straight matches'' and ``cross matches''.
As noted in the rules above, it is desirable to give a somewhat lower score to matches that require re-ordering.
Note, however, that scoring for continuity already provides some score for order, because if words match after re-ordering their glue elements will not.
We therefore decided to avoid the overhead of measuring any additional deviations in order, and make do with scoring continuity as detailed above.
The price is that a comparison of ``one\_and\_two\_and\_three\_and\_four'' with ``one\_or\_two\_or\_three\_or\_four'' will achieve the same score (when reordering is allowed) as a comparison with ``four\_or\_three\_or\_two\_or\_one'': in both cases 4 of 7 words are matched, and no glue elements.
\subsection{Algorithmic Effects}
\label{sect:algo-score}
It should be noted that the scoring depends not only on the formula, but also on algorithmic decisions.
We explicitly decided not to strive for the optimal match, meaning the one that would lead to the highest score.
The reason was a desire to better match human intuitions.
This decision led to the selection of the following algorithms for matching.
When matching letters, we start with the longest consecutive substring, and use it as an anchor.
This may lead to a suboptimal score as shown above in Section \ref{sect:pyseqmat}.
When matching words, we likewise search for the longest sequence of matching words.
Again, this can lead to ``missed'' matches for other words, or not matching the longest words, and a reduced score.
For example, consider the matching of ``multi\_multiplayer'' with ``multiplayers\_layer''.
Matching at the letters level finds ``multiplayer'' as the first match, and then does not find any additional matches, for a final score of 0.665.
But with word matching, ``multi'' is matched with ``multiplayers'', and ``multiplayer'' is matched with ``layer'', which together with the glue connecting them leads to a score of 0.734.
Beyond demonstrating possible differences in matching, this example also shows that it is probably impossible to find a single formulation that will be optimal in some sense for all possible cases.
\subsection{Examples}
\newcommand{\m}[1]{{\color{orange}#1}}
\newcommand{\n}[1]{{\color{magenta}#1}}
\newcommand{\s}[1]{{\color{red}#1}}
\newcommand{\g}[1]{{\color{gray}#1}}
\newcommand{\beg}{\begin{center
\begin{tabular}{|p{0.38\textwidth}|c|p{0.45\textwidth}|}
\hline
}
\newcommand{\fin}{\hline
\end{tabular}\end{center}
}
\newcommand{\f}[1]{\hline
\multicolumn{3}{|l|}{#1:} \\
\hline
}
\newcommand{\e}[4]{\begin{tabular}{@{}l@{}}
#1 \\ #2
\end{tabular} &
#3 &
\parbox{0.44\textwidth}{#4} \\
\hline
}
We start with a simple example, comparing the multi-word strings ``FirstLightAFire'' and\linebreak ``LightTheFireFirst''.
As noted above, the Python Sequence Matcher function gives different results depending of the otrder of the inputs.
Our ordered matcher finds the optimal match regardless of input order.
\beg
\f{\code{difflib\_match\_ratio()}}
\e{\m{First}LightAFire}{LightTheFire\m{First}}{0.312}{matches 5 of 16 letters}
\e{\m{Light}The\m{Fire}First}{First\m{Light}A\m{Fire}}{0.562}{switch inputs, now 9 of 16 letters match}
\f{\code{ordered\_match()}}
\e{First\m{Light}A\m{Fire}}{\m{Light}The\m{Fire}First}{0.557}{finds optimal matching (the slightly lower score is due to partial continuity)}
\fin
When we match words instead of letters, the score is slightly reduced, because matching a long word match does not add more to the score than matching a short word.
And when stop words are ignored, the score is increased because the denominator is smaller.
\beg
\f{\code{ordered\_words\_match()}}
\e{First\m{Light}A\m{Fire}}{\m{Light}The\m{Fire}First}{0.400}{matches 2 of 4 words and no glue}
\f{\code{ordered\_words\_match(ignore\_stop\_words=True)}}
\e{First\m{Light}\g{A}\m{Fire}}{\m{Light}\g{The}\m{Fire}First}{0.625}{matches 2 of 3 words (ignoring ``a'' and ``the'') and 1 glue}
\fin
If we allow reordering, more letters or words can be matched.
\beg
\f{\code{unordered\_match()}}
\e{\m{FirstLight}A\m{Fire}}{\m{Light}The\m{FireFirst}}{0.867}{14 of 16 letters + 11 of 15 glue}
\f{\code{unordered\_words\_match()}}
\e{\m{FirstLight}A\m{Fire}}{\m{Light}The\m{FireFirst}}{0.600}{3 of 4 words + 0 of 3 glue}
\fin
In words matching, each word is a unit.
This is exemplifid by comparing ``multiword\_name'' with ``multiple\_words\_name''.
Using the default threshold of 2/3, only ``name'' matches.
Reducing the threshold to 0.57 allows ``multiword'' to match ``multiple'', but the ``word'' part is left unmatched.
Reducing the threshold even further, to 0.5, allows ``multiword'' to match ``words'', which adds the benefit of matching adjacent words.
Finally, matching based on letters does even better, as it does not respect word boundaries.
\beg
\f{\code{ordered\_words\_match()} [using the default \code{min\_word\_match\_degree=2/3}]}
\e{multiword\_\m{name}}{multiple\_words\_\m{name}}{0.286}{matches 1 word out of 2.5 and no glue}
\f{\code{ordered\_words\_match(min\_word\_match\_degree=0.57)}}
\e{\m{multi}\n{word}\_\m{name}}{\m{multi}\n{ple}\_words\_\m{name}}{0.452}{matches 2 words out of 2.5, with scores of 0.588 and 1, and no glue}
\f{\code{ordered\_words\_match(min\_word\_match\_degree=0.5)}}
\e{\n{multi}\m{word}\_\m{name}}{multiple\_\m{word}\n{s}\_\m{name}}{0.637}{lower threshold allows matching 2 words and glue for a higher score}
\f{\code{ordered\_match()}}
\e{\m{multiword}\_\m{name}}{\m{multi}ple\_\m{word}s\_\m{name}}{0.857}{matches 13 of 15 letters and 10 glues}
\fin
As another example consider the names ``MultiplyDigitExponent'' and ``DigitsPowerMultiplying''.
the Python Sequence Matcher function matches ``multiply'' and two additional letters.
Our ordered match does the same if the minimal match length is set to 1.
With the default minimal required match of 2 it only matches ``multiply''.
\beg
\f{\code{difflib\_match\_ratio()}}
\e{\m{Multiply}D\m{ig}itExponent}{DigitsPower\m{Multiplyi}n\m{g}}{0.465}{10 letters out of 21.5}
\f{\code{ordered\_match(min\_len=1)}}
\e{\m{Multiply}D\m{ig}itExponent}{DigitsPower\m{Multiplyi}n\m{g}}{0.460}{lower score due to partial continuity}
\f{\code{ordered\_match()} [using the default \code{min\_len=2}]}
\e{\m{Multiply}DigitExponent}{DigitsPower\m{Multiply}ing}{0.371}{8 letters of 21.5 and partial continuity}
\fin
When matching words, if we require exact matches then none are found.
But ``digit'' matches ``digits'' with a score of 0.909, and
``multiply'' matches ``multiplying'' with a score of 0.842.
Due to the order constraint, only one of these can be used, and the higher one is selected.
\beg
\f{\code{ordered\_words\_match(min\_word\_match\_degree=1)}}
\e{MultiplyDigitExponent}{DigitsPowerMultiplying}{0.000}{no perfect matches}
\f{\code{ordered\_words\_match()} [using the default \code{min\_word\_match\_degree=2/3}]}
\e{Multiply\m{Digit}Exponent}{\m{Digit}\n{s}PowerMultiplying}{0.227}{one out of 3 words matches with a score of 0.909, and no glue}
\fin
if semantic matching is used, ``exponent'' is found to be related to ``power''.
If we require perfect matching, by setting a matching threshold of 1, this is applied to this semantic match, and there are no additional perfect matches.
With the default matching threshold the semantic match is combined with a regular partial match.
\beg
\f{\code{ordered\_semantic\_match(min\_word\_match\_degree=1)}}
\e{MultiplyDigit\s{Exponent}}{Digits\s{Power}Multiplying}{0.250}{one semantic match considered a perfect match, and no glue}
\f{\code{ordered\_semantic\_match()} [using the default \code{min\_word\_match\_degree=2/3}]}
\e{Multiply\m{Digit}\s{Exponent}}{\m{Digit}\n{s}\s{Power}Multiplying}{0.519}{regular match scoring 0.909, semantic match with default 2/3, and one glue}
\fin
And all the above options can also be combined with reordering.
\beg
\f{\code{unordered\_match(min\_len=1)}}
\e{\m{MultiplyDigit}Ex\m{po}n\m{en}t}{\m{Digit}s\m{Po}w\m{e}r\m{Multiply}i\m{n}g}{0.782}{17 matching letters and 12 glues}
\f{\code{unordered\_match()} [using the default \code{min\_len=2}]}
\e{\m{MultiplyDigit}Ex\m{po}nent}{\m{Digit}s\m{Po}wer\m{Multiply}ing}{0.693}{2 is the default to avoid matching anagrams}
\f{\code{unordered\_words\_match(min\_word\_match\_degree=1)}}
\e{MultiplyDigitExponent}{DigitsPowerMultiplying}{0.000}{no perfect matches}
\f{\code{unordered\_words\_match()} [using the default \code{min\_word\_match\_degree=2/3}]}
\e{\m{MultiplyDigit}Exponent}{\m{Digit}\n{s}Power\m{Multiply}\n{ing}}{0.438}{two matches with scores of 0.909 and 0.842, and no glue matches}
\f{\code{unordered\_semantic\_match()} [using the default \code{min\_word\_match\_degree=2/3}]}
\e{\m{MultiplyDigit}\s{Exponent}}{\m{Digit}\n{s}\s{Power}\m{Multiply}\n{ing}}{0.729}{the above two matches, a semantic match scoring 2/3, and one glue}
\fin
\section{Code Design and implementation}
\newcommand{\class}[1]{\bigskip\noindent\textsf{\textbf{\Large #1}}}
\newcommand{\member}[1]{\textsf{\textbf{\small #1}}}
\newcommand{\method}[1]{\medskip\underline{\textsf{\textbf{#1}}}}
{\setlength{\parindent}{0pt}\setlength{\parskip}{1ex}
\class{class NamesMatcher}
The main class that includes all the functionality is \code{NamesMatcher}.
In its typical usecase it accepts two names (strings) to compare, and a set of parameters that control nuances of the matching.
It then provides a set of functions that return the score for different types of matches, e.g.\ based on letters or words, and with or without reordering.
The constructor for \code{NamesMatcher} is:
\begin{tabbing}
xxxx\=xxxx\=xxxxxxxxxxxxxxxxxxxxxxxxxx\= \+\kill
\code{NamesMatcher(} \+ \\
\code{name\_1=NONE,} \> \# first name \\
\code{name\_2=NONE,} \> \# second name \\
\code{case\_sensitivity=False,} \> \# \code{True} to retain case differences \\
\code{word\_separators='\_~\textbackslash t\textbackslash n',} \> \# to separate words for word matching \\
\code{support\_camel\_case=True,} \> \# to separate words for word matching \\
\code{numbers\_behavior=NUMBERS\_SEPARATE\_WORD,} \# how to treat digits \\
\code{stop\_words\_list=$\left<\right.$\emph{see below}$\left.\right>$} \> \# words to ignore when matching \-\\
\code{)}
\end{tabbing}
The parameters are:
\member{case\_sensitivity}: whether to retain letter case in the comparisons.
The default is to fold all letters to lowercase, so for example \code{cRaZYcaP} is the same as \code{crazyCap}.
If you are analyzing code in a language that distinguishes between upper and lower case you might want to set this to \code{True}.
Also if you are just comparing two strings.
But if you are interested in the \emph{meanings} of names, it is better to ignore case differences.
\member{word\_separators}: letters that signify a word break.
This is only relevant if you are using matching functions that operate on words.
A set of such letters can be provided, and the appearance any one of them in a name indicates a word break.
It is impossible to break only on a sequence of several letters.
\member{support\_camel\_case}:
This too is only relevant if you are using matching functions that operate on words.
The default is to recognize camelCase as an indication for word breaks.
Note: camelCase and word separators may be combined.
Thus ``FileMenu\_saveAsOption'' will be separated into 5 words.
\member{numbers\_behavior}:
how to treat digits that appear in names.
There are three options:
\begin{enumerate}
\item NUMBERS\_SEPARATE\_WORD = a number is treated as a separate word, namely break words on both sides of the number
\item NUMBERS\_IGNORE = match only on letters and ignore numbers as if they didn't exist
\item NUMBERS\_LEAVE = digits are considered to be lowercase letters and conjoined with adjacent letters as one word
\end{enumerate}
\member{stop\_words\_list}: a list of words to ignore when matching words.
The default list includes the words a, are, as, at, be, but, by, for, if, of, on, so, the, there, was, where, were.
This is derived from lists commonly used in information retrieval.
However, some words are intentionally not included, such as ``is'' (which is often used in Boolean variable names like \code{isUpper}) and logical operators (``and'', ``or'', and ``not'').
In place of the constructor, you can also use setters later.
The provided setters are:
\member{set\_name\_1(n)}
\member{set\_name\_2(n)}
\member{set\_names(n\_1, n\_2)}
\member{set\_case\_sensitivity(cs)}
\member{set\_word\_separators(s)}
\member{set\_support\_camel\_case(b)}
\member{set\_numbers\_behavior(nb)}
\member{set\_stop\_words(sw)}
In addition there are getters for all the parameters, and also a couple of special ones for internal representations of the names:
\member{get\_norm\_names()}:
return both names after normalization.
If a name is undefined, \code{None} is returned.
Normalization means three things:
\begin{itemize}
\item Convert the name to all lowercase (if \code{case\_sensitivity} was not set)
\item Erase word separators
\item If \code{numbers\_behavior} was set to \code{NUMBERS\_IGNORE}, erase numbers
\end{itemize}
So the normalized version of ``defaultIs\_FOObar'' is ``defaultisfoobar''.
\member{get\_words()}:
return an array of the words in name.
The procedure for breaking a name into words is:
\begin{enumerate}
\item Break on the letters identified as word separators, and erase those letters.
\item Break on both sides of numbers if \code{numbers\_behavior} was set to \code{NUMBERS\_SEPARATE\_WORD}.
\item Handle camelCase notation, unless \code{support\_camel\_case} was set to \code{False}.
This is done in two steps:
\begin{enumerate}
\item If an uppercase letter is followed by lowercase letters, break before the uppercase one.
This handles cases like ``camelCase'' $\Rightarrow$ camel+Case, and also ``USAToday'' $\Rightarrow$ USA+Today.
\item Break on an uppercase letter that appears after a lowercase letter.
This handles cases like ``theUSA'' $\Rightarrow$ the+USA.
\end{enumerate}
If \code{numbers\_behavior} was set to \code{NUMBERS\_LEAVE}, numbers are treated as lowercase letters.
\end{enumerate}
The individual words are normalized as described above.
The main API methods provided by \code{NamesMatcher} are variants of the \code{ratio()} method of Python's Sequence Matcher.
They each perform a different type of matching and compute its score.
Scores are in the range [0,1], with 0 representing no relation whatsoever and 1 representing complete identity.
In addition to the score, these functions also provide full details of the matches that were found.
This is conveyed by an object of class \code{MatchingBlocks}, which is described below.
The API methods are:
\method{ordered\_match()}
This method finds the matches that maximize the ratio between the names.
It is a basic string matching routine, working on individual letters, rather similar to Python's Sequence Matcher.
Logically it starts the matching with the longest consecutive match, and then continues recursively on both sides, thereby maintaining order.
In practice, however, the implementation uses dynamic programming rather than recursion.
The method signature is
\begin{tabbing}
xxxx\=xxxx\=xxxxxxxxxxxxxxxxxxxxxxxxxx\= \+\kill
\code{ordered\_match(} \+\\
\code{min\_len=2,}\\
\code{continuity\_heavy\_weight=False} \-\\
\code{)}\\
\end{tabbing}
The parameters are:
\member{min\_len}: the minimum number of consecutive letters that will be considered as a match.
The default is 2 to avoid the impact of matching individual unrelated letters.
\member{continuity\_heavy\_weight}: the weight given to continuity in the match.
Setting this to \code{True} sets the weight of each continuity element to 1, like the weight of each matching letter, rather than the default where all of them together have a weight of 1.
In addition the method, as all others, is modulated by the parameters of the \code{NamesMatcher} object.
For this method the only relevant parameter is \code{case\_sensitivity}.
To perform simple string matching on the strings as they appear set \code{case\_sensitivity} to \code{True} and \code{min\_len} to 1.
As this method operates on letters and not on words, it does not respect the \code{word\_separators} parameter of \code{NamesMatcher}.
In other words, the word separator letters will be matched like any other letter.
Note: this method uses dynamic programming for its calculation.
As a result its running time is about $m^{2}n^{2}$, where $m$ and $n$ are number of letters in the first and second names, respectively.
\method{unordered\_match()}
This method also finds the matches that maximize the ratio between the names, but it allows cross-matching, that is matches that do no maintain the original order in the two names being matched.
Logically it starts the matching with the longest consecutive match, and then continues recursively to match the concatenations of the leftovers from both sides.
As a result the found matches need not respect the original order.
The implementation, however, is iterative rather than recursive.
Each iteration is composed of two steps.
First, we find the longest consecutive match, and record it.
Then we overwrite the matching letters to block them out.
In each name, the overwriting is done with some letter that does not appear in the other name, to avoid spurious additional matches.
The iterations continue in this manner until no additional matches are found.
Blocking out is used rather than erasing the matching letters because this way the indices of the letters in subsequent matches remain as in the original names.
The method signature and parameters are similar to the previous method:
\begin{tabbing}
xxxx\=xxxx\=xxxxxxxxxxxxxxxxxxxxxxxxxx\= \+\kill
\code{unordered\_match(} \+\\
\code{min\_len=2,}\\
\code{continuity\_heavy\_weight=False} \-\\
\code{)}\\
\end{tabbing}
Note that if \code{min\_len} is set to 1 this method will identify anagrams as perfect matches.
\method{ordered\_words\_match()}
This method finds the word matches that maximize the ratio between the names.
Like the other methods based on words it respects word boundaries, and will not match one word with parts of multiple other words.
Logically the method starts by finding the matching sequence of words with the highest total ratio, and continues recursively on both sides, thereby maintaining order.
The implementation, however, uses dynamic programming rather than recursion.
If multiple highest matching sequences are found with exactly the same score, all of them are checked to find the one that leads to the maximal total score.
Note that this method does not guarantee that the found match will include the individual maximal matching word, because some other sequence may lead to a higher total score.
Likewise, it does not guarantee that the final match includes the maximal number of matching words, because other shorted matches may include words with higher individual scores.
The method signature is
\begin{tabbing}
xxxx\=xxxx\=xxxxxxxxxxxxxxxxxxxxxxxxxx\= \+\kill
\code{ordered\_words\_match(} \+\\
\code{min\_word\_match\_degree=2/3,}\\
\code{prefer\_num\_of\_letters=False,}\\
\code{ignore\_stop\_words=False} \-\\
\code{)}\\
\end{tabbing}
The parameters are:
\member{min\_word\_match\_degree}: a float in the range $(0,1]$, which defines the minimum score for two words to be considered as a match.
Setting this to 1 means a perfect match is required.
\member{prefer\_num\_of\_letters}: When there are two or more matches with the same maximal ratio, setting this to \code{True} will cause the best match to be chosen based on the number of letters rather then the number of words.
\member{ignore\_stop\_words}: if \code{True}, ignore any word appearing in the list of stop words and do not count them when scoring the match.
This is only done if there is a perfect match with the word.
Note: this method uses dynamic programming for its calculation.
As a result its running time is about $m^{2}n^{2}$, where $m$ and $n$ are number of words in the first and second names, respectively.
\method{unordered\_words\_match()}
This method also finds the word matches that maximize the ratio between the names, but it allows cross-matching, that is matches that do no maintain the original order in the two names being matched.
Logically the method starts by finding the matching sequence of words with the highest total ratio, and continues recursively to match the concatenations of the leftovers from both sides. As a result the found matches need not respect the original order.
The implementation works by erasing the found match and repeating as long as additional matches are found, as described above for \code{unordered\_match()}.
The method signature and parameters are similar to the previous method:
\begin{tabbing}
xxxx\=xxxx\=xxxxxxxxxxxxxxxxxxxxxxxxxx\= \+\kill
\code{unordered\_words\_match(} \+\\
\code{min\_word\_match\_degree=2/3,}\\
\code{prefer\_num\_of\_letters=False,}\\
\code{ignore\_stop\_words=False} \-\\
\code{)}\\
\end{tabbing}
\method{ordered\_semantic\_match()}
This and the next method are the same as the previous two, except for allowing semantic matches between individual words.
This aims to identify semantically similar names even if different words are used.
The implementation is based on the following considerations regarding what words are considered to be semantically equivalent:
\begin{itemize}
\item Synonyms are considered to be semantically equivalent and therefore match.
Synonyms are identified based on a an open thesaurus%
\footnote{https://raw.githubusercontent.com/zaibacu/thesaurus/master/en\_thesaurus.jsonl}.
\item Words that differ only in number, that is singular and plural, are considered to be semantically equivalent and therefore match.
This includes ending with ``s'' or ``es'', and a list of special cases (e.g.\ ``half'' and ``halves'')%
\footnote{https://github.com/tagucci/pythonrouge/blob/master/pythonrouge/RELEASE-1.5.5/data/WordNet-2.0-Exceptions/noun.exc}.
\item Abbreviations and their extensions are considered to be semantically equivalent and therefore match.
This is identified by one word being a prefix of the other, coupled with the requirement that the shorter one be at least 3 letters long.
\end{itemize}
The method signature is
\begin{tabbing}
xxxx\=xxxx\=xxxxxxxxxxxxxxxxxxxxxxxxxx\= \+\kill
\code{ordered\_semantic\_match(} \+\\
\code{min\_word\_match\_degree=2/3,}\\
\code{prefer\_num\_of\_letters=False,}\\
\code{ignore\_stop\_words=False} \-\\
\code{)}\\
\end{tabbing}
The first parameters has an added role:
\member{min\_word\_match\_degree}: a float in the range $(0,1]$, which defines the minimum score for two words to be considered as a match.
This is also used as the score for semantically matching words, when the calculated score is lower.
And the last one may have special significance:
\member{ignore\_stop\_words}: stop words (in, if, of, the, that, etc.) are considered semantically meaningless.
To avoid diluting the score with such meaningless matches, these words can be removed from consideration by setting this parameter to \code{True}.
The list of stop words is set by a parameter to the \code{NamesMatcher} constructor.
\method{unordered\_semantic\_match()}
Same as the previous method, except that reordering of words is allowed.
The reordering is done as in \code{unordered\_words\_match()}.
The method signature and parameters are similar to the previous method:
\begin{tabbing}
xxxx\=xxxx\=xxxxxxxxxxxxxxxxxxxxxxxxxx\= \+\kill
\code{unordered\_semantic\_match(} \+\\
\code{min\_word\_match\_degree=2/3,}\\
\code{prefer\_num\_of\_letters=False,}\\
\code{ignore\_stop\_words=False} \-\\
\code{)}\\
\end{tabbing}
\method{unedit\_match()}
This method is a variant on \code{unordered\_match()}, in which found matches are indeed erased rather than being blocked out.
This enables subsequent matches to span both sides of previous matches, which may be useful in some cases.
Note that this only makes a difference for short matches, where either or both of the matching parts individually are shorter than \code{min\_len}.
As the found matches may be discontinuous, this requires a complicated recording of matches locations.
The method signature is
\begin{tabbing}
xxxx\=xxxx\=xxxxxxxxxxxxxxxxxxxxxxxxxx\= \+\kill
\code{unedit\_match(} \+\\
\code{min\_len=2,}\\
\code{continuity\_heavy\_weight=False} \-\\
\code{)}\\
\end{tabbing}
In addition to the above, \code{NamesMatcher} also includes 3 methods implementing traditional string matching algorithms.
These are actually wrappers to implementations in other libraries.
They return the score of the found match, and not a full \code{MatchingBlocks} object like the previous methods.
These methods are:
\method{edit\_distance(enable\_transposition=False)}
An implementation of edit distance calculation, based on insert, delete, and substitute operations.
This has two versions, which come from the \code{strsimpy} library.
The default is to use the \code{Levenshtein()} method.
The alternative, used is \code{enable\_transposition} is set to \code{True}, is to use the \code{damerau()} method.
This adds a fourth basic operation, which is to transpose adjacent letters.
\method{normalized\_edit\_distance(enable\_transposition=False)}
This is an implementation of the edit distance calculation, like the previous method.
The difference is that the calculated edit distance is normalized relative to the length of the longer input.
\method{difflib\_sequence\_matcher()}
This is a wrapper for Python's Sequence Matcher \code{ratio()} function.
\class{class MatchingBlocks}
As noted above, most of the matching methods return all the data about their results in a \code{MatchingBlocks} object.
Such objects contain the following members:
\member{name\_1}: the first name as input to the matching (could be normalized or array of words)
\member{name\_2}: the second name as input to the matching (could be normalized or array of words)
\member{matching\_type}: LETTERS\_MATCH or WORDS\_MATCH
\member{ratio}: the calculated ratio between the two names
\member{matches}: array of matches (\code{OneMatch} objects, describing the locations and lengths of all matches)
\member{cont\_type}: a Boolean indicating if the match is necessarily continuous or not (discontinuous only for \code{unedit\_match()})
\member{continuity\_heavy\_weight}: how glue elements were weighted
\hide{
The following classes are used to store necessary data.
\comment{consider globally replacing ``var'' with ``name''}
\comment{add defined global constants (like default word match threshold?)}
\class{class Var}
\begin{quote}
\method{Members:}\\
\member{name}: the original name (string)\\
\member{words}: list of words that compose the name\\
\member{norm\_name}: the name after normalization\\
\member{separator}: a select character that does not appear in the name, for internal use while searching for a match
\end{quote}
\class{class OneMatch}
\begin{quote}
\method{Members:}\\
\member{i}: the index of the match in the first name\\
\member{j}: the index of the match in the second name\\
\member{k}: the length of the match (in letters or words)\\
\member{l}: the length of the match in letters when matching words\\
\member{r}: the ratio (the score for this match)
\end{quote}
}
}
\section{Limitations}
We believe our matching functions provide significant advantages over previous ones, especially for measuring the similarity of names in code.
For example, they avoid the asymmetry of Python's Sequence Matcher.
However, they have their limitations.
In our implementation we preferred breadth over depth:
we wanted to incorporate many ideas, and made do with a basic implementation of each one.
Thus the results may be improved by using better dictionaries or word-splitting procedures \cite{hill14,hucka18}.
In addition, our implementation assumes that it will only be called to compare reasonably short names, and not long texts.
In some of the functions we use dynamic programming or other algorithms that do not scale very well.
One of the perennial problems with splitting is to identify conjoined words like ``multiword'' or ``schoolbus''.
The common approach is to try all possible splittings and compare to a dictionary.
This might be reasonable for 2 words, but not for more.
In our case, if both names include the same conjuncts the problem is moot.
And if one contains the individual base words, or even just some of them, comparing the results of letter-matching with word-matching can provide the necessary information on how to split.
Also, we argued above in Section \ref{sect:algo-score} that matching words should start with the highest single match, even if this comes at the expense of not achieving the highest total score.
A possible alternative may be to check all possible matches, and find the combination that leads to the highest score.
Our choice was based on anecdotal evidence that this leads to matches that seem better.
But it may be that better compromises can be found.
Our scoring function also completely ignores reordering, except as detected by lack of continuity.
And indeed, it seems hard to create a formula that acknowledges both continuity and order preservation.
When names with only two words are considered, continuity and order are actually the same thing, so this would lead to double counting.
This may also happen when there are more words, e.g.\ when the last two are switched.
In other cases we need to divide the extra score between the two attributes in some way.
And if we want to retain the preference for higher scores for more matches, the total attributed to continuity and order is reduced as the number of words grows.
Future work may better resolve these issues.
Finally, our work like the vast majority of work on comparing names places a focus on the matching letters which compose words.
However, the mapping of words to meanings is not one-to-one.
We acknowledge this by providing functions that attempt to take semantics into account by looking for synonyms.
However, it is also important to try to avoid homonyms --- words with the same spelling that mean different things \cite{arnaoudova10}.
A possible approach is to use natural language approaches based on big data to identify words that appear in similar contexts.
However, such approaches suffer from possible confounding of synonyms and antonyms \cite{ali19}.
For example, Table 1 in the groundbreaking paper by Alon et al.\ introducing code2vec includes ``notEqual'' as one of the tokens that appear in the same contexts as ``equal'' \cite{alon19b}.
Dealing with this would require a whole new level of analysis, which we leave to future work.
\bibliographystyle{myabbrv}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,128 |
Win each race in order to be able to advance in the championship. Complete 3 racing modes - circuit, knockout and time attack. The 'Circuit racing' implies a large number of competitors racing in close proximity to the finish line. In the 'Knockout Race you compete against 4 or 5 other drivers and, in order to stay in the game, you need to finish every lap before at least one other competitor. Last, but not least, in the 'Time Attack' Race you'll be all by yourself on the track but you will have to race against the best time of the other competitors. | {
"redpajama_set_name": "RedPajamaC4"
} | 765 |
Your deposits will be returned to you after a 10 administration fee or charge of 25 has been deducted, whichever is greatest.View our online casino reviews to see an up to date list of all the top online casinos and their welcome bonuses.
welcome bonus refers to a reward given to a player when they sign up as a member. Maximum amount of Cashback bonus credited shall be as follows: 25 for account VIP statuses of Bronze, Chrome or Silver. Coupons (i) Any coupons redeemed must meet wagering requirements of particular games. In order to earn 10 Casimba Points, Player A must therefore wager 100 x 2 200 before the Casimba Points will be declared valid. For Example: A Player has purchased 100 and received a bonus of 100, therefore has a total balance of 200. Should You bet higher than this while the Welcome bonus is in play, the casino reserves the right to confiscate all winnings. Casino Superlines on casino nd free spins 11.8.2018 laittanut varmaan koko vuoden kovimman tervetulobonuksen, jolle ei ole voittajaa näköpiirissä. Loistava, suomen kielellä toteutettu sivusto, upea pelivalikoima ja tällainen tervetulobonus, niin ykkösvalinta oli aivan selkeä. Heres an example: Upon successful account validation you received 20 free spins on the Mega Gems slot machine and after completing the free spins you ended up with winnings of 200 in Bonus Money. (iv) The Casino welcome bonus is subject to standard play-through requirements as laid out in the Promotional Terms and Conditions above with the addition that you must wager on the total amount of cash deposited and bonus funds received. Therefore, please make sure that you set your settings on Unique Casino to receive emails and text messages, simba casino if you wish to take advantage of these offers. Muistat vain käydä sivuillamme sännöllisesti, niin sinäkin olet mukana nauttimassa näistä netin parhaista casinobonuksista, joita et muualta löydä. When claiming a welcome bonus, birthday bonus, bonus wheel bonus or special bonus, any existing Bonus Money balance will be lost and your wagering progress will be reset. View the best casinos for bonuses. As soon as you make your first deposit and your account has been verified, you will be granted 20 free spins on one of our most popular slot machines. Unique Casino reserves the right to change the structure of the bonus program at any time. This fee varies in accordance with the changes. In case of suspicion of a user registering more than one account, Unique Casino reserves the right to combine all funds into one account and deactivate any bonuses. (viii) Whilst bonus or free spin promotional offers are advertised on specific games, they may be accessed on a variety of other games. Withdrawal requirements apply only to bonuses or winnings derived from them (Bonus Money balance not with money you have deposited (Cash Money balance). Suomi-Kasino tekee pelaamisesta ja sen ymmärtämisestä helpompaa, ja sinun tarvitsee vain astua sisän nettikasinoiden viihdyttävän maailmaan kanssamme. Viihtyisiä peli- ja lukuhetkiä, toivottaa koko Suomi-Kasinon tiimi. . Pelaajan näkökulmasta nettikasinolla on monta tekijä, jotka vaikuttavat olennaisesti kasinon viihtyvyyteen, pelattavuuteen ja luotettavuuteen, oli se sitten suomi casino tai ulkomainen netti kasino. (vii) Acceptance of any prize shall constitute consent on the winners part to allow the use of the winners name, image, voice and/or likeness by the casino for editorial, advertising, promotional, marketing and/or other purposes without further compensation except where prohibited by law. For example, Black or Red betting on Roulette or covering more than 25 of the 37 numbers on the table. Nykypäivänä uusia kasinoita tulee joka kuukausi, jolloin varsinkin uudelle pelaajalle voi olla haastavaa selvittä eri kasinoiden tarjoamien bonusten ja palveluiden sisältöä yksiselitteisesti. Suomikasino kokemuksia voitkin siis lueskella. Kyllä näillä kolmella netticasinolla kelpaa aloittaa pelaaminen, sillä sen verran kovatasoiset tervetulobonukset on nyt laitettu tarjolle. (vi) If you have never made a deposit, any gameplay using bonus funds will not unlock bonus funds or bonus winnings from free spins and all winnings will return directly to your bonus account until you make your first deposit. These rewards are usually the start of the comps tier system, with the player picking up further bonuses as they become a regular player.
75 for account VIP status of Diamond. Ilmaiskierrokset, suomiKasino on pelaajan asialla ja meidän tehtävänämme on auttaa sinua ymmärtämän kasinoiden maailmassa käytettyjä termejä. SuomiKasinon parhaat kasinovinkit, the welcome bonus will usually be a small reward like a drink. Uusi asiakas saa vieläpä 10 ilmaiskierrosta ilman talletusta ja ne ovat ilman ehtoja. Any eligible bonuses will be displayed there under Available Bonuses. Address, kun useita nettikasinoihin pitkän casino perehtyneitä ammattilaisia kokoontui ja pätti luoda yhden tiiviin kokonaisuuden. Jossa käsitellän internetin kasinoiden sisältöä, joiden toiminta, kuten bonukset. Iv Unless otherwise stated, joka antaa bonuksia, suomiKasino syntyi.
Sitten on myös ne pelipaikat, jotka tarjoavat ilmaista casino rahaa.Hyvinä esimerkkeinä ovat Mr Green.Tarkista myös mikä bonuksen kierrätysvaatimus on ja mitä pelejä sillä voi pelata.
Suomenkielisiä netticasinoita, voi tulla hyviä tarjouksia, free Spins Bonus Spins. Mutta edelleenkin keskitason kasinoita, what is a Welcome Bonus, suspend. Joilta saa todella hyviä casinobonuksia, iii Coupons can be withdrawn or terminated at any time and Casimba reserves the right to refuse players the use of coupons at any time. Free spins, joiden bonukset auttavat sinua tutustumaan uuteen nettikasinoon helposti. Unique ja muut bonukset, jossa voit viettä aikaa ja voittaa kenties huikeita summia. Vi All winnings from the bonus spins are considered to be bonus money casino siirto and will be converted to real ilmaiset kierrokset casino money only after the initial bonus wagering requirements are met unless stated otherwise in the Promotional Terms and Conditions. Olitpa sitten aivan uusi kasinopelaaja tai jo kaiken nähnyt konkari.
Se tarkoittaa varmasti entistä kovempia kampanjoita, joten saatamme kenties nähdä uuden Top-3 listan vuoden lopussa.Winnings from deposited money bets are always available for withdrawal.
(iii) For additional Bingo Term and Conditions please click here.
These winnings can be withdrawn as described in section Deposit Bonuses.(xvii) Any other bonuses received, such as redemption of Loyalty Points will be added to your bonus account and will be subject to standard wagering requirements.(viii) The casinos decision regarding the award of all prizes shall be final and binding on all participants in the contest, and no queries, challenges or appeals may be made or entertained regarding the decision. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,221 |
Senior Design Challenge faculty receive award
On Jan. 15, the Dartmouth Center for the Advancement of Learning announced that design thinking lecturer Eugene Korsunskiy and Thayer School of Engineering professor Peter Robbie won the 2018 Apgar Award for Innovation in Teaching for their "Senior Design Challenge" course. The new two-term course, Engineering 15.02, "Senior Design Challenge," provides students with the opportunity to create solutions to real world issues, forge connections in industry and hone professional skills.
https://www.thedartmouth.com/article/2019/01/senior-design-challenge-faculty-receive-award
Audrey Geisel remembered for her whimsy and business
https://www.thedartmouth.com/article/2019/01/audrey-geisel-remembered-for-her-whimsy-and-business
"One" event at '53 Commons will highlight food from Hanover restaurants
Updated Jan. 23 at 8:22 p.m.
https://www.thedartmouth.com/article/2019/01/one-event
College celebrates 2019 MLK day with Franchesca Ramsey
On Monday night, comedian and social justice activist Franchesca Ramsey delivered the keynote address at the College's 2019 Martin Luther King Jr. Celebration Feature Presentation. Over the weekend and in the upcoming weeks, Dartmouth held and will hold events ranging from presentations on topics such as mental health and sexual assault to films centered around social justice.
https://www.thedartmouth.com/article/2019/01/college-celebrates-2019-mlk-day
Alumni Gym extends hours due to cold weather
Due to Hanover's chilly temperatures and fewer outdoor activity options, winter term means extended hours for campus facilities such as the Alumni Gym. On Fridays, Saturdays and Sundays, the gym stays open for an extra hour until 10 p.m., as opposed to 9 p.m. during the fall, spring and summer terms.
https://www.thedartmouth.com/article/2019/01/gibbs-winter-hours
Study finds that border wall harms U.S. economy
The current border wall between the U.S. and Mexico — constructed over the last 13 years under the Secure Fence Act of 2006 — barely affects migration patterns between the two countries and harms the U.S. economy, according to a working paper recently published by Dartmouth professor of economics Treb Allen and his colleagues at Stanford University.
https://www.thedartmouth.com/article/2019/01/border-liu
Researchers study hysteresis in vaccination decisions
Vaccines were first introduced two centuries ago as a disease prevention mechanism. Since then, medical professionals have used them routinely for their consistently safe and beneficial effects. However, recent research by mathematics professor Feng Fu and graduate student Xingru Chen has demonstrated that decreasing vaccination rates in developed countries are worsened by the hysteresis effect.
https://www.thedartmouth.com/article/2019/01/thomas-vaccine
Q&A with Russian professor Lynn Patyk
Russian professor Lynn Patyk believes that things that appear to be unambiguous moral evils — like terrorism — are more complicated than we make them out to be. Her research focuses on the ways in which modern terrorism has been shaped by literary narratives. In her first-year seminar, Russian 7.01 "Who is the Terrorist?" and Russian 10, "Russian Civilization," Patyk teaches how "early thinkers" like Russian authors Mikhail Bulgakov and Fyodor Dostoevsky can shed light on Russia's political ethos. She aims to trace terrorism back to its earliest roots — a mode of popular dissent.
https://www.thedartmouth.com/article/2019/01/patyk-q-a
Members of the 2019 Trips directorate are announced
Dartmouth Outing Club First-Year Trips director Maddy Waters '19 and assistant director Dorothy Qu '19 announced the 2019 Trips directorate on Friday morning.
https://www.thedartmouth.com/article/2019/01/members-of-the-2019-trips-directorate-are-announced
Town hall focuses on C3I and anniversary celebrations
Around 70 members of the Dartmouth community crowded into Spaulding Auditorium on Jan. 16 for the quarterly town hall meeting. Executive vice president Rick Mills led the discussion, which focused on the new Campus Climate and Culture Initiative — or C3I — and the College's 250th anniversary celebrations. The next town hall will be held on Mar. 27 and will cover the College's plan to build a new biomass power plant and the expansion of graduate housing in Lebanon. The 250th celebration co-chairs — Vice President for Alumni Relations Cheryl Bascomb '82 and English professor Donald Pease — and Title IX coordinator Kristi Clemens joined him to address items on the agenda.
https://www.thedartmouth.com/article/2019/01/town-hall-focuses-on-c3i-and-anniversary-celebrations
Carol Folt resigns as UNC chancellor
Former interim College President Carol Folt announced her resignation from her position as chancellor of the University of North Carolina at Chapel Hill on Monday. Folt also announced that she had ordered the removal of a Confederate statue on campus out of safety concerns.
https://www.thedartmouth.com/article/2019/01/carol-folt-resigns-as-unc-chancellor
After delay, construction begins on new indoor practice facility
Following a long delay, construction officially began this past Monday on a new building on campus. Contractors began laying down hardpack to allow for the movement of heavy vehicles for the 70,000-square-foot indoor athletic facility to be located near Thompson Arena and Burnham Field, adjacent to the Boss Tennis Center.
https://www.thedartmouth.com/article/2019/01/after-delay-construction-begins-on-new-indoor-practice-facility
Pine Park trails will close in February
Some of the College's most scenic trails will be closed as trees are removed to improve the health of the century-old and dying Pine Park. The project is set to start at the beginning of February if weather conditions hold and will last two to four weeks, according to associate director of Facilities Operation and Management Tim McNamara '78 A&S '12.
https://www.thedartmouth.com/article/2019/01/pine-park-trails-will-close-in-february
Q&A with music librarian Memory Apata
Music and performing arts librarian Memory Apata, who has been working at the College for only three years, is already head of the Paddock Music Library in the Hopkins Center for the Arts. Apata, the first to attend college in her family, double majored in vocal performance and German at the University of Arkansas at Little Rock. She now works as a professional musician and performer and is also pursuing a Master of Arts in Liberal Studies at Dartmouth and a Master of Science in Library and Information Science at Simmons College.
https://www.thedartmouth.com/article/2019/01/q-a-with-music-librarian-memory-apata
Montgomery Fellow Jake Sullivan discusses policy
Jake Sullivan, a former top advisor in the Obama Administration, participated in a conversation Wednesday with Ambassador Daniel Benjamin, the director of the Dickey Center for International Understanding, in Filene Auditorium.
https://www.thedartmouth.com/article/2019/01/montgomery-fellow-jake-sullivan-discusses-policy
NH Democrats introduce firearms ban in school zones
On Jan. 2, House Bill 101 — which would allow school districts to regulate firearms in school zones — was introduced by seven Democrats in the New Hampshire House of Representatives.
https://www.thedartmouth.com/article/2019/01/nh-democrats-introduce-firearms-ban-in-school-zones
Dartmouth denies knowingly permitting sexual misconduct in filing, stresses its prompt action
Updated Jan. 16, 2019 at 11:56 p.m.
https://www.thedartmouth.com/article/2019/01/dartmouth-denies-knowingly-permitting-sexual-misconduct-in-filing-stresses-its-prompt-action
Kirsten Gillibrand '88 enters presidential race
Kirsten Gillibrand '88 entered the 2020 presidential race on Jan. 15.
https://www.thedartmouth.com/article/2019/01/kirsten-gillibrand-88-enters-presidential-race
EPA unveils rule change, Dartmouth analyzes toxic metals
Just before the federal government shut down in the final days of 2018, the Environmental Protection Agency unveiled a proposed rule change that would alter how the federal government determines air pollutant regulation. The rule change would prevent the EPA from considering certain benefits — such as positive health outcomes — associated with reducing mercury levels during its cost-benefit calculations.
https://www.thedartmouth.com/article/2019/01/epa-unveils-rule-change-dartmouth-analyzes-toxic-metals
Physicians for Human Rights holds fifth annual health conference on planetary health
The seventh annual Geisel Physicians for Human Rights conference focused on something not always talked about in conjunction with human health: planetary health.
https://www.thedartmouth.com/article/2019/01/physicians-for-human-rights-holds-fifth-annual-health-conference-on-planetary-health | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,664 |
FLORENCE + THE MACHINE 'LUNGS' LP
LABEL: Republic
VINYL RELEASE DATE: 8/31/2010
ALBUM RELEASE DATE: 2009
VARIANT: Black Vinyl LP
Vinyl LP pressing. 2009 debut album from the hotly tipped UK outfit fronted by Florence Welch. Lungs, produced by Paul Epworth, James Ford and Steve Mackay, is an intoxicating mix of delicate fragility, dark humor and twisted Tim Burton style fairy-tales. From the live favorite 'You've Got the Love' to the raw Blues-tinged 'Girl with One Eye' to the beautifully painful 'Between Two Lungs', the album is crammed with crowd pleasers. Also boasting fresh tracks like new single 'Rabbit Heart (Raise It Up)', 'Drumming' - with it's epic denseness, the terrifyingly brilliant 'Howl' and 'Hurricane Drunk' with it's paradoxical charms of heartbreak, love and loss, Lungs promises to leave US wanting more of the insanely captivating Florence Welch. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,382 |
Q: asp.net 4.5 cookies not working in Chromium OS I cant get Google Chromium OS to set/read cookies from an ASP.NET 4.5 page.
I am using IIS 8 on windows 8.
Here is the simple web form example:
<%@ Page Language="VB" %>
<!DOCTYPE html>
<script runat="server">
Protected Sub Page_Load(sender As Object, e As EventArgs)
If Not IsPostBack Then
Dim cookie As New HttpCookie("TestCookie")
cookie.Expires = Date.UtcNow.AddDays(1)
cookie.Value = "Hello from Cookie!"
Response.Cookies.Add(cookie)
End If
End Sub
Protected Sub Button1_Click(sender As Object, e As EventArgs)
Dim cookie As HttpCookie = Request.Cookies("TestCookie")
If Not IsNothing(cookie) Then
Label1.Text = cookie.Value
Else
Label1.Text = "Cookie not found!"
End If
End Sub
</script>
<html xmlns="http://www.w3.org/1999/xhtml">
<head runat="server">
<title></title>
</head>
<body>
<form id="form1" runat="server">
<div>
<asp:Button ID="Button1" runat="server" Text="Button" OnClick="Button1_Click" />
<asp:Label ID="Label1" runat="server" Text="Label"></asp:Label>
</div>
</form>
</body>
</html>
When I click the button to read the cookie - it always returns Nothing (cookie not found)
I have checked my cookie settings are enabled in Chromium.
When I check the Chromium settings to see what cookies are being stored, it lists only the ASPNET Session ID cookie from my website domain, so it is storing the session cookie.
Has anybody else experienced this issue?
I am using IIS 8 on Windows 8.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,981 |
\section{Introduction}
Now a days it is being felt the role of Lie algebras in explaining many physical phenomena is inevitable and desirable. Starting from the application of Lie algebras like $su(2),su(3),so(3)$ in particle physics; to the application of $g_{2}$, $e_{8}$ and their so called extension, affine and hyperbolic Kac-Moody algebras in conformal field theories, string theories, M-theories etc; the role of these types of algebras have increased by leaps and bounds. To be more specific, the structure of these algebras as well as their representation theories play an important role in various branches of physics. For example, in elementary particle physics and especially in model building it is quite important to have effective branching rules for Lie algebra representation.
\par
A splint \cite{Richter2012} of a root system for a simple Lie algebra appears naturally on studies of (regular) embedding of reductive subalgebras. A splint can be used to construct branching rules. Now it is well understood that implementation of splints properties drastically simplifies calculation of branching coefficient.
\par
An embedding \cite{ Ly2015, L1996} $\iota$ of a root system $\Delta$ in to a root system $\Delta^{\prime}$ is a bijection map of roots $\Delta$ to a (proper) subset of $\Delta^{\prime}$ that commute with vector composition law in $\Delta$ and $\Delta^{\prime}$.
\[\iota:\Delta\longrightarrow \Delta^{\prime}\]
\[\iota(\alpha+\beta)=\iota(\alpha)+\iota(\beta), \forall \alpha,\beta \in \Delta.\]
Note that the image Im($\iota$) must not inherit the root system properties with the exception of addition rules equivalent to the addition rules in $\Delta_{1}$ (for preimages).Two embeddings $\iota_{1}$ and $\iota_{2}$ can be splinter of $\Delta$ when the later can be represented a disjoint union of images $\iota_{1}$ and $\iota_{2}$. The term splint was introduced by D.Ritcher\cite{Richter2012} where a classification of splints for simple Lie algebras was obtained. At the same time there it was also mentioned that a splint must have tight connections with the injection fan construction. A fan \cite{Nazarov2012} $\Gamma\subset\Delta$ was introduced as a subset of a root system describing recurrence properties of branching coefficient for maximal embeddings. Injection fan is an efficient tool to study branching rules. It is now known that splint is a natural tool to study reduction properties of $g$-modules with respect to a subalgebra $a\hookrightarrow g$. There is a one to one correspondence between weight multiplicities in irreducible modules of splint and branching coefficient for a reduced module.
\par
In many mathematical physics application like supersymmetry we require some algebraic structure which can be readily transcribed for the propose of application to both bosonic and fermionic sectors in a systematic and consistent framework. So it is natural to visualize, evaluate and interpret possible consequences of supersymmetic extension of these type simple Lie algebras. The constructs in this case so generated are called simple Lie superalgebras.
\par
Like Lie algebra, Lie superalgebras have wide applications in physics and so called classical Lie superalgebras have been classified which have properties similar to simple Lie algebra. Having this in mind in this paper we construct the splints of Lie superalgebras. Hope this paper will be a small step forward in this direction of calculation of branching coefficient on different branching rule similar to the role of splints in case of Lie algebras. We also hope the determination of splints for classical Lie superalgebras will pave the way for simplification of calculation of branching coefficients on different branching rule in representation theory. The theory of classical Lie superalgebras \cite{Frappat1989} runs quite parallel to that of Lie algebras, however the migration from Lie algebras to Lie superalgebras is not so direct as perceived. Determination of splints is mainly based on the root system of corresponding algebras.The theorem and techniques used to prove the main theorems in our paper runs similar to that of Ritcher \cite{Richter2012} on splints of Lie algebras. But there are some major differences which we like to mention here. At the outset we point out that in case of Lie algebra all the root bases of a particular algebra are equivalent. This statement immediately implies that under a transformation of the Weyl group the root system will be transformed into an equivalent one with same Dynkin diagram. However in case of Lie superalgebra, a particular superalgebra may have many inequivalent root systems and hence different Dynkin diagrams due to presence of degenerate and non-degenerate odd roots along with bosonic roots. Out of all these bases the one which contains the least number of odd roots is called a distinguished basis. In this paper we restrict ourselves to the distinguished basis only.
\par
In case of Lie algebras we have Weyl reflection with respect to one root (even) type only but in case of Lie superalgebras we have Weyl reflection with respect to both even and odd root. However the Weyl reflections with respect to odd roots do not respect grading; as a result an even root may be mapped to a odd root and vice versa. So in consistent with the given definition of splint, embedding etc. for Lie superalgebras, we consider Weyl reflections only with respect to even roots. Similar attempts \cite{Ransingh2013} have been taken earlier by some authors resulting some partial results for splints but lacking in mathematical rigorousness and proofs. So in this paper we tried to classify the splints of Lie superalgebras once again which has been lying unsolved for many years.
\par
The aim in this article is therefore to provide all instances of this splintering of root systems for classical Lie superalgebras. This is achieved in a case-by-case analysis.
\par
The paper is organized as follows. After a brief introduction to the term splints and motivation for classifying splints of Lie superalgebras in section I we present the root systems of classical Lie superalgebras $A(m,n),B(m,n),B(0,n),C(n+1),D(m,n)$ in sections III, IV and V respectively. Before this in short we give some definitions in section II. We prove lemmas, propositions etc in each chapter corresponding to the individual type of Lie superalgebra which are helpful in determining the splints of the corresponding algebras. At the end of each section we provide a table which lists all the splints obtained through case by case approach. Similar studies are being done in section VI for exceptional Lie superalgebras $G(3),F(4)$ and $D(2,1;\alpha)$. Section VII contains few concluding remarks.
\section{Definitions}
Let $\Delta$ and $\Delta^{\prime}$ be positive root systems of two different Lie superalgebras with $\Delta=\Delta_{0}+\Delta_{1}$ and $\Delta^{\prime}=\Delta^{\prime}_{0}+\Delta^{\prime}_{1}$ where $\Delta_{0},\Delta_{1}$ and $\Delta^{\prime}_{0},\Delta^{\prime}_{1}$ are even and odd roots of $\Delta$ and $\Delta^{\prime}$ respectively. Then the map $\iota:\Delta\hookrightarrow \Delta^{\prime}$
is an embedding if
\begin{enumerate}
\item $\iota$ is a injective function and $\iota(\gamma)= \iota(\alpha)+\iota(\beta)$ for all $\alpha,\beta,\gamma \in \Delta$ such that $\gamma = \alpha+\beta $
\item $\iota(\Delta_{0})\subseteq \Delta^{\prime}_{0}$ and $\iota(\Delta_{1})\subseteq \Delta^{\prime}_{1}$ .
\end{enumerate}
A root system $\Delta$ splinters as $(\Delta_{1},\Delta_{2})$ if there are two embedding $\iota_{1}:\Delta_{1}\hookrightarrow \Delta$ and $\iota_{2}:\Delta_{2}\hookrightarrow \Delta$ where
\begin{enumerate}
\item $\Delta$ is the disjoint union of the images of $\iota_{1}$ and $\iota_{2}$ and
\item neither the rank of $\Delta_{1}$ nor the rank of $\Delta_{2}$ exceeds the rank of $\Delta$.
\end{enumerate}
Suppose $\iota:\Delta\hookrightarrow \Delta^{\prime}$ is embedding and suppose that $(,)_{0}$ and $(,)_{1}$ are normalization of $\Delta$ and $\Delta^{\prime}$ respectively. Then the embedding $\iota$ is metric if there is a non-zero integer scalar $\lambda$ such that $(\alpha,\beta)_{0} = \lambda(\iota(\alpha),\iota(\beta))_{1}$ for $\alpha,\beta \in \Delta$ and non-metric otherwise.\\
Here we have found all the splints up to equivalence with Weyl group $W$ (Weyl reflections are with respect to even roots only). If $\Delta$ is a distinguished simple root system then the splints $(\Delta_{1},\Delta_{2})$ and $(\Delta_{1}^\prime,\Delta_{2}^\prime)$ of $\Delta$ are equivalent, if there exists $\sigma \in W$ such that $\sigma. (((\Delta_{1} \cup (-\Delta_{1})) |_{\Delta_{0}},(\Delta_{2} \cup (-\Delta_{2})) |_{\Delta_{0}}) = ((\Delta_{1}^\prime \cup (-\Delta_{1}^\prime)) |_{\Delta_{0}},(\Delta_{2}^\prime \cup (-\Delta_{2}^\prime)) |_{\Delta_{0}})$ and similar restriction for odd roots of $\Delta$ also.
Here we like to mention that Lie superalgebras have Weyl reflections with respect to both isotopic and non-isotopic odd roots. However, in that case we get non-equivalent classes, because grading will not be respected. \\
\section{Splints of Lie superalgebra $A(m-1,n-1)$}
The basic Lie superalgebra $A(m-1,n-1)$ has rank $m+n-1$ and the positive root system is given by
\[\Delta=\{\varepsilon_{i}-\varepsilon_{j},\delta_{k}-\delta_{l},\delta_{k}-\varepsilon_{i}: 1\leq i\neq j \leq m , 1\leq k \neq l \leq n \},\]
with the normalization
\[(\varepsilon_{i},\varepsilon_{j})=\delta_{ij},~~(\delta_{k},\delta_{l})=\delta_{kl},~~(\varepsilon_{i},\delta_{k})=0 ~~~~~ for ~~1\leq i,j \leq m , 1\leq k,l \leq n .\]
\begin{lemma}
If $\Delta$ is a distinguished simple root system and $\Delta\hookrightarrow A(m-1,n-1)$, then $\Delta \cong A(r,s)$ for some $r\leq m-1,~s\leq n-1$.
\end{lemma}
\begin{proof}
As the highest root of $A(m-1,n-1)$ is a linear combination of distinguished simple roots,then every coefficient is equal to 1 .
\end{proof}
\begin{lemma}
$A(m-1,0)$ and $A(0,n-1)$ are metrically embedded in $A(m-1,n-1)$.
\end{lemma}
\begin{lemma}
If $A(r_{1},s_{1})\hookrightarrow A(m-1,n-1)$ and $A(r_{2},s_{2})\hookrightarrow A(m-1,n-1)$ are embeddings with disjoint images, then $r_{1}+r_{2}\leq m ,~ s_{1}+s_{2}\leq n$ .
\end{lemma}
\begin{proof}
As $A_{l}\hookrightarrow A_{n}$ and $ A_{k}\hookrightarrow A_{n}$ are embeddings with disjoint images, then $k+l\leq n$.
\end{proof}
\begin{lemma}
Suppose $m\geq3$,~$n\geq3$ and either $r\geq3,~s\geq2$ or $r\geq2,~s\geq3$. If $A(m-1,n-1)$ has a splint where $A(r-1,s-1)$ is a component, then $A(m-2,n-2)$ has a splint having $A(r-2,s-2)$ as a component.
\end{lemma}
\begin{proof}
Suppose $(\Delta_{1},\Delta_{2})$ is a splint of $A(m-1,n-1)$ with $\iota:A(r-1,s-1)\hookrightarrow \Delta_{1}$ as a component. Without loss of generality, one may assume that the roots in the image of $i$ have the form $\{\varepsilon_{i}\pm\varepsilon_{j},\delta_{k}\pm\delta_{l},\delta_{k}\pm\varepsilon_{i}\}$ where $1\leqslant i\neq j\leqslant r , 1\leqslant k \neq l\leqslant s$. If we are restricting the splint to the embedding $\iota_{1}:A(m-2,n-2)\hookrightarrow A(m-1,n-1)$ and all the components are embedded metrically, this yields a splint of $A(m-2,n-2)$ having $A(r-2,s-2)$ as a component.
\end{proof}
\begin{proposition}
Assume $m,n \geq 6$ and if $(\Delta_{1},\Delta_{2})$ is a splint of $A(m-1,n-1)$ having $A(r,s)$ as a component, then $r \in \{0,1,m-1,m-2\}$ and $s \in \{0,1,n-1,n-2\}$
\end{proposition}
\begin{proof}
We can argue by preceding results and table of $A(m-1,n-1)$.
\end{proof}
\begin{lemma}
Suppose $\Delta$ is a positive root system of a Lie superalgebra and $\Delta^{\prime}$ is a root system of $A(m-1,n-1)$ or $D(m,n)$. If $\iota:\Delta\hookrightarrow \Delta^{\prime}$ is an embedding, then $\Delta$ is either $A(m-1,n-1)$ or $D(m,n)$ and $\iota$ is metric.
\end{lemma}
\begin{proof}
$A(m-1,n-1),D(m,n)$ are simply laced, hence $\Delta$ has type $A(m-1,n-1)$ or $D(m,n)$. Suppose rank of $\Delta$ is 2, then $\Delta$ is either $A(0,1),A(1,0)$ or $A(1,1)$. These are metrically embedded in $A(m-1,n-1)$. Suppose rank of $\Delta$ is greater than 2, then given any odd root $ \alpha \in \Delta$ there is a even root $\beta \in \Delta$ such that $\alpha+\beta \in \Delta$. Hence, we always have an embedding $A(1,0)$ or $A(0,1) \hookrightarrow \Delta$ . As every embedding $A(1,0)$ or $A(0,1) \hookrightarrow \Delta^{\prime}$ is metric , so $\iota$ is metric.
\end{proof}
\begin{lemma}
$F(4)$ and $G(3)$ are not embedded in $A(m-1,n-1)$, $B(m,n)$, $C(n+1)$ and $D(m,n)$
and $D(2,1;\alpha)$ is not embedded in $A(m-1,n-1)$ and $C(n+1)$.
\end{lemma}
\begin{proof}
As even root in $A(m-1,n-1)$, $B(m,n)$, $C(n+1)$ and $D(m,n)$ are linear combination of distinguished simple roots with coefficient one.
\end{proof}
If $(\Delta_{1},\Delta_{2})$ is a splinter of $A(m-1,n-1)$ and $\Delta_{1}\cap A(m-1,0)\neq\phi$ and $\Delta_{2}\cap A(m-1,0)\neq\phi$ , then we find a splinter of $A(m-1,0)$ if we restrict to $\Delta_{1}$ and $\Delta_{2}$. As $A(0,0)$ has only one odd root, so $A(0,0)$ does not splint. So all the splinter of $A(m,n)$ which are given in the table of $A(m-1,n-1)$ are explicitly described below.
\begin{enumerate}
\item The splinter ($A(2,n)+A_{2},2D_{2}+2nA(0,0)$) of $A(4,n)$ is given by
\begin{align*}
\Delta_{1} &= \{\varepsilon_{i}-\varepsilon_{j},\delta_{k}-\delta_{l},\delta_{k}-\varepsilon_{j}: 1\leq i \neq j \leq 3, 1\leq k \neq l \leq n\},\\
\Delta_{2} &=\{\varepsilon_{1}-\varepsilon_{j},\varepsilon_{2}-\varepsilon_{j},\delta_{k}-\varepsilon_{j}:4\leq j \leq 5, 1\leq k\leq n\}.
\end{align*}
\item The splinter ($A(m-1,0)+A_{n-1},(mn-m)A(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1} &= \{\varepsilon_{i}-\varepsilon_{j},\delta_{1}-\varepsilon_{j},\delta_{k}-\delta_{l}: 1\leq i \neq j \leq m, 1\leq k \neq l \leq n\},\\
\Delta_{2} &= \{\delta_{k}-\varepsilon_{l}:2\leq k \leq n, 1\leq l\leq m\}.
\end{align*}
\item The splinter ($A(0,n-1)+A_{m-1},(mn-n)A(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\delta_{i}-\delta_{j},\delta_{j}-\varepsilon_{1}, \varepsilon_{k}-\varepsilon_{l} :1\leq i \neq j \leq n,1\leq k \neq l \leq m\},\\
\Delta_{2}&=\{\delta_{k}-\varepsilon_{l}: 1\leq k \leq m, 2\leq l\leq n\}.
\end{align*}
\item If $m-n=1$ ,then the splinter ($A(n-1,n-1)$ , $nA_{1}+nA(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\varepsilon_{i}-\varepsilon_{j},\delta_{i}-\delta_{j},\delta_{i}-\varepsilon_{j}:1\leq i\neq j\leq n\},\\
\Delta_{2}&= \{\varepsilon_{i}-\varepsilon_{m},\delta_{i}-\varepsilon_{m}: 1 \leq i \leq n \}.
\end{align*}
\item The splinter ($A(1,n)+A_{m-2}$ , $(m-2)A_{1}+n(m-2)A(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\varepsilon_{1}-\varepsilon_{2},\delta_{k}-\delta_{l},\delta_{k}-\varepsilon_{1},\delta_{k}-\varepsilon_{2}: 1\leq k \neq l \leq n\} \cup \{\varepsilon_{i}-\varepsilon_{j}:2\leq i \neq j \leq m\},\\
\Delta_{2}&= \{\varepsilon_{1}-\varepsilon_{j},\delta_{i}-\varepsilon_{j}: 3\leq j \leq m ,1\leq i \leq n\}.
\end{align*}
\item The splinter ($A(m,1)+A_{n-2}$ , $(n-2)A_{1}+m(n-2)A(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\varepsilon_{k}-\varepsilon_{l},\delta_{1}-\delta_{2},\delta_{1}-\varepsilon_{k},\delta_{2}-\varepsilon_{k}: 1\leq k \neq l \leq m\} \cup \{\delta_{i}-\delta_{j}:2\leq i \neq j \leq n\},\\
\Delta_{2}&= \{\delta_{1}-\delta_{j},\delta_{j}-\varepsilon_{k}: 3\leq j \leq n ,1\leq k \leq m\}.
\end{align*}
\item For $m,n\geq 2$, the splinter ($A(m-2,n-2)+A(1,0), (m+n-3)A_{1}+(m+n-3)A(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\varepsilon_{i}-\varepsilon_{j},\delta_{k}-\delta_{l},\delta_{k}-\varepsilon_{i}: 2\leq i \neq j \leq m,2\leq k \neq l \leq n\} \cup \{\varepsilon_{1}-\varepsilon_{2},\delta_{1}-\varepsilon_{1},\delta_{1}-\varepsilon_{2}\},\\
\Delta_{2}&= \{\varepsilon_{1}-\varepsilon_{i},\delta_{1}-\delta_{k},\delta_{1}-\varepsilon_{i},\delta_{k}-\varepsilon_{1}: 3\leq i \neq m ,2\leq k \leq n\}.
\end{align*}
\item For $m,n\geq 2$, the splinter ($A(m-1,n-2),(n-1)A_{1}+mA(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\varepsilon_{i}-\varepsilon_{j},\delta_{k}-\delta_{l},\delta_{k}-\varepsilon_{i}: 1\leq i \neq j \leq m, 1\leq k \neq l \leq n-1\},\\
\Delta_{2}&= \{\delta_{k}-\delta_{n},\delta_{n}-\varepsilon_{i}: 1\leq k \leq n-1, 1\leq i \leq m\}.
\end{align*}
\item For $m,n\geq 2$, the splinter ($A(m-2,n-1),(m-1)A_{1}+nA(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\varepsilon_{i}-\varepsilon_{j},\delta_{k}-\delta_{l},\delta_{k}-\varepsilon_{i}: 1\leq i \neq j \leq m-1, 1\leq k \neq l \leq n\},\\
\Delta_{2}&= \{\varepsilon_{j}-\varepsilon_{m},\delta_{i}-\varepsilon_{m}: 1\leq j \leq m-1, 1\leq i \leq n\}.
\end{align*}
\item For $m=n$, the splinter ($A(m-1,m-2),(m-1)A_{1}+mA(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\varepsilon_{i}-\varepsilon_{j},\delta_{k}-\delta_{l},\delta_{k}-\varepsilon_{i}: 1\leq i \neq j \leq m, 1\leq k \neq l \leq m-1\},\\
\Delta_{2}&= \{\delta_{i}-\delta_{m},\delta_{m}-\varepsilon_{j}: 1\leq i \leq m-1, 1\leq j \leq m\}.
\end{align*}
\item For $m=n$ , the splinter ($A(m-2,m-1),(m-1)A_{1}+mA(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\varepsilon_{i}-\varepsilon_{j},\delta_{k}-\delta_{l},\delta_{k}-\varepsilon_{i}: 1\leq i \neq j \leq m-1, 1\leq k \neq l \leq m\},\\
\Delta_{2}&= \{\varepsilon_{i}-\varepsilon_{m},\delta_{m}-\varepsilon_{j}: 1\leq i \leq m-1, 1\leq j \leq m\}.
\end{align*}
\item For $m=n$, the splinter ($A(m-2,m-2),2(m-1)A_{1}+(2m-1)A(0,0)$) of $A(m-1,n-1)$ is given by
\begin{align*}
\Delta_{1}&= \{\varepsilon_{i}-\varepsilon_{j},\delta_{i}-\delta_{j},\delta_{i}-\varepsilon_{j}: 1\leq i \neq j \leq m-1\},\\
\Delta_{2}&= \{\varepsilon_{i}-\varepsilon_{m},\delta_{i}-\delta_{m},\delta_{i}-\varepsilon_{m},\delta_{m}-\varepsilon_{j}: 1\leq i \leq m-1, 1\leq j \leq m\}.
\end{align*}
\end{enumerate}
\FloatBarrier
\begin{table}[b]
\caption {$A(m,n)$} \label{tab:title}
\begin{tabular}{ | b{3cm} | m{6cm}| m{6cm} | }
\hline
$\Delta$ & $\Delta_{1}$ & $\Delta_{2}$ \\ \cline{1-3}
$A(1,0)$ & $A_{1}$ & $2A(0,0)$ \\
\hline
$A(0,1)$ & $A_{1}$ & $2A(0,0)$ \\
\hline
$A(1,1)$ & $A(0,1)$ & $A_{1}+2A(0,0)$ \\
& $A(1,0)$ & $A_{1}+2A(0,0)$ \\
& $2A_{1}$ & $4A(0,0)$ \\
\hline
$A(1,2)$ & $A(0,2)$ & $2A_{1}+3A(0,0)$ \\
& $A(1,1)$ & $2A_{1}+2A(0,0)$ \\
& $A_{2}+2A(0,0)$ & $A(1,0)+2A(0,0)$ \\
& $A_{1}+A_{2}$ & $6A(0,0)$ \\
\hline
$A(2,2)$ & $A(2,1)$ & $2A_{1}+3A(0,0)$ \\
& $A(1,1)+A_{1}$ & $A(1,0)+2A_{1}+3A(0,0)$ \\
& $A_{2}+A_{2}$ & $9A(0,0)$ \\
\hline
$A(0,2)$ & $A_{1}+A(0,1)$ & $A_{1}+A(0,0)$ \\
& $A_{2}$ & $3A(0,0)$ \\
\hline
$A(4,4)$ & $A(2,4)+A_{2}$ & $2D_{2}+10A(0,0)$ \\
& $A(4,2)+A_{2}$ & $2D_{2}+10A(0,0)$ \\
\hline
$A(4,n)$ & $A(2,n)+A_{2}$ & $2D_{2}+2nA(0,0)$ \\
\hline
$A(m-1,n-1)$ &$A(m-1,0)+A_{n-1}$ & $(mn-m)A(0,0)$\\
&$A(0,n-1)+A_{m-1}$ & $(mn-n)A(0,0)$\\
\hline
$A(m-1,n-1)$ &$A(1,n)+A_{m-2}$ & $(m-2)A_{1}+n(m-2)A(0,0)$\\
&$A(m,1)+A_{n-2}$ & $(n-2)A_{1}+m(n-2)A(0,0)$\\
\hline
if $m-n=1$, $A(m-1,n-1)$ &$A(n-1,n-1)$ & $nA_{1}+nA(0,0)$\\
\hline
\end{tabular}
\end{table}
\FloatBarrier
\begin{table}[h]
\begin{tabular}{ | b{3cm} | m{6cm}| m{6cm} | }
\hline
$A(m-1,m-1)$ &$A(m-1,m-2)$ & $(m-1)A_{1}+mA(0,0)$\\
&$A(m-2,m-1)$ & $(m-1)A_{1}+mA(0,0)$\\
&$A(m-2,m-2)$ & $2(m-1)A_{1}+(2m-1)A(0,0)$\\
\hline
$A(m-1,n-1)$ for $m,n\geqslant2$ & $A(m-2,n-2)+A(1,0)$ & $(m+n-3)A_{1}+(m+n-3)A(0,0)$ \\
& $A(m-2,n-1)$ & $(m-1)A_{1}+nA(0,0)$ \\
& $A(m-1,n-2)$ & $(n-1)A_{1}+ mA(0,0)$ \\
\hline
\end{tabular}
\end{table}
\section{Splints of Lie superalgebra $B(m,n)$ and $B(0,n)$ }
The basic Lie superalgebra $B(m,n)$ has rank $m+n$ and the positive root system is given by
\[\Delta=\{\varepsilon_{i}\pm\varepsilon_{j},\varepsilon_{i},\delta_{k}\pm\delta_{l},2\delta_{k},\delta_{k}\pm\varepsilon_{i},\delta_{k}: 1\leq i\neq j \leq m , 1\leq k \neq l \leq n \},\]
with the normalization
\[(\varepsilon_{i},\varepsilon_{j})=-\delta_{ij},~~(\delta_{k},\delta_{l})=\delta_{kl},~~(\varepsilon_{i},\delta_{k})=0 ,~~~~~ for ~~1\leq i,j \leq m , 1\leq k,l \leq n .\]
\begin{lemma}
$C(n+1)$ is not embedded in $B(m,n)$ for $m>3,~n\geq2$.
\end{lemma}
\begin{proof}
Suppose $C(n+1) \hookrightarrow B(m,n)$. As the even roots of $C_{3}$ does not embed in $B_{m}$ for $m\geq2$, hence the image of even part of $C(n+1)$ under the map $\iota$ is $\{\delta_{k}\pm\delta_{l},2\delta_{k}\}$ where $1\leq k \neq l \leq n$. Now without loss of generality, the distinguished simple root system of $C(n+1)$ under the map $\iota$ is $\{\alpha_{1},\alpha_{2},\cdots\alpha_{n-1},2\alpha_{n}+2\alpha_{n+1}+\cdots+2\alpha_{n-1}\} \cup \{\beta\}$, where $\beta$ is an odd root of $B(m,n)$ and $\alpha_{1}= \delta_{1}-\delta_{2}$, $\alpha_{2}= \delta_{2}-\delta_{3}$,$\cdots$, $\alpha_{n-1}= \delta_{n-1}-\delta_{n}$ which belong to distinguished simple roots of even part of $B(m,n)$. $C(n+1)$ has an odd root $\beta+\alpha_{1}+\alpha_{2}+\cdots+\alpha_{n-1}+2\alpha_{n}+2\alpha_{n+1}+\cdots+2\alpha_{n-1}$ but $B(m,n)$ has no such odd root.
\end{proof}
\begin{lemma}
$B(m,n-1)$ and $B(m-1,n)$ are not a component of $B(m,n)$.
\end{lemma}
\begin{proof}
Suppose $(\Delta_{1},\Delta_{2})$ is a splint of $B(m,n)$ and $B(m,n-1)\hookrightarrow \Delta_{1}$. Without loss of generality, we may assume that the image of $B(m,n-1)$ under $\iota$ is $\{\varepsilon_{i}\pm\varepsilon_{j},\varepsilon_{i},\delta_{k}\pm\delta_{l},2\delta_{k},\delta_{k}\pm\varepsilon_{i},\delta_{k}:1\leqslant i\neq j\leqslant m , 1\leqslant k \neq l\leqslant n-1\}$. $B(0,n)$ is metrically embedded in $B(m,n)$. So restricting the splints to $B(0,n)$, we get a splints of $B(0,n)$ say $\Delta_{2}^\prime=\{\delta_{k}\pm\delta_{n},2\delta_{k} ,\delta_{k}:1\leq k \leq n-1 \}$. But the rank of $\Delta_{2}^\prime$ is greater then $B(0,n)$. Hence we get a contradiction.
\end{proof}
We can describe all the splinter of $B(m,n)$ in the following way,
\begin{enumerate}
\item The splinter $(A(0,1),A_{1}+2A(0,0))$ of $B(1,1)$ is given by
\begin{align*}
\Delta_{1}&=\{\delta_{1}-\varepsilon_{1},\varepsilon_{1},\delta_{1}\},\\
\Delta_{2}&=\{\delta_{1}+\varepsilon_{1},2\delta_{1}\}.
\end{align*}
\item The splinter $(A(0,1)+A_{1},3A_{1}+4A(0,0))$ of $B(1,2)$ is given by
\begin{align*}
\Delta_{1}&=\{\delta_{1}-\delta_{2},\delta_{1}-\varepsilon_{1},\delta_{2}-\varepsilon_{1},\varepsilon_{1}\},\\
\Delta_{2}&=\{\delta_{1}+\delta_{2},2\delta_{1},2\delta_{2},\delta_{2}+\varepsilon_{1},\delta_{1}+\varepsilon_{1},\delta_{1},\delta_{2}\}.
\end{align*}
Another splinter of $B(1,2)$ is ($B(0,2),A_{1}+4A(0,0)$) which is given by
\begin{align*}
\Delta_{1}&=\{\delta_{1}\pm\delta_{2},2\delta_{1},2\delta_{2},\delta_{1},\delta_{2}\},\\
\Delta_{2}&=\{\varepsilon_{1},\delta_{1}\pm\varepsilon_{1},\delta_{2}\pm\varepsilon_{1}\}.
\end{align*}
\item The splinter ($A(1,1)+2A_{1},4A_{1}+6A(0,0)$) of $B(2,2)$ is given by
\begin{align*}
\Delta_{1}&=\{\varepsilon_{1}-\varepsilon_{2},\delta_{1}-\delta_{2},\delta_{1}-\varepsilon_{1},\delta_{1}-\varepsilon_{2},\delta_{2}-\varepsilon_{1},\delta_{2}-\varepsilon_{2}\}\cup \{\varepsilon_{1}+\varepsilon_{2},\delta_{1}+\delta_{2}\},\\
\Delta_{2}&=\{\varepsilon_{1},\varepsilon_{2},2\delta_{1},2\delta_{2}\}\cup\{\delta_{1}+\varepsilon_{1},\delta_{1}+\varepsilon_{2},\delta_{2}+\varepsilon_{1},\delta_{2}+\varepsilon_{2},\delta_{1},\delta_{2}\}.
\end{align*}
\item $B(0,2)$ has two additional splints. The first one ($A_{2},A_{1}+2A(0,0)$) is given by
\begin{align*}
\Delta_{1}&= \{\delta_{1}\pm\delta_{2},2\delta_{2}\},\\
\Delta_{2}&= \{2\delta_{1},\delta_{1},\delta_{2}\}.
\end{align*}
and the second one ($2A_{1}+A(0,0),2A_{1}+A(0,0)$) is given by
\begin{align*}
\Delta_{1}&= \{\delta_{1}+\delta_{2},2\delta_{2}\}\cup\{\delta_{1}\}, \\
\Delta_{2}&= \{\delta_{1}-\delta_{2},2\delta_{1}\}\cup\{\delta_{2}\}.
\end{align*}
\item The splinter ($A_{1}+B(0,2),A_{1}+A_{2}+A(0,0)$) of $B(0,3)$ is given by \begin{align*}
\Delta_{1}&= \{\delta_{1}\pm\delta_{2},2\delta_{1},2\delta_{2},\delta_{1},\delta_{2}\}\cup\{\delta_{2}-\delta_{3}\},\\
\Delta_{2}&=\{\delta_{2}+\delta_{3}\}\cup\{\delta_{1}\pm\delta_{3},2\delta_{3}\}\cup\{\delta_{3}\}.
\end{align*}
\item The splinter ($D_{n},nB(0,1))$ of $B(0,n)$ is given by
\begin{align*}
\Delta_{1}&= \{\delta_{k}\pm\delta_{l}:1\leq k \neq l \leq n\},\\
\Delta_{2}&= \{2\delta_{k},\delta_{k}:1\leq k \leq n\}.
\end{align*}
\item The splinter ($C_{n},nA(0,0))$ of $B(0,n)$ is given by
\begin{align*}
\Delta_{1}&= \{\delta_{k}\pm\delta_{l},2\delta_{k}:1\leq k \neq l \leq n\},\\
\Delta_{2}&= \{\delta_{k}:1\leq k \leq n\}.
\end{align*}
\item The splinter $(B(0,n)+B_{m} , 2mnA(0,0))$ and $(B_{m}+C_{n}, (2mn+n)A(0,0))$ of $B(m,n)$ are equivalent because when we restrict to even roots both the splinter are same. Hence consider the splinter $(B(0,n)+B_{m} , 2mnA(0,0))$ which is given by
\begin{align*}
\Delta_{1}&= \{\delta_{k}\pm\delta_{l},2\delta_{k},\delta_{k}\}\cup\{\varepsilon_{i}\pm\varepsilon_{j}\}, ~where ~ 1\leq i \neq j \leq m, 1\leq k \neq l \leq n\\
\Delta_{2}&= \{\delta_{i}-\varepsilon_{k}: 1\leq i \neq j \leq m, 1\leq k \neq l \leq n\}.
\end{align*}
\item For $m\geqslant 2,~n\geqslant 1$ the splinter $(D(m,n), mA_{1}+nA(0,0))$ is given by
\begin{align*}
\Delta_{1}&= \{\delta_{k}\pm\delta_{l},2\delta_{k},\varepsilon_{i}\pm\varepsilon_{j},\delta_{k}-\varepsilon_{i}: 1\leq i \neq j \leq m, 1\leq k \neq l \leq n\},\\
\Delta_{2}&= \{\delta_{i},\varepsilon_{k}: 1\leq i \leq m, 1\leq k \leq n\}.
\end{align*}
\end{enumerate}
\begin {table}[h]
\caption {$B(m,n)$} \label{tab:title}
\begin{tabular}{ | b{3cm} | m{6cm}| m{6cm} | }
\hline
$\Delta$ & $\Delta_{1}$ & $\Delta_{2}$ \\ \cline{1-3}
$B(0,1)$ & $A_{1}$ & $A(0,0)$ \\
\hline
$B(1,1)$ & $A(0,1)$ & $A_{1}+2A(0,0)$ \\
\hline
$B(1,2)$ & $B(0,2)$ & $A_{1}+4A(0,0)$ \\
& $A(0,1)+A_{1}$ & $3A_{1}+4A(0,0)$ \\
\hline
$B(2,1)$ &$A(1,0)+A_{1}$ & $3A_{1}+3A(0,0)$ \\
\hline
$B(2,2)$ & $A(1,1)+2A_{1}$ & $4A_{1}+6A(0,0)$ \\
\hline
\end{tabular}
\end {table}
\begin {table}[h]
\begin{tabular}{ | b{3cm} | m{6cm}| m{6cm} | }
\hline
$B(0,2)$ & $A_{2}$ & $A_{1}+2A(0,0)$ \\
& $2A_{1}+A(0,0)$ & $2A_{1}+A(0,0)$ \\
\hline
$B(0,3)$ & $A_{1}+B(0,2)$ & $A_{1}+A_{2}+A(0,0)$ \\
\hline
$B(0,n)$ & $D_{n}$ & $nB(0,1)$ \\
\hline
$B(0,n)$ & $C_{n}$ & $nA(0,0)$ \\
\hline
$B(m,n)$ & $B(0,n)+B_{m}$ & $2mnA(0,0)$ \\
\hline
$B(m,n)$ for $m\geqslant 2, n\geqslant 1$& $D(m,n)$ & $mA_{1}+nA(0,0)$ \\
\hline
\end{tabular}
\end {table}
\section{Splints of Lie superalgebra $C(n+1)$}
The basic Lie superalgebra $C(n+1)$ has rank $n+1$ and the positive root system is given by
\[\Delta=\{\delta_{k}\pm\delta_{l},2\delta_{k},\varepsilon\pm\delta_{k}: 1\leq k \neq l \leq n \},\]
with the normalization
\[(\varepsilon,\varepsilon)=1,~~(\delta_{k},\delta_{l})=-\delta_{kl},~~(\varepsilon,\delta_{k})=0 ~~~~~ for ~~1\leq k,l \leq n .\]
\begin{lemma}
$C(n)$ is not a component of $C(n+1)$ for $n\geqslant3$.
\end{lemma}
\begin{proof}
Suppose $(\Delta_{1},\Delta_{2})$ is a splint of $C(n+1)$ and $C(n)\hookrightarrow \Delta_{1}$. Then the other components of $\Delta_{1}$ are isomorphic to either $A_{1}$ or $A(0,0)$ and components of $\Delta_{2}$ are isomorphic to either $A_{1}$ or $D_{2}$, which implies rank of $\Delta_{2}$ is greater than $n+1$ . Hence a contradiction.
\end{proof}
\begin{lemma}
$B(m,n)$ is not embedded in $C(n+1)$.
\end{lemma}
\begin{proof}
Consider an even root $\alpha$ and the odd root $\beta$ in the distinguished simple root system of $B(m,n)$. Then $\alpha+2\beta$ is a odd root, but $C(n+1)$ has no such roots.
\end{proof}
\begin{lemma}
$B(0,n)$ is not embedded in $C(n+1)$.
\end{lemma}
\begin{proof}
$B(0,n)$ has an odd root $\beta$ such that $2\beta$ is an even root, but $C(n+1)$ has no such roots.
\end{proof}
\begin{lemma}
$D(r,s)$ is not embedded in $C(n+1)$ for $r,s\leq n$
\end{lemma}
\begin{proof}
We can observe from the properties of $D(r,s)$ that there are even roots which are linear combination of even as well as odd roots. But $C(n+1)$ does not have such type of even roots.
\end{proof}
We can describe all the splinters of $C(n+1)$ in the following way,
\begin{enumerate}
\item For $n\geq1$, $C(n+1)$ has a splint that is ($C_{n},2nA(0,0)$) is given by
\begin{align*}
\Delta_{1}&=\{\delta_{k}\pm\delta_{l},2\delta_{k}:1\leq k \neq l \leq n\},\\
\Delta_{2}&=\{\varepsilon\pm\delta_{k}:1\leq k \neq l \leq n\}.
\end{align*}
\item $C(3)$ has two additional splinters that are ($A_{2}, C(2)+2A(0,0)$) which is given by
\begin{align*}
\Delta_{1}&=\{\delta_{1}\pm\delta_{2},2\delta_{1}\},\\
\Delta_{2}&=\{2\delta_{2}\varepsilon\pm\delta_{2}\}\cup\{\varepsilon\pm\delta_{1}\}
\end{align*}
and ($C(2)+A_{1},C(2)+A_{1}$) which is given by
\begin{align*}
\Delta_{1}&=\{2\delta_{1},\varepsilon\pm\delta_{1},\}\cup\{\delta_{1}-\delta_{2}\},\\
\Delta_{2}&=\{2\delta_{2},\varepsilon\pm\delta_{2},\}\cup\{\delta_{1}+\delta_{2}\}.
\end{align*}
\item $C(4)$ has two additonal splinters that are ($A_{1}+B_{2}+2A(0,0),A_{1}+A_{2}+4A(0,0)$) which is given by
\begin{align*}
\Delta_{1}&=\{\delta_{2}-\delta_{3}\}\cup\{2\delta_{1},2\delta_{2},\delta_{1}\pm\delta_{2}\}\cup\{\varepsilon\pm\delta_{3}\},\\
\Delta_{2}&=\{\delta_{2}+\delta_{3}\}\cup\{2\delta_{3},\delta_{1}\pm\delta_{3}\}\cup\{\varepsilon\pm\delta_{1},\varepsilon\pm\delta_{2}\}
\end{align*}
and ($C(3)+A_{1},D_{2}+D_{2}+2A(0,0)$) is given by
\begin{align*}
\Delta_{1}&=\{\delta_{1}\pm\delta_{2},2\delta_{1},2\delta_{2},\varepsilon\pm\delta_{1},\varepsilon\pm\delta_{2}\}\cup\{2\delta_{3}\},\\
\Delta_{2}&=\{\delta_{1}\pm\delta_{3}\}\cup\{\delta_{2}\pm\delta_{3}\}\cup\{\varepsilon\pm\delta_{3}\}.
\end{align*}
\end{enumerate}
\begin {table}[h]
\caption {$C(n+1)$} \label{tab:title}
\begin{center}
\begin{tabular}{ | b{3cm} | m{6cm}| m{6cm} | }
\hline
$\Delta$ & $\Delta_{1}$ & $\Delta_{2}$ \\ \cline{1-3}
$C(2)$ & $A(1)$ & $2A(0,0)$ \\
\hline
$C(3)$ & $A_{2}$ & $C(2)+2A(0,0)$\\
& $C(2)+A_{1}$ & $C(2)+A_{1}$\\
\hline
$C(4)$ & $A_{1}+B_{2}+2A(0,0)$ & $A_{1}+A_{2}+4A(0,0)$\\
& $C(3)+A_{1}$ & $D_{2}+D_{2}+2A(0,0)$\\
\hline
$C(n)$ & $C_{n}$ & $2nA(0,0)$ \\
\hline
\end{tabular}
\end{center}
\end {table}
\newpage
\section{Splints of Lie superalgebra $D(m,n)$}
The basic Lie superalgebra $D(m,n)$ has rank $m+n$ and the positive root system is given by
\[\Delta=\{\varepsilon_{i}\pm\varepsilon_{j},\delta_{k}\pm\delta_{l},2\delta_{k},\delta_{k}\pm\varepsilon_{i}: 1\leq i\neq j \leq m , 1\leq k \neq l \leq n \},\]
with the normalization
\[(\varepsilon_{i},\varepsilon_{j})=-\delta_{ij},~~(\delta_{k},\delta_{l})=\delta_{kl},~~(\varepsilon_{i},\delta_{k})=0 ~~~~~ for ~~1\leq i,j \leq m , 1\leq k,l \leq n .\]
\begin{lemma}
Suppose $m\geqslant2$,~$n\geqslant3$ and $r\geqslant2$. If $D(m,n)$ has a splinter where $D(m,r)$ is a component, then $D(m,n-1)$ has a splinter having $D(m,r-1)$ as a component.
\end{lemma}
\begin{proof}
Suppose $(\Delta_{1},\Delta_{2})$ is a splint of $D(m,n)$ having $\iota:D(m,r)\hookrightarrow \Delta_{1}$ as a component. Without loss of generality, one can assume that the roots in the image of $\iota$ have the form $\{\varepsilon_{i}\pm\varepsilon_{j},\delta_{k}\pm\delta_{l},2\delta_{k},\delta_{k}\pm\varepsilon_{i}\}$ where $1\leqslant i\neq j\leqslant m , t+1\leqslant k \neq l\leqslant n$ ,when $ r=n-t$ for some $t\in \mathbb{Z}$.
Consider restricting the splint to the embedding $\iota_{1}:D(m,n-1)\hookrightarrow D(m,n)$, where the image of $\iota_{1}$ consists of roots of the form $\{\varepsilon_{i}\pm\varepsilon_{j},\delta_{k}\pm\delta_{l},2\delta_{k},\delta_{k}\pm\varepsilon_{i}\}$ where $1\leqslant i\neq j\leqslant m ,2\leqslant k\neq l\leqslant n$. Since $\iota_{1}$ is metric and all components of $\Delta_{1}$ and $\Delta_{2}$ are embedded metrically, this yields a splint of $D(m,n-1)$ having $D(m,r-1)$ as a component.
\end{proof}
\begin{proposition}
For $m\geqslant 4$, $n\geqslant 1$ or $m\geqslant2$, $n>3$ and either $n-2\leqslant m$, $m\geqslant n$ or $m-2\leqslant n , n \geqslant m$. If $(\Delta_{1},\Delta_{2})$ is a splinter of $D(m,n)$ having $D(r,s)$ as a component, then $r,s\in\{1,n-1,m-1\}$.
\end{proposition}
\begin{proof}
One may argue by contradiction using previous lemma and table of $D(m,n)$.
\end{proof}
\begin{lemma}
$A(m-1,n-1)$ is not a component of $D(m,n)$ for either $m\geqslant 4,~n\geqslant 1$ or $m\geqslant 2 ,~n>3$ and not a component of $C(n+1)$ for $n\geq4$.
\end{lemma}
\begin{proof}
Suppose $(\Delta_{1},\Delta_{2})$ is a splint of $D(m,n)$ and $A(m-1,n-1)\hookrightarrow \Delta_{1}$. Then other components of $\Delta_{1}$ are isomorphic to $A_{1}$ or $A(0,0)$. Also all components of $\Delta_{2}$ are isomorphic to $A_{1}$ or $A(0,0)$. Then rank of $\Delta_{2}$ is greater than $m+n$, which is a contradiction. Similar argument for $C(n+1)$ .
\end{proof}
\begin{lemma}
$B(m,n)$and $B(0,n)$ are not embedded in $D(m,n)$.
\end{lemma}
\begin{proof}
As $B(m,n)$ has a $\beta$ odd root such that $2\beta$ is an even root, but $D(m,n)$ has no such root.
\end{proof}
\begin{lemma}
$C(n+1)$ is not embedded in $D(m,n)$.
\end{lemma}
\begin{proof}
As $D(m,n)$ is embedded in $B(m,n)$ and $C(n+1)$ is not embedded in $B(m,n)$.
\end{proof}
We can describe all the splinters of $D(m,n)$ in the following way,
\begin{enumerate}
\item The splinter ($A(1,0),2A_{1}+2A(0,0)$) of $D(2,1)$ is given by
\begin{align*}
\Delta_{1}&=\{\varepsilon_{1}-\varepsilon_{2},\delta_{1}-\varepsilon_{1},\delta_{1}-\varepsilon_{2}\},\\
\Delta_{2}&=\{2\delta_{1},\varepsilon_{1}+\varepsilon_{2}\}\cup\{\delta_{1}+\varepsilon_{1},\delta_{1}+\varepsilon_{2}\}.
\end{align*}
\item The splinter ($A(1,1),4A_{1}+A(0,0)$) of $D(2,2)$ is given by
\begin{align*}
\Delta_{1}&=\{\varepsilon_{1}-\varepsilon_{2},\delta_{1}-\delta_{2},\delta_{1}-\varepsilon_{1},\delta_{1}-\varepsilon_{2},\delta_{2}-\varepsilon_{1},\delta_{2}-\varepsilon_{2}\},\\
\Delta_{2}&=\{\varepsilon_{1}+\varepsilon_{2},\delta_{1}+\delta_{2},2\delta_{1},2\delta_{2}\}\cup\{\delta_{1}+\varepsilon_{1},\delta_{1}+\varepsilon_{2},\delta_{2}+\varepsilon_{1},\delta_{2}+\varepsilon_{2}\}.
\end{align*}
\item The splinter ($A(2,0),4A_{1}+3A(0,0)$) of $D(3,1)$ is given by
\begin{align*}
\Delta_{1}&=\{\varepsilon_{1}-\varepsilon_{2},\varepsilon_{1}-\varepsilon_{3},\varepsilon_{2}-\varepsilon_{3},\delta_{1}-\varepsilon_{1},\delta_{1}-\varepsilon_{2},\delta_{1}-\varepsilon_{3}\},\\
\Delta_{2}&=\{\varepsilon_{1}+\varepsilon_{2},\varepsilon_{1}+\varepsilon_{3},\varepsilon_{2}+\varepsilon_{3},2\delta_{1}\}\cup\{\delta_{1}+\varepsilon_{1},\delta_{1}+\varepsilon_{2},\delta_{1}+\varepsilon_{3}\}.
\end{align*}
\item The splinter($A(2,1)+A_{1},5A_{1}+6A(0,0)$)of $D(3,2)$ is given by
\begin{align*}
\Delta_{1}&=\{\varepsilon_{1}-\varepsilon_{2},\varepsilon_{1}-\varepsilon_{3},\varepsilon_{2}-\varepsilon_{3},\delta_{1}-\delta_{2},\delta_{1}-\varepsilon_{1},\delta_{1}-\varepsilon_{2},\delta_{1}-\varepsilon_{3},\delta_{2}-\varepsilon_{1},\delta_{2}-\varepsilon_{2},\delta_{2}-\varepsilon_{3}\}\cup\{2\delta_{2}\},\\
\Delta_{2}&=\{\varepsilon_{1}+\varepsilon_{2},\varepsilon_{1}+\varepsilon_{3},\varepsilon_{2}+\varepsilon_{3},\delta_{1}+\delta_{2},2\delta_{1}\}\cup\{\delta_{1}+\varepsilon_{1},\delta_{1}+\varepsilon_{2},\delta_{1}+\varepsilon_{3},\delta_{2}+\varepsilon_{1},\delta_{2}+\varepsilon_{2},\delta_{2}+\varepsilon_{3}\}.
\end{align*}
\item The splinter($A(1,2)+2A_{1},5A_{1}+6A(0,0)$)of $D(2,3)$ is given by
\begin{align*}
\Delta_{1}&=\{\varepsilon_{1}-\varepsilon_{2},\delta_{1}-\delta_{2},\delta_{1}-\delta_{3},\delta_{2}-\delta_{3},\delta_{1}-\varepsilon_{1},\delta_{2}-\varepsilon_{1},\delta_{3}-\varepsilon_{1},\delta_{1}-\varepsilon_{2},\delta_{2}-\varepsilon_{2},\delta_{3}-\varepsilon_{2}\}\cup\{2\delta_{1},2\delta_{2}\},\\
\Delta_{1}&=\{\varepsilon_{1}+\varepsilon_{2},\delta_{1}+\delta_{2},\delta_{1}+\delta_{3},\delta_{2}+\delta_{3},\delta_{1}+\varepsilon_{1},\delta_{2}+\varepsilon_{1},\delta_{3}+\varepsilon_{1},\delta_{1}+\varepsilon_{2},\delta_{2}+\varepsilon_{2},\delta_{3}+\varepsilon_{2}\}\cup\{2\delta_{3}\}.
\end{align*}
\item For either $n-2\leqslant m$ or $m\geqslant n$ the splinter ($D(m,n-1)+A_{1}, (2n-2)A_{1}+2mA(0,0)$) of $D(m,n)$ is given by
\begin{align*}
\Delta_{1}&=\{\varepsilon_{i}\pm\varepsilon_{j},\delta_{k}\pm\delta_{l},2\delta_{k},\delta_{k}\pm\varepsilon_{i}: 1\leq i\neq j \leq m , 2\leq k \neq l \leq n \}\cup\{2\delta_{1}\},\\
\Delta_{2}&=\{\delta_{1}\pm\delta_{l},\delta_{1}\pm\varepsilon_{i}: 1\leq i\leq m ,2\leq l \leq n \}.
\end{align*}
Similarly, for either $m-2\leqslant n$ or $ n \geqslant m$ the splinter ($D(m-1,n), (2m-2)A_{1}+2nA(0,0)$) of $D(m,n)$ is given by
\begin{align*}
\Delta_{1}&=\{\varepsilon_{i}\pm\varepsilon_{j},\delta_{k}\pm\delta_{l},2\delta_{k},\delta_{k}\pm\varepsilon_{i}: 2\leq i\neq j \leq m , 1\leq k \neq l \leq n \},\\
\Delta_{2}&=\{\varepsilon_{1}\pm\varepsilon_{i},\delta_{1}\pm\varepsilon_{k}: 2\leq i\leq m ,1\leq l \leq n \}.
\end{align*}
\item The splinter ($D_{m}+C{n},2mnA(0,0)$) of $D(m,n)$ is given by
\begin{align*}
\Delta_{1}&=\{\varepsilon_{i}\pm\varepsilon_{j},\delta_{k}\pm\delta_{l},2\delta_{k}: 1\leq i\neq j \leq m , 1\leq k \neq l \leq n \},\\
\Delta_{2}&=\{\delta_{i}\pm\varepsilon_{k}: 1\leq i\leq m ,1\leq k \leq n \}.
\end{align*}
\end{enumerate}
\begin {table}[h]
\caption {$D(m,n)$} \label{tab:title}
\begin{center}
\begin{tabular}{ | b{3cm} | m{6cm}| m{6cm} | }
\hline
$\Delta$ & $\Delta_{1}$ & $\Delta_{2}$ \\ \cline{1-3}
$D(2,1)$ & $A(1,0)$ & $2A_{1}+2A(0,0)$ \\
\hline
$D(2,2)$ & $A(1,1)$ & $4A_{1}+A(0,0)$ \\
\hline
\end{tabular}
\end{center}
\end {table}
\begin {table}[h]
\begin{center}
\begin{tabular}{ | b{3cm} | m{6cm}| m{6cm} | }
\hline
$D(3,1)$ & $A(2,0)$ & $4A_{1}+3A(0,0)$ \\
\hline
$D(2,3)$ & $A(1,2)2+A_{1}$ & $5A_{1}+6A(0,0)$ \\
\hline$D(3,2)$ & $A(2,1)+A_{1}$ & $5A_{1}+6A(0,0)$ \\
\hline
$D(m,n)$ & $D_{m}+C{n}$ & $2mnA(0,0)$ \\
\hline
$D(m,n)$ for either $n-2\leqslant m$ or $m\geqslant n$ & $D(m,n-1)+A_{1}$ & $(2n-2)A_{1}+2mA(0,0)$\\
\hline
$D(m,n)$ for either $m-2\leqslant n$ or $ n \geqslant m$ & $D(m-1,n)$ & $(2m-2)A_{1}+2nA(0,0)$\\
\hline
\end{tabular}
\end{center}
\end {table}
\section{Splints of Lie superalgebras $G(3),F(4),D(2,1;\alpha)$}
\begin{enumerate}
\item The positive root system $G(3)$ is given by
\[\Delta=\{2\delta,\varepsilon_{i},\varepsilon_{i}-\varepsilon_{j},\delta,\varepsilon_{i}\pm\delta: 1\leq i\neq j \leq 3~and~ \varepsilon_{1}+\varepsilon_{2}+\varepsilon_{3}=0 \},\]
with the normalization
\[(\varepsilon_{i},\varepsilon_{j})=-3\delta_{ij}+1,~~(\delta,\delta)=2,~~(\varepsilon_{i},\delta)=0 ~~~~~ for ~~1\leq i,j \leq 3 . \]
Where the distinguished simple root system is given by;
\[\alpha_{1}=\delta+\varepsilon_{3},\alpha_{2}=\varepsilon_{1},\alpha_{3}=\varepsilon_{2}-\varepsilon_{1}.\]
The root system $G(3)$ has two splints and the splints are $(A_{2}+3A(0,0),A_{2}+A_{1}+4A(0,0))$ and $(B_{2}+A_{1}+3A(0,0),2A_{1}+4A(0,0)),$ these are given by
\begin{align*}
\Delta_{1}&= \{\alpha_{2},\alpha_{2}+\alpha_{3},2\alpha_{2}+\alpha_{3}\} \cup \{\alpha_{1}+\alpha_{2},\alpha_{1}+\alpha_{2}+\alpha_{3},\alpha_{1}+3\alpha_{2}+\alpha_{3}\}, \\
\Delta_{2}&= \{\alpha_{3},3\alpha_{2}+\alpha_{3},3\alpha_{2}+2\alpha_{3}\} \cup \{\alpha_{1},\alpha_{1}+2\alpha_{2}+\alpha_{3},\alpha_{1}+3\alpha_{2}+2\alpha_{3},\alpha_{1}+4\alpha_{2}+2\alpha_{3}\} \cup \{2\alpha_{1}+4\alpha_{2}+2\alpha_{3}\}.
\end{align*}
And another one is
\begin{align*}
\Delta_{1}&= \{\alpha_{2},\alpha_{3},\alpha_{2}+\alpha_{3},2\alpha_{2}+\alpha_{3}\} \cup \{2\alpha_{1}+4\alpha_{2}+2\alpha_{3}\} \cup \{\alpha_{1},\alpha_{1}+\alpha_{2},\alpha_{1}+\alpha_{2}+\alpha_{3}\},\\
\Delta_{2}&= \{3\alpha_{2}+\alpha_{3},3\alpha_{2}+2\alpha_{3}\} \cup \{\alpha_{1}+2\alpha_{2}+\alpha_{3},\alpha_{1}+3\alpha_{2}+2\alpha_{3},\alpha_{1}+4\alpha_{2}+2\alpha_{3},\alpha_{1}+3\alpha_{2}+\alpha_{3}\}.
\end{align*}
\item The positive root system of $F(4)$ is given by
\[\Delta=\{\delta,\varepsilon_{i}\pm\varepsilon_{j},\varepsilon_{i},
\frac{1}{2}(\varepsilon_{1}\pm\varepsilon_{2}\pm\varepsilon_{3}\pm\delta): 1\leq i\neq j \leq 3\}\]
with the normalization
\[(\varepsilon_{i},\varepsilon_{j})=-2\delta_{ij},~~(\delta,\delta)=6,~~(\varepsilon_{i},\delta)=0 ~~~~~ for ~~1\leq i,j \leq 3 .\]
Where the distinguished simple root system is given by;
\[\alpha_{1}=\frac{1}{2}(\delta-\varepsilon_{1}-\varepsilon_{2}-\varepsilon_{3}),\alpha_{2}=\varepsilon_{3},\alpha_{3}=\varepsilon_{2}-\varepsilon_{3},\alpha_{4}=\varepsilon_{1}-\varepsilon_{2}.\]
In the root system of $F(4)$ we can observe that the root system of $C(4)$,$B(0,3)$,$B(0,2)$ are not embedded in $F(4)$. Only the root system of $D(2,1)$ is embedded in $F(4)$ which is identified as \[\{\alpha_{2}+\alpha_{3},2\alpha_{2}+\alpha_{3}+\alpha_{4},2\alpha_{1}+3\alpha_{2}+2\alpha_{3}+\alpha_{4}\}\cup\{\alpha_{1},\alpha_{1}+\alpha_{2}+\alpha_{3},\alpha_{1}+2\alpha_{2}+\alpha_{3}+\alpha_{4},\alpha_{1}+3\alpha_{2}+2\alpha_{3}+\alpha_{4}\}.\] So $A(2,1)$ is also embedded in $F(4)$. Hence the root system $F(4)$ has only one splint \[(A_{1}+B_{3},8A(0,0)),\]
where $\Delta_{1}$ and $\Delta_{2}$ are all even roots and odd roots respectively.
\item The positive root system of $D(2,1;\alpha)$ is given by
\[\Delta=\{2\varepsilon_{i},
(\varepsilon_{1}\pm\varepsilon_{2}\pm\varepsilon_{3}): 1\leq i \leq 3\},\]
with the normalization
\[(\varepsilon_{1},\varepsilon_{1})=-\dfrac{(1+\alpha)}{2},~~(\varepsilon_{2},\varepsilon_{2})=-\dfrac{1}{2},~~(\varepsilon_{3},\varepsilon_{3})=-\dfrac{\alpha}{2},~~(\varepsilon_{i},\varepsilon_{j})=0 ~~for~~ i\neq j . \]
Where the distinguished simple root system is given by;
\[\alpha_{1}=\varepsilon_{2}-\varepsilon_{1},\alpha_{2}=2\varepsilon_{2},\alpha_{3}=2\varepsilon_{3}.\]
In a similar way the root system $D(2,1;\alpha)$ has two splinters that are $(A(1,0)+A_{1},A_{1}+2A(0,0))$ and $(3A_{1},4A(0,0))$ and these are given by \begin{align*}
\Delta_{1}&=\{\alpha_{1},\alpha_{2},\alpha_{1}+\alpha_{2}\}\cup \{\alpha_{3}\},\\ \Delta_{2}&=\{2\alpha_{1}+\alpha_{2}+\alpha_{3}\}\cup \{\alpha_{1}+\alpha_{3},\alpha_{1}+\alpha_{2}+\alpha_{3}\}
\end{align*}
and \begin{align*}
\Delta_{1}&=\{\alpha_{1},\alpha_{3},2\alpha_{1}+\alpha_{2}+\alpha_{3}\},\\
\Delta_{2}&=\{\alpha_{1},\alpha_{1}+\alpha_{2},\alpha_{1}+\alpha_{3},\alpha_{1}+\alpha_{2}+\alpha_{3}\}
\end{align*}
respectively.
\end{enumerate}
\section{Concluding remarks}
In this paper we have determined splints of all classical Lie superalgebras up to equivalence with Weyl group of the corresponding algebra. We hope results of this paper can help us to some extent in determining the branching coefficient. We want to delve in to this aspect of research in future.
\section{Acknowledgement}
One of the author prof. K.C.Pati thank National Board of Higher Mathematics(DAE), India for the Project Grant No. 2$\mid$48(25)$\mid$2016 R\&DII/4341 dt: 27.03.17 .
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 23 |
Ramsagar (), located in the village Tajpur in Dinajpur District. It is the most-frequently visited tourist destination in Dinajpur.
Location
It is situated about 8 kilometers south of the Dinajpur town.
Description
The lake is about 1,079 meters long from north to south, and 192.6 meters wide from east to west. It was created in the mid-1750s, funded by Raja Ram Nath, after whom the lake is named. The excavation cost 30,000 taka at that time, and about 1.5 million labourers took part in the project.
References
Wetlands of Bangladesh | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,219 |
/* $Id$ */
package com.zoho.projects.model;
import java.util.HashMap;
/**
* This class is used to make an object for bug.
*
* @author ramesh-2099
*
*/
public class Bug
{
private long id;
private String key;
private long projectId;
private String flag;
private String title;
private String description;
private String reporterId;
private String reportedPerson;
private String createdTime;
private String createdTimeFormat;
private long createdTimeLong;
private String assigneeId;
private String assigneeName;
private boolean closed;
private String url;
private String timesheetUrl;
private long classificationId;
private String classificationType;
private long severityId;
private String severityType;
private long statusId;
private String statusType;
private long reproducibleId;
private String reproducibleType;
private long moduleId;
private String moduleName;
private long milestoneId;
private String dueDate;
private String dueDateFormat;
private long dueDateLong;
/**
* Set the bug id.
*
* @param id ID of the bug.
*/
public void setId(long id)
{
this.id = id;
}
/**
* Get the bug id.
*
* @return Returns the bug id.
*/
public long getId()
{
return id;
}
/**
* Set the key for the bug.
*
* @param key Key for the bug.
*/
public void setKey(String key)
{
this.key = key;
}
/**
* Get the key for the bug.
*
* @return Returns the bug key.
*/
public String getKey()
{
return key;
}
/**
* Set the project id.
*
* @param projectId ID of the project.
*/
public void setProjectId(long projectId)
{
this.projectId = projectId;
}
/**
* get the project id.
*
* @return Returns the project id.
*/
public long getProjectId()
{
return projectId;
}
/**
* Set the flag for the bug.
*
* @param flag Flag for the bug.
*/
public void setFlag(String flag)
{
this.flag = flag;
}
/**
* Get the flag for the bug.
*
* @return Returns the flag for the bug.
*/
public String getFlag()
{
return flag;
}
/**
* Set the bug title.
*
* @param title Title for the bug.
*/
public void setTitle(String title)
{
this.title = title;
}
/**
* Get the bug title.
*
* @return Returns the bug title.
*/
public String getTitle()
{
return title;
}
/**
* Set the bug description.
*
* @param description Description for the bug.
*/
public void setDescription(String description)
{
this.description = description;
}
/**
* Get the bug description.
*
* @return Returns the bug description.
*/
public String getDescription()
{
return description;
}
/**
* Set the reporter id.
*
* @param reporterId ID of the reporter.
*/
public void setReporterId(String reporterId)
{
this.reporterId = reporterId;
}
/**
* Get the reporter id.
*
* @return Returns the reporter id.
*/
public String getReporterId()
{
return reporterId;
}
/**
* Set the reported person.
*
* @param reportedPerson Reported person for the bug.
*/
public void setReportedPerson(String reportedPerson)
{
this.reportedPerson = reportedPerson;
}
/**
* Get the reported person.
*
* @return Returns the reported person for the bug.
*/
public String getReportedPerson()
{
return reportedPerson;
}
/**
* Set the created time.
*
* @param createdTime Created time for the bug.
*/
public void setCreatedTime(String createdTime)
{
this.createdTime = createdTime;
}
/**
* Get the created time.
*
* @return Returns the created time for the bug.
*/
public String getCreatedTime()
{
return createdTime;
}
/**
* Set the created time format.
*
* @param createdTime Created time format for the bug.
*/
public void setCreatedTimeFormat(String createdTimeFormat)
{
this.createdTimeFormat = createdTimeFormat;
}
/**
* Get the created time format.
*
* @return Returns the created time format for the bug.
*/
public String getCreatedTimeFormat()
{
return createdTimeFormat;
}
/**
* Set the created time long.
*
* @param createdTimeLong Created time long for the bug.
*/
public void setCreatedTimeLong(long createdTimeLong)
{
this.createdTimeLong = createdTimeLong;
}
/**
* Get the created time long.
*
* @return Returns the created time long for the bug.
*/
public long getCreatedTimeLong()
{
return createdTimeLong;
}
/**
* Set the assignee id for the bug.
*
* @param assigneeId ID of the assignee.
*/
public void setAssigneeId(String assigneeId)
{
this.assigneeId = assigneeId;
}
/**
* Get the assignee id.
*
* @return Returns the assignee id.
*/
public String getAssigneeId()
{
return assigneeId;
}
/**
* Set the assignee name.
*
* @param assigneeName Name of the assignee.
*/
public void setAssigneeName(String assigneeName)
{
this.assigneeName = assigneeName;
}
/**
* Get the assignee name.
*
* @return Returns the assignee name.
*/
public String getAssigneeName()
{
return assigneeName;
}
/**
* Set the bug is closed or not.
*
* @param closed Boolean for the bug is closed or not.
*/
public void setClosed(boolean closed)
{
this.closed = closed;
}
/**
* Get the bug is closed or not.
*
* @return Returns true if the big is closed else returns false.
*/
public boolean isClosed()
{
return closed;
}
/**
* Set the bug URL.
*
* @param url URL for the bug.
*/
public void setURL(String url)
{
this.url = url;
}
/**
* Get the bug URL.
*
* @return Returns the bug URL.
*/
public String getURL()
{
return url;
}
/**
* Set the time sheet URL.
*
* @param timesheetUrl URL for the time sheet.
*/
public void setTimesheetURL(String timesheetUrl)
{
this.timesheetUrl = timesheetUrl;
}
/**
* Get the time sheet URL.
*
* @return Returns the time sheet URL.
*/
public String getTimesheetURL()
{
return timesheetUrl;
}
/**
* Set the classification id.
*
* @param classificationId ID of the classification.
*/
public void setClassificationId(long classificationId)
{
this.classificationId = classificationId;
}
/**
* Get the classification id.
*
* @return Returns the classification id.
*/
public long getClassificationId()
{
return classificationId;
}
/**
* Set the classification type.
*
* @param classificationType Type of the classification.
*/
public void setClassificationType(String classificationType)
{
this.classificationType = classificationType;
}
/**
* Get the classification type.
*
* @return Returns the classification type.
*/
public String getClassificationType()
{
return classificationType;
}
/**
* Set the severity id.
*
* @param severityId ID of the severity.
*/
public void setSeverityId(long severityId)
{
this.severityId = severityId;
}
/**
* Get the severity id.
*
* @return Returns the severity id.
*/
public long getSeverityId()
{
return severityId;
}
/**
* Set the severity type.
*
* @param severityType Type of the severity.
*/
public void setSeverityType(String severityType)
{
this.severityType = severityType;
}
/**
* Get the severity type.
*
* @return Returns the severity type.
*/
public String getSeverityType()
{
return severityType;
}
/**
* Set the status id.
*
* @param statusId ID of the status.
*/
public void setStatusId(long statusId)
{
this.statusId = statusId;
}
/**
* Get the status id.
*
* @return Returns the status id.
*/
public long getStatusId()
{
return statusId;
}
/**
* Set the status type.
*
* @param statusType Type of the status.
*/
public void setStatusType(String statusType)
{
this.statusType = statusType;
}
/**
* Get the status type.
*
* @return Returns the status type.
*/
public String getStatusType()
{
return statusType;
}
/**
* Set the reproducible id.
*
* @param reproducibleId Reproducible id of the bug.
*/
public void setReproducibleId(long reproducibleId)
{
this.reproducibleId = reproducibleId;
}
/**
* Get the reproducible id.
*
* @return Returns the reproducible id.
*/
public long getReproducibleId()
{
return reproducibleId;
}
/**
* Set the reproducible type.
*
* @param reproducibleType Reproducible type of the bug.
*/
public void setReproducibleType(String reproducibleType)
{
this.reproducibleType = reproducibleType;
}
/**
* Get the reproducible type.
*
* @return Returns the reproducible type.
*/
public String getReproducibleType()
{
return reproducibleType;
}
/**
* Set the module id.
*
* @param moduleId ID of the module.
*/
public void setModuleId(long moduleId)
{
this.moduleId = moduleId;
}
/**
* Get the module id.
*
* @return Returns the module id.
*/
public long getModuleId()
{
return moduleId;
}
/**
* Set the module name.
*
* @param moduleName Name of the module.
*/
public void setModuleName(String moduleName)
{
this.moduleName = moduleName;
}
/**
* Get the module name.
*
* @return Returns the module name.
*/
public String getModuleName()
{
return moduleName;
}
/**
* Set the milestone id.
*
* @param milestoneId ID of the milestone.
*/
public void setMilestoneId(long milestoneId)
{
this.milestoneId = milestoneId;
}
/**
* Get the milestone id.
*
* @return Returns the milestone id.
*/
public long getMilestoneId()
{
return milestoneId;
}
/**
* Set the due date.
*
* @param dueDate Due date for the bug.
*/
public void setDueDate(String dueDate)
{
this.dueDate = dueDate;
}
/**
* Get the due date.
*
* @return Returns the due date.
*/
public String getDueDate()
{
return dueDate;
}
/**
* Set the due date format.
*
* @param dueDate Due date format for the bug.
*/
public void setDueDateFormat(String dueDateFormat)
{
this.dueDateFormat = dueDateFormat;
}
/**
* Get the due date format.
*
* @return Returns the due date format.
*/
public String getDueDateFormat()
{
return dueDateFormat;
}
/**
* Set the due date long.
*
* @param dueDateLong Due date long for the bug.
*/
public void setDueDateLong(long dueDateLong)
{
this.dueDateLong = dueDateLong;
}
/**
* Get the due date long.
*
* @return Returns the due date long.
*/
public long getDueDateLong()
{
return dueDateLong;
}
/**
* Convert the Bug object into HashMap.
*
* @return Returns the HashMap object.
*/
public HashMap<String, Object> toParamMAP()
{
HashMap<String, Object> requestBody = new HashMap<String, Object>();
if(title != null)
{
requestBody.put("title", title);
}
if(description != null)
{
requestBody.put("description", description);
}
if(assigneeId != null)
{
requestBody.put("assignee", assigneeId);
}
if(flag != null)
{
requestBody.put("flag", flag);
}
if((Long)classificationId != null && classificationId > 0)
{
requestBody.put("classification_id", classificationId);
}
if((Long)milestoneId != null && milestoneId > 0)
{
requestBody.put("milestone_id", milestoneId);
}
if(dueDate != null)
{
requestBody.put("due_date", dueDate);
}
if((Long)moduleId != null && moduleId > 0)
{
requestBody.put("module_id", moduleId);
}
if((Long)severityId != null && severityId > 0)
{
requestBody.put("severity_id", severityId);
}
if((Long)reproducibleId != null && reproducibleId > 0)
{
requestBody.put("reproducible_id", reproducibleId);
}
return requestBody;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,375 |
Classic tricolor soft Vitello leather satchel bag by MICHAEL Michael Kors. Fashioned from soft, supple leather, this Hamilton Traveler bag by MICHAEL Michael Kors carries sophistication and style wherever it goes.
10-1/4" W x 8-1/2" H x 5-1/2" D. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,065 |
\section{Introduction}
One of the major challenges in detecting cosmological signals such as the cosmic microwave background (CMB) radiation and 21-cm emissions from the epoch of reionization (EoR) is the removal of foreground emissions from our Galaxy and extragalactic sources. In general, these foreground components are dominant (can be several orders of magnitude higher depending on the frequency) in comparison to the primordial signals.
The low-frequency part of the CMB black-body spectrum is dominated by diffuse synchrotron and free-free emissions, while thermal dust emissions and the cosmic infrared background are dominant on the higher frequency side. Moreover, synchrotron and dust emissions are highly polarized.
In many component-separation and cleaning algorithms, modelling each foreground component is a key step, and understanding both spectral and statistical properties of the foreground emissions is important in developing these pipelines~\cite{Eriksen:2004ss,Delabrouille:2008qd}.
In modelling and simulating foregrounds at low frequencies, the small scale fluctuations are generally assumed to be statistically isotropic Gaussian random fields (see for example, \cite{Tegmark:1999ke,Jelic:2008jg,PySM:2017}).
For example, in the commonly used \texttt{Hammurabi} code~\cite{Waelkens:2008gp}, the turbulent component of the Galactic magnetic field is usually assumed to be statistically isotropic and Gaussian distributed. The assumptions of Gaussianity and statistical isotropy (henceforth, SI) of the foregrounds at small scales and away from the Galactic plane simplify their modelling.
However, their validity based on physical grounds is not clear.
Since the interactions that govern the Galactic emissions are in general non-linear, we do not expect that the interaction may be expressed as a small perturbation term added to an interaction-free physical system.
It is not clear that the statistical nature of each foreground component will approach Gaussianity at smaller scales. It is possible that if we remove the larger scale fluctuations, the fields do approach Gaussianity as a manifestation of the central limit theorem. However, it is important to test this as a function of resolution or scale. Further, the foreground fields are obviously anisotropic on the full sky since most of the emissions come from regions around the plane of the Galactic equator. It is important to test whether, after masking the Galactic regions, the fields approach SI as we probe down to smaller scales.
Several techniques have been devised to probe the Gaussianity and SI of random fields in cosmology. Search methods for non-Gaussian deviations include cumulants such as skewness and kurtosis,
bispectrum~\cite{Komatsu:2001rj}, the Kullback-Leibler divergence~\cite{Ben-David:2015sia} etc. Some of the methods for testing SI are Bipolar Spherical Harmonics (BiPoSH) \cite{Souradeep:2006dz} and power-tensor method \cite{Rath:2015oga}.
Morphological statistics such as scalar Minkowski functionals (MFs)~\cite{Adler:1981,Tomita:1986} are computed in real space and contain information of all orders of $n$-point functions. This makes them particularly advantageous over Fourier space methods such as the bispectrum and trispectrum in searches for non-Gaussianity in situations where the non-Gaussian nature of the field is a priori unknown, and/or when the field is highly non-Gaussian.
MFs have been widely used in CMB cosmology to search for primordial non-Gaussianity~\cite{Gott:1990,
Schmalzing:1998,COBE_NG:2000,Chingangbam:2009vi,Chingangbam:2017sap,Ade:2015ava,Buchert:2017uup}. They have also been used to detect residual foreground contamination in WMAP data~\cite{Chingangbam:2013}, and to study the properties of synchrotron radiation~\cite{Rana:2018oft}. Related topological quantities like Betti numbers were also employed to understand the morphology of the interstellar turbulence \cite{2018MNRAS.475.1843M}.
Tensor-valued generalizations of the scalar MFs on two- and three-dimensional Euclidean space, which we will refer to as Minkowski tensors (MTs),
carry additional information related to intrinsic anisotropy and alignment of structures~\cite{Schroder2D:2009,Chingangbam:2017uqv}.
The rank-2 translation invariant MTs contain the scalar MFs as their traces.
They have been generalized to random fields on curved two-dimensional manifolds, in particular, spaces of constant curvature such as the sphere, in~\cite{Chingangbam:2017uqv}.
MTs have been used to study departure from SI of the CMB~\cite{Vidhya:2016,Joby:2018}, to probe the effect of weak lensing on the morphology of CMB fields~\cite{Goyal:2019vkq}, the time evolution of the fields of the EoR~\cite{Kapahtia:2017qrg,Kapahtia:2019ksk}, and matter density evolution and redshift space distortion~\cite{Appleby:2018tzk}.
The all-sky 408 MHz synchrotron map obtained by Haslam et al.~\cite{Haslam:1981,Haslam:1982} has been an important input for modelling the synchrotron in the CMB component separation methods for WMAP and Planck~\cite{2013ApJS..208...20B,Ade:2015qkp}. Various statistical properties that focus on the two-point function of this map have been well studied~\cite{Cho:2010kw,Mertsch:2013pua}. The data has been de-striped and renewed by Remazeilles et al.~\cite{Remazeilles:2014mba}.
We refer to this version as the {\em Haslam} map.
Ben-David et al.~\cite{Ben-David:2015b} reported that this map is Gaussian at scales smaller than roughly $3^{\circ}$, using skewness and kurtosis statistics for the investigation. Rana et al.~\cite{Rana:2018oft} used the bispectrum and MFs to probe the non-Gaussianity of the Haslam map and reported findings that are in agreement with~\cite{Ben-David:2015b}.
In this paper, we examine in detail the non-Gaussian nature and SI of the Haslam map using the Minkowski tensors as a unified statistical tool. Further, we calculate the generalized skewness and kurtosis cumulants that enter in the perturbative expansion of scalar MFs for weakly non-Gaussian fields about the zeroth-order Gaussian expressions~\cite{Matsubara:2011,Matsubara:2020}. We compare the non-Gaussian deviations of the MFs that are obtained using the analytic expressions with the exact numerical calculations. This comparison allows us to demonstrate that the perturbative expansions of the MFs about the zeroth-order forms expected for Gaussian fields are valid in the cooler regions of the Haslam map. Moreover, the leading source of non-Gaussianity is the second-order perturbation terms, and hence, the kurtosis determines the nature of non-Gaussian deviations in the Haslam map.
The paper is organized as follows. Section \ref{sec:sec2} presents a brief discussion of the Galactic synchrotron emissions, followed by a description of the Haslam map.
In section \ref{sec:sec3}, we briefly review Minkowski tensors and scalar MFs. We also give the analytic formulae for the scalar MFs for weakly non-Gaussian random fields and present the methods we use for the numerical computation of MFs and MTs. Section \ref{sec:sec4} contains the pipeline for our analysis and simulations of Gaussian maps with the Haslam power spectrum. Section \ref{sec:sec5} contains our calculations and main results. We end with a summary of our results and a discussion of their implications in section \ref{sec:sec6}
. Appendix \ref{sec:a1checks} contains a discussion of the consistency checks between the Haslam map and the simulations. We show the probability distribution function (PDF) of the Haslam map in appendix \ref{sec:pdf}.
In appendix \ref{sec:a2fnlgnl}, we show the agreement between exact numerical calculation and the analytic perturbative formulae of non-Gaussian deviations of scalar MFs for primordial local type non-Gaussianity.
\section{Galactic synchrotron radiation and the Haslam map}
\label{sec:sec2}
Relativistic electrons interacting with magnetic fields emit synchrotron radiation. Cosmic rays (CR), which include relativistic electrons, arrive at our Galaxy from all directions. They interact with the Galactic magnetic field and emit synchrotron radiation roughly in the frequency range of 20 MHz to 100 GHz. The intensity of the synchrotron emission depends on the number density of CR electrons and the strength of the magnetic field, both of which vary with respect to direction. As a consequence, the intensity of Galactic synchrotron emission shows variations across the sky.
Let the energy distribution of relativistic electrons be given by the power law form
\begin{equation}
N_e(E) {\rm d}E \propto E^{-p}{\rm d}E,
\end{equation}
where $p$ is the index which in this case depends on the CR composition. Let $I_{\rm sync}(\hat n,\nu)$ denote the intensity of synchrotron emission in sky direction $\hat n$, at frequency $\nu$. Let $B_{\perp}$ be the magnitude of the magnetic field perpendicular to the line-of-sight radial coordinate $r$. Then $I_{\rm sync}(\hat n,\nu)$ can be related to $B_{\perp}$ as
\begin{equation}
I_{\rm sync}(\hat n,\nu) \propto \nu^{\beta_{\textsf{s}}} \int {{\rm d}}r B_{\perp}^{-\beta_{\textsf{s}}+1}(\hat n)
\end{equation}
The spectral index ($\beta_{s}$), which is related to $p$ as $\beta_{s}=-(p-1)/2$, shows variations in the sky given the difference in the magnetic field strength as well as the CR distribution along the line-of-sight. The spectra also exhibit steepening at higher frequency bands due to the radiative losses and the aging effects of CR electrons, and the presence of multiple components~\cite{1959ApJ...130..241W,1986rpa..book.....R,2012ApJ...747....5L}.
Our attention in this work is on $I_{\rm sync}(\hat n,\nu)$ as a fluctuating field on the sphere. Radio telescopes used in sky surveys do not measure $I_{\rm sync}$ directly. Rather, what is measured is the brightness temperature $T_{\rm sync}$ which is related to $I_{\rm sync}$ as $T_{\rm sync}=I_{\rm sync}/\nu^{2}$.
Sky surveys to obtain $T_{\rm sync}(\hat n,\nu) $ have been conducted at a number of radio frequencies. Of these, the 408 MHz Haslam map obtained by Haslam et al.~\cite{Haslam:1981,Haslam:1982} is most widely used in the CMB component separation pipelines. In this frequency range and in terms of brightness temperature, the best-fit value of spectral index ($\beta_s$) is -2.7 with an uncertainty~$\Delta\beta_{\textsf{s}}$=0.12~\cite{2003A&A...410..847P}. This low-frequency radio map is free from other interstellar radiation fields such as the free-free and spinning dust emissions which makes it an ideal synchrotron intensity map for the parametric component separation techniques.
The angular power spectrum of the Haslam map has been studied in several earlier works. It follows a power law form, $C_{\ell}=\ell^{-\alpha}$, with $\alpha$ $\sim$ 3~\cite{2008A&A...479..641L}. The angular features carry a wealth of information regarding the structure of the Galactic magnetic field.
Cho \& Lazarian~\cite{Cho:2010kw} analyzed how the angular spectrum of synchrotron emission is related to the MHD turbulence in the interstellar medium. Lazarian \& Pogosian~\cite{2012ApJ...747....5L} carried out extensive theoretical calculations to explain the observed correlations of synchrotron fluctuations in terms of the CR electron spectra and the axisymmetric nature of the magnetic turbulence.
Despite various post-processing techniques applied, the earlier versions of the Haslam data contain residuals from strong radio sources and has artefacts such as striations due to the scanning strategies. To minimise the errors arising from these artefacts, a new cleaned 408 MHz map with fewer artefacts and reduced systematics was prepared by Remazeilles et al. \cite {Remazeilles:2014mba}. In this map, the brightness temperature values are given in kelvin unit. For our analysis in this paper, we will focus on the low brightness temperature regions of this renewed map to study its statistical properties using Minkowski tensors.
\section{Overview of tensorial Minkowski functionals in two dimensions}
\label{sec:sec3}
Tensorial Minkowski Functionals (also referred to as Minkowski tensors) are geometrical quantities that encode the morphological properties of structures. They are defined on flat space. For analyzing all-sky data, such as the Haslam map, we need to analyze it on the sphere. The generalization of MTs to curved space was given in~\cite{Chingangbam:2017uqv}. We briefly outline the notations and the method described there, analytic expressions and methods for their numerical calculation.
\subsection{Definition of tensorial and scalar Minkowski functionals}
In this section, we introduce tensorial and scalar Minkowski functionals in a unified way. Let us first consider a closed curve, denoted by $C$, on the unit sphere, $\mathcal{S}^2$. Let ${\rm d}a$ be the infinitesimal area element in the region enclosed by the curve, ${\rm d}\ell$ be the infinitesimal arc length of the curve and $\kappa$ the geodesic curvature of the curve. Let $\hat{T}$ denote the unit tangent vector to the curve.
The rank-2 Minkowski tensors (MTs) denoted by $\mathcal{W}_k$, with $k=0,1,2$, are defined to be~\cite{Chingangbam:2017uqv},
\begin{equation}
\mathcal{W}_{0}= \frac{B_0}{2}\, \mathbb{I} \int{\rm d}a, \quad\
\mathcal{W}_{1}= B_1\int_{C}\,\hat{T}\otimes \hat{T} \, {\rm d}\ell, \quad
\mathcal{W}_{2}= \frac{B_2}{2\pi}\,\int_{C} \hat{T}\otimes \hat{T}\, \kappa \,{\rm d}\ell. \label{eqn:mt}
\end{equation}
In the above, $\mathbb{I}$ is the $2\times 2$ identity matrix, and $\otimes$ denotes the symmetric tensor product given by $\hat{T}\otimes \hat{T}=\frac{1}{2}\big(\hat{T_{i}}\hat{T_{j}}+\hat{T_{j}}\hat{T_{i}}\big)$. The coefficients $B_k$ are constants which we leave unspecified here so as to focus on the geometrical meaning of $\mathcal{W}_{k}$.
The three scalar Minkowski functionals denoted by $V_k$ are given by the traces of $\mathcal{W}_k$, as given below,
\begin{equation}
V_{0} = B_0\,\int {\rm d}a,\quad V_{1} = B_1\,\int_C {\rm d}\ell,\quad V_{2} = \frac{B_2}{2\pi}\,\int_C \kappa \, {\rm d}\ell. \label{eqn:smf}
\end{equation}
$V_0$ is proportional to the area enclosed by the curve and $V_1$ to the perimeter of the curve. $V_{2}$, usually referred to as the {\em genus} in cosmology\footnote{It differs from the mathematical definition of the genus by one.}, equals $B_2$ for a single curve if the space is flat, while on curved space it equals $B_2$ plus a term which is proportional to $V_0$. Therefore, the Minkowski tensors combine the information contained in the scalar MFs along with new information of the shape of structures encoded in $\mathcal{W}_{1}$.
Next, we consider smooth random fields on $\mathcal{S}^2$. Let $u$ denote the random field. The boundaries of a level or excursion set of the field, $u=\nu$, where $\nu$ denotes the chosen field level or threshold value, form smooth closed curves. Let $Q_{\nu}$ denote the set of points in the excursion set and ${\partial Q_{\nu}}$ denote its boundary. The subscript is used to remind us that the excursion set depends on $\nu$. Then, we can generalize the definition of $\mathcal{W}_k$ to the excursion set by the following,
\begin{equation}
\mathcal{W}_{0}(\nu)= \frac{B_0}{2}\, \mathbb{I} \int_{Q_{\nu}}{\rm d}a, \quad\
\mathcal{W}_{1}(\nu)= B_1\,\int_{\partial Q_{\nu}} \hat{T}\otimes \hat{T} \, {\rm d}\ell, \quad
\mathcal{W}_{2}(\nu)= \frac{B_2}{2\pi}\int_{\partial Q_{\nu}} \hat{T}\otimes \hat{T}\, \kappa \,{\rm d}\ell. \label{eqn:mt_field}
\end{equation}
$\mathcal{W}_{1}$, the tensorial analogue of the contour length $V_{1}$, encodes the information of the existence of any particular alignment for the structures. Structures that have no elongation in any particular direction will have $\mathcal{W}_{1}$ proportional to the identity matrix. Let
$\overline{\mathcal{W}}_{1}$ denote the sum over the $\mathcal{W}_{1}$ for all the curves in a given threshold. Let $\Lambda_{1}$ and $\Lambda_{2}$ be its eigenvalues. Then, we can define the parameters $\alpha$ as,
\begin{equation}
\alpha=\frac{\Lambda_{1}}{\Lambda_{2}} \hspace{2cm} \Lambda_{1}<\Lambda_{2}
\end{equation}
$\alpha$ gives the measure of the relative alignment or the deviation from SI of the field. $\alpha=1$ is obtained when $\overline{\mathcal{W}}_{1}$ is proportional to the identity matrix, and it implies that the field preserves SI, whereas deviation from unity indicates the presence of alignment for the structures.
Before we proceed, a discussion regarding our notation is in order.
When applying to random fields in cosmology, the scalar and tensorial MFs are usually expressed per unit area in the form of densities. We use the same symbols $\mathcal W_k$ and $V_k$, with $k=0,1,2$, to denote the densities by including the area factor in the coefficients. In the next subsection in the place of $B_k$, we will use coefficients $A_k$ which include the area factors and whose values are commonly used in the literature.
Thus, $V_0$ gives the area fraction of the excursion set, $V_1$ the total boundary contour length per unit area, and $V_2$ the genus per unit area at each field threshold. Similarly, $\mathcal{W}_1$, denotes the contour MT per unit area.
\subsection{Analytical formulation of scalar MFs for mildly non-Gaussian fields}
\label{sec:ana}
Let $u$ denote a generic Gaussian random field having zero mean and standard deviation $\sigma$, and let $\nu$ now denote threshold values of the normalized field $u/\sigma$. Then the expectation values of the scalar MFs per unit area, as functions of the threshold $\nu$ are given by~\cite{Tomita:1986},
\begin{equation}
V_{k}(\nu)=A_k\,e^{-\nu^{2}/2}v^{(\rm G)}_k(\nu),
\label{eqn:gmf}
\end{equation}
where $k=0,1,2$ and the coefficients $A_k$ are
\begin{equation}
A_{k}=\frac{1}{(2\pi)^{(k+1)/2}}\frac{\omega_{2}}{\omega_{2-k}\omega_{k}}\Big(\frac{\sigma_{1}}{\sqrt{2}\sigma}\Big)^{k}.
\end{equation}
The numerical factors are $\omega_0=1,\ \omega_1=2,\ \omega_2= \pi$, and $\sigma_1\equiv \sqrt{\langle |\nabla u|^2\rangle}$, where $\nabla u$ is the gradient of the field . The functions $v^{(\rm G)}_k$ are
\begin{eqnarray}
v_0^{\rm (G)}(\nu) &=& \sqrt{\frac{\pi}{2}}\,e^{\nu^{2}/2}\,\text{erfc}\left(\frac{\nu}{\sqrt{2}}\right),\\
v^{(\rm G)}_1 &=& 1,\\
v^{(\rm G)}_2(\nu) &= & \nu.
\end{eqnarray}
The superscript `G' stands for Gaussian.
For mildly non-Gaussian fields, again denoted by $u$,
the scalar MFs can be expressed in the same form as eqn.~\ref{eqn:gmf}, but with $v^{(\rm G)}_k$ replaced by $v_k$, which can be expanded in powers of the standard deviation $\sigma$~\cite{Matsubara:2011} as,
\begin{equation}
v_{k}=v_{k}^{(\rm G)}+v_{k}^{(1)}\sigma+v_{k}^{(2)}\sigma^{{2}}+\mathcal{O}(\sigma^{3}).
\end{equation}
The first-order non-Gaussian terms are given in terms of three skewness cumulants, denoted by $S_0, S_1, S_2$, as,
\begin{eqnarray}
v_{0}^{(1)}(\nu)&=&\frac{S_0}{6}H_{2}(\nu),\\
v_{1}^{(1)}(\nu)&=&\frac{S_0}{6}H_{3}(\nu)-\frac{S_1}{4}H_{1}(\nu),\\
v_{2}^{(1)}(\nu)&=&\frac{S_0}{6}H_{4}(\nu)-\frac{S_1}{2}H_{2}(\nu)-\frac{S_2}{2}H_{0}(\nu).
\end{eqnarray}
where $H_n$($\nu$) are the Hermite polynomials. The second-order non-Gaussian terms are given in terms of four kurtosis cumulants, denoted by $K_0, K_1, K_2, K_3$, as,
\begin{eqnarray}
v_{0}^{(2)}(\nu)&=&\frac{S_0^2}{72}H_{5}(\nu)+\frac{K_0}{24}H_{3}(\nu), \\
v_{1}^{(2)}(\nu)&=&\frac{S_0^2}{72}H_{6}(\nu) +\frac{K_0-S_0S_1}{24}H_4(\nu)
-\frac{1}{12} \left(K_1+\frac{3}{8}S_1^2\right) H_2(\nu)-\frac{K_3}{8}, \\
v_{2}^{(2)}(\nu)&=&\frac{S_0^2}{72}H_{7}(\nu)+\frac{K_0-2S_0S_1}{24}H_{5}(\nu)-\frac{1}{6}\left(K_1+\frac{1}{2}S_0S_2\right)H_{3}(\nu) \nonumber \\
&& -\frac{1}{2}\left(K_2+\frac{1}{2}S_1S_2\right)H_{1}(\nu).
\end{eqnarray}
In terms of the field $u$, its gradient $\nabla u$, and Laplacian $\nabla^{2} u$, the skewness and kurtosis cumulants are defined as follows
\begin{eqnarray}
S_0 &=& \frac{\langle u^{3}\rangle_c}{\sigma^{4}}, \quad S_1=\frac{\langle u^{2}\nabla^{2}u\rangle_c}{\sigma^{2}\sigma^{2}_{1}}, \quad S_2= \frac{2\langle |\nabla u|^{2}\nabla^{2}u\rangle_c}{\sigma_{1}^{4}}, \label{eqn:skew}\\
K_0 &=& \frac{\langle u^{4}\rangle_c}{\sigma^{6}}, \ K_1=\frac{\langle u^{3}\nabla^{2}u\rangle_c}{\sigma^{4}\sigma^{2}_{1}}, \
K_2=\frac{2\langle u|\nabla u|^{2}\nabla^{2}u\rangle_c+\langle |\nabla u|^{4}\rangle_c}{\sigma^{2}\sigma_{1}^{4}}, \ K_3=\frac{\langle |\nabla u|^{4}\rangle_c}{2\sigma^{2}\sigma_{1}^{4}}. \label{eqn:kurt}
\end{eqnarray}
The subscript $c$ indicates that these quantities are the connected cumulants. As the field is mean-free, the third-order cumulants are equal to the third-order moments. Fourth-order cumulants are given in terms of the moments~\cite{Matsubara:2020} as,
\begin{eqnarray}
\langle u^{4} \rangle_{c}&=& \langle u^{4} \rangle -3\sigma^{4} \\
\langle u^{3}\nabla^{2}u\rangle_c &=& -3\langle u^{2}|\nabla u|^{2} \rangle_{c}=-3(\langle u^{2}|\nabla u|^{2} \rangle -\sigma^{2}\sigma_{1}^{2}) \\
\langle u|\nabla u|^{2} \nabla^{2} u\rangle_{c} &=& \langle u|\nabla u|^{2} \nabla^{2} u\rangle +\sigma_{1}^{4} \\
\langle |\nabla u|^{4} \rangle_{c} &=& \langle |\nabla u|^{4} \rangle -2\sigma_{1}^{4}
\end{eqnarray}
\subsection{Computing scalar and tensorial Minkowski functionals}
\subsubsection{Method 1 - using field derivatives }
\label{sec:method1}
Given the field $u$, we rescale it to make it mean-free and unit standard deviation. MFs can be computed at each threshold values $\nu$ in terms of $u$ and its derivatives. The line integrals in eq.~\ref{eqn:mt_field} can be converted into surface integrals. $V_0$ is expressed in terms of the field $u$ as,
\begin{equation}
\text{V}_{0}(\nu)=\int_{S^{2}}\Theta(u-\nu)\hspace{1mm}{\rm d}a,
\end{equation}
where $\Theta$ is the step function.
Using $\hat{T}_{i}=\epsilon_{ij}\frac{u_{;j}}{|\nabla u|}$,
where $\epsilon$ is the two dimensional anti-symmetric Levi-Civita tensor and $u_{;j}$ the $j$-th component of the covariant derivative, we get
\begin{eqnarray}
\overline{\mathcal{W}}_{1}&=&\frac{1}{4}\int_{S^{2}} \delta (u-\nu)\hspace{1mm}\frac{1}{|\nabla u|}\hspace{1mm}\mathcal{M} \hspace{1mm}{\rm d}a,\\
\overline{\mathcal{W}}_{2} &=& \frac{1}{2\pi}\int_{S^{2}} \delta (u-\nu)\hspace{1mm}\frac{\kappa}{|\nabla u|}\hspace{1mm}\mathcal{M} \hspace{1mm} {\rm d}a.
\end{eqnarray}
The expression for $\kappa$ is
\begin{equation}
\kappa=\frac{2u_{;1}u_{;2}u_{;12}-u_{;1}^{2}u_{;22}-u_{;2}^{2}u_{;11}}{|\nabla u|^{3}}
\end{equation}
and $\mathcal{M}$ is,
\[
\mathcal{M}=
\begin{bmatrix}
u_{;2}^{2} & -u_{;1}u_{;2} \\
-u_{;1}u_{;2} & u_{;1}^{2}
\end{bmatrix}
\]
For a field in discretized space, the $\delta$-function is approximated to be
$\delta(u-\nu)=\frac{1}{\Delta \nu}$,
if $u$ lies between $\nu-\Delta \nu/2$ and $\nu+\Delta \nu/2$, and zero elsewhere. Here, $\Delta \nu$ is the bin size of the threshold values.
Using this method, we compute $V_0$, $\mathcal{W}_1$ and $\mathcal{W}_2$. From the eigenvalues of $\mathcal{W}_1$, we calculate $\alpha$. Further, by taking the traces of $\overline{\mathcal{W}}_{1}$ and $\overline{\mathcal{W}}_{2}$, we obtain $V_1$ and $V_2$. All these quantities are then divided by the total area to get their corresponding densities.
The $\delta$ function approximation is shown to have inherent numerical error in~\cite{Lim:2012}. This error will be present in the calculations of $\mathcal{W}_1$ and $\mathcal{W}_2$, and in $V_1$ and $V_2$. For comparison, we will compute $V_1$ and $V_2$ using the geometric method, which is described in the next subsection. It was shown in~\cite{Goyal:2019vkq} that the numerical errors in the two eigenvalues of $\mathcal{W}_1$ are comparable and, hence, get cancelled out when computing $\alpha$. Therefore, the calculation of $\alpha$ is unbiased.
\subsubsection{Method 2 - geometric method for scalar MF estimation }
\label{sec:method2}
The geometric estimation of MFs is carried out by first identifying the structures from the excursion sets at different field thresholds.
In the following, we briefly outline the method followed by the \texttt{CND$\_$REG2D}~\cite{Ducout:2013} code that we have used, and refer the reader to the original papers for the details.
The excursion sets are obtained as a binary field by identifying pixels where the fields have values below or above the chosen threshold $\nu$. The algorithm identifies each structure (connected region or hole) by marking boundary pixels as different from the pixels in the inner part of the structures.
The total number of pixels included in each structure will constitute the first MF, area fraction ${V}_{0}$. Next, the
genus, ${V}_{2}$, is obtained by computing the vertices of the pixel grid at the boundaries of the structures. It uses the Gauss-Bonnet theorem, which relates the genus to the integration of the curvature along the boundary. As topological properties are invariant under the continuous transformation of the boundary, summing the vertices with appropriate weights will give the genus of the region. The estimation of the next MF, the contour length, ${V}_{1}$, is a bit more involved. The length of the perimeter of the polygon formed by the boundary gives ${V}_{1}$. Due to the pixellated form, the error in the estimation of the length can be large. In order to control the error, interpolation of field values between adjoining boundary pixels is performed so as to smoothen the pixelated boundary and obtain a sufficiently accurate estimate of the length of the polygon.
\section{Analysis pipeline and Gaussian isotropic simulations}
\label{sec:sec4}
We focus our analysis on cooler parts of the sky by applying different brightness temperature cuts to mask the regions above the chosen cutoff temperatures. We also analyze at different angular scales.
For this purpose, we process the map following an appropriate pipeline. For comparison, we also generate 1000 Gaussian isotropic simulations using the Haslam power spectrum. The pre-processing pipeline and the Gaussian isotropic simulations are described below.
\subsection{Masking}
\label{sec:mask}
Since our target region for analysis are the regions away from the Galactic center where the emission is very strong, we mask the map as described below.
\begin{itemize}
\item First, we degrade the Haslam map from $N_{\rm side}$= 512 to 128
since the resolution of processed 408 MHz map is $56^{\prime}$~\cite{Remazeilles:2014mba}. This map has mean value 34.4~K. We rescale each pixel value with the mean value. Then, we apply a Galactic cut ($ \mid b\mid< 10^{\circ}$) to avoid the
contamination from the Galactic plane.
\item We mask the bright Loop-I ring, coming from an old supernovae remnant. The mask region includes $\pm 4^{\circ}$ width cut around a
circle of radius $58^{\circ}$ entered at ($l$,$b$) = ($329^{\circ}$; $17^{\circ}$. 5).
\item Let us denote the brightness temperature cut by $u_c$. We construct five sky masks by applying different choices of $u_c$. Pixels having field values above $u_c$ are set to zero. We carry out the analysis for the values $u_c=22,25, 30, 40, 60$ K. Our results will be presented for the cases $u_c=25$ and 60 K. The effective fractional sky coverages are 0.74 for $u_c= 60$ K, 0.69 for $u_c= 40$ K, 0.56 for $u_c= 30$ K, 0.41 for $u_c= 25$ K and 0.27 for $u_c= 22$ K .
\end{itemize}
To avoid the leakage of power due to sharp cutoff between the
masked and the unmasked regions in the map, we apodize the masks by convolving with a $5^{\circ}$ FWHM Gaussian. Such a smooth Gaussian filter function minimizes the leakage of the signal towards the edges of the unmasked region.
\begin{figure}[t]
\centering
\includegraphics[width=8.1cm,height=4.7cm]{Haslam_fullmap.png}\quad\quad
\includegraphics[scale=0.36]{fsky_uc_v5.png}
\
\\
\vskip .2cm
\includegraphics[width=8.9cm,height=4.8cm]{PatchofSky.png}\quad\quad\quad
\includegraphics[scale=0.6]{Contour.png}
\caption{{\em Top}: The left panel shows the reprocessed version of the all sky 408 MHz Haslam map. The field values are given in kelvin unit and have mean value 34.4~K. The right panel shows the sky-fraction ($f_{sky}$) as a function of different temperature cuts ($u_c$) used in our analysis.
{\em Bottom}: The left panel is the mean-free and normalized ($u/\sigma$) version of the same map after applying the brightness temperature cut $u_c=60$\,K and band-passing with multipole cut $\ell_{c}=30$.
Excursion set boundaries are shown in the right panel for different field thresholds (different colours), corresponding to the cut-out patch on the lower left of the left panel. The boundaries are quite thick due to the choice of large field threshold bins.}
\label{fig:fig1}
\end{figure}
\subsection{Band-passing}
\label{sec:bp}
In order to focus our analysis on specific angular scales of interest, we use a band-pass filter of the following form:
\begin{equation}
f(\ell)=\frac{1}{4}\left\{1+ {\rm tanh}\left(\frac{\ell-\ell_{c}}{\Delta \ell}\right)\right\}\left\{1-\text{tanh}\left(\frac{\ell-180}{\Delta \ell}\right)\right\}.
\end{equation}
This filter cuts off the Fourier amplitudes ($a_{\ell m}$s) below a multipole scale $\ell_c$, and above $\ell=180$. The upper multipole cutoff is in accordance with the $56'$ beam size of the Haslam map. $\Delta\ell$ sets the width of the cutoff region of the filter. We use $\Delta\ell = 10$ for the results presented in this paper. We have checked that the results are robust for a reasonable range of $\Delta\ell$.
We vary $\ell_c$ to study the statistics of the map at different scales.
We have also used other suitable filters such as a cosine filter and our results are found to be robust.
The final maps, which have undergone the aforementioned pre-processing steps, are, then, mean-subtracted and rescaled with the standard deviation. Computations of tensorial and scalar Minkowski functionals are done on these mean-free, unit standard deviation versions of the Haslam map.
The top left panel of figure~\ref{fig:fig1} shows the Haslam map. The top right panel gives the sky-fraction ($f_{sky}$) left for the analysis after the application of various temperature cuts ($u_c$) on the map. The bottom left panel shows the mean-free and normalized ($u/\sigma$) version of the same map obtained after applying temperature cut $u_c=60$\,K, and band-passed with multipole cut $\ell_c=30$. The bottom right panel shows iso-field contours of a slice of the field shown in the lower left of the left panel. Different colours of the contours correspond to different field thresholds ($\nu$). The lines are thick due to the choice of large field threshold bins.
\subsection{Gaussian isotropic simulations}
In order to quantify the non-Gaussianity and anisotropy of the Haslam map, we need to compare it with suitable Gaussian isotropic simulations. For this purpose, we obtain 1000 Gaussian isotropic simulations that are generated by using the full power spectrum of the Haslam map corrected for cut-sky, pixel and beam correction. This input spectrum is made using the publicly available code \texttt{PolSpice} \cite{Polspice,Chon:2004}. A detailed consistency check carried out for these simulations is discussed in appendix~\ref{sec:a1checks}. The pre-processing pipeline discussed in sections \ref{sec:mask} and \ref{sec:bp} is applied to each simulation map so that both simulation and data maps are identically pre-processed. This is necessary to ensure that the comparison of the statistics that we compute from the data and simulation maps makes sense.
\section{Analysis of Gaussianity and SI of Galactic synchrotron emission -- results}
\label{sec:sec5}
This section presents the results obtained from analyzing the Haslam map and its comparison with Gaussian isotropic simulations.
\subsection{Spectra of the Haslam map}
\begin{figure}[t]
\begin{center}
\includegraphics[scale=0.55]{rc_plot_after_tuhin_v3.png}
\end{center}
\caption{{\em Top}: $\sigma$ (left) and $\sigma_1$ (right) of the Haslam map for $u_c=60$ K (red diamond) and 25 K (green circle) as a function of $\ell_c$. Mean and 1$\sigma$ error bars obtained from 1000 Gaussian isotropic simulations are also shown. Since the simulations are obtained using the power spectrum of the Haslam data, $\sigma$ and $\sigma_1$ for the observed data and simulations match within $1\sigma$, as expected.
{\em Bottom}: The left panel shows the correlation length, $r_c\equiv \sigma/\sigma_1$ versus $\ell_c$ for $u_c=60$ K and 25 K. The middle panel shows $r_c$ for $u_c=60$ K fitted with two different
power law functions towards the low and high $\ell_{c}$ regimes, indicating a transition in the nature of the field at the intermediate $\ell_{c}$ scales. The right panel shows $r_{c}$ for $u_c=25$ K fitted by a single function.}
\label{fig:rc}
\end{figure}
We first discuss the spectral parameters $\sigma$ and $\sigma_{1}$, and their ratio $r_{c}\equiv \sigma \slash \sigma_{1}$. Given the mean-free field $u$, $\sigma\equiv\sqrt{\langle u^{2}\rangle}$ and $\sigma_1\equiv\sqrt{\langle |\nabla u|^{2}\rangle}$.
The top panels of figure~\ref{fig:rc}, show $\sigma$ (left) and $\sigma_1$ (right) for varying $\ell_{c}$, for the Haslam map for different values of $u_c$. The mean over 1000 Gaussian simulations is also shown along with the 1$\sigma$ error bars.
We can see that both $\sigma$ and $\sigma_1$ decrease with decrease of $u_{c}$ and towards higher $\ell_{c}$, indicating a drop in the level of fluctuations of the field and its gradient, as we go to lower temperatures as well as smaller scales. Moreover, both these parameters for the Haslam map fall within 1$\sigma$ error bars obtained from Gaussian simulations. This is expected as the simulations are generated from the power spectrum of the Haslam map and validates the correctness of these simulations.
The bottom panels show $r_c$. This quantity gives a measure of the typical size of structures (hot and cold spots) in the field. The left panels shows $r_c$ for both $u_c=60$ and 25 K, so as to enable their visual comparison. We see that higher $u_c$ has slightly larger structures towards lower $\ell_c$.
This indicates that if we include sky regions with higher temperature, then there are larger regions having correlated temperature values. $r_c$ also decreases with increasing $\ell_c$, which is expected due to the subtraction of large scale fluctuations, and the fact that $\sigma$ decreases faster than $\sigma_1$. We have fitted the fall of $r_c$ with respect to $\ell_c$ with power law functions (shown in the middle and right bottom panels of figure~\ref{fig:rc}). For $u_c=60 $ K, we could fit it with two functions towards the low and high $\ell_c$ regimes, indicating a transition in the nature of the field at the intermediate scales. For $u_c=25$, we are able to fit $r_c$ with a single function. This could be a hint to the difference in the nature of the field in the cooler regions of the synchrotron sky (smaller $u_c$), as seen in our further analysis.
\subsection{Skewness and Kurtosis of the Haslam map}
\label{sec:cumulants}
\begin{figure}[t]
\includegraphics[scale=0.68]{Moments_after25Kcorrect_v1.png}
\caption{\small Skewness and kurtosis cumulants (defined in section \ref{sec:ana}) of the Haslam map for the case of temperature cut values $u_{c}=60\,$K (red) and $u_{c}=25\,$K (green), plotted as functions of the multipole cut $\ell_c$. Different line types for each colour represent different values of $s_m$, and the associated sky fraction.}
\label{fig:moments}
\end{figure}
In order to probe the non-Gaussian nature of the Haslam map, we next analyze the skewness, $S_i$, and kurtosis cumulants, $K_i$, defined in eqs.~\ref{eqn:skew} and \ref{eqn:kurt}. Since $\sigma$ varies with $\ell_c$, we interpret the cumulants with the appropriate power of $\sigma$ multiplied to them, i.e., $S_i\sigma$ and $K_i\sigma^2$.
These quantities are the coefficients of the Hermite polynomials in the expressions for the first and second-order non-Gaussian deviations of the MFs, up to numerical factors. Hence, it is meaningful to compare them directly.
To minimize the effects of the mask boundary on the calculation of $S_i\sigma$ and $K_i\sigma^2$, and the scalar and tensorial MFs, we must stay sufficiently far away from the boundary. Upon smoothing the binary mask, pixels near the mask boundaries acquire values between zero and one. A rough estimate shows that a smoothed mask pixel value $>0.89$ roughly corresponds to $>2\theta_s$ distance from the mask boundary, $\theta_s$ being the smoothing scale. We introduce a parameter, $s_m$, whose value is between zero and one, to control how far away a smoothed mask pixel is from the boundary. Pixels for which the smoothed mask has values $> s_m$ are included in the calculations. As $s_m$ increases towards one, the sky fraction will decrease, and hence, the statistical significance of the results will decrease. Therefore, it is best to select an optimum value of $s_m$ such that the numerical error is minimized and the statistical significance is maximized.
Figure~\ref{fig:moments} shows $S_i\sigma$ (left column) and $K_i\sigma^2$ (right column) as functions of the multipole cut $\ell_c$, for $u_c=60$\,K (red lines) and 25\,K (green lines). We show the results for different values of $s_m$. The inset boxes show the zoomed in plots towards higher $\ell_c$ values. For lower $\ell_c$, we see a large variation of the cumulants with $s_m$. Towards higher $\ell_c$, they show approximately convergent behaviour for the larger $s_m$ values, indicating that the effect of the mask boundary is minimized. Therefore, we will interpret the non-Gaussian behaviour of the Haslam map using $s_m= 0.9$, for which the cumulants are shown by dot-dash lines in the plots..
The results for the cumulants are as follows:
\begin{itemize}
\item All four kurtosis cumulants have values whose magnitudes are considerably larger than those of the skewness ones, for both values of $u_c$ and for all $\ell_c$. This corroborates our inference from visual inspection of the probablity distribution functions (PDFs) of the Haslam map shown in figure~\ref{fig:pdf} in appendix \ref{sec:pdf}.
\item $S_i\sigma$ show clear decrease both with decreasing $u_c$ and towards high $\ell_c$. We see that $S_0\sigma$ and $S_1\sigma$ show rough oscillatory behaviour up to intermediate values of $\ell_c$.
Towards high $\ell_c$, all three $S_i\sigma$ decrease monotonically. %
\item All the kurtosis cumulants also decrease from higher to lower values of $u_c$, and at all $\ell_c$.
Towards high $\ell_c$, the magnitudes of all the $K_i\sigma^2$ show mild monotonic decrease, except $K_2\sigma^2$ which appears to saturate at a small but finite value. $K_0\sigma^{2}$ and $K_1\sigma^{2}$ also exhibit rough oscillatory behavior similar to skewness parameters.
\end{itemize}
Based on the above points, we conclude that the non-Gaussian nature of the Haslam map at the range of scales probed here is predominantly sourced by kurtosis terms. Moreover, at smaller scales, the field shows convergence towards Gaussian behaviour. However, we note that it is important to probe down to even smaller scales, which is not feasible with the Haslam map. The next subsection will discuss the level of non-Gaussianity measured using the Minkowski functionals.
Although beyond the scope of this paper, from the behaviour of the skewness and kurtosis parameters as functions of $\ell_c$, it will be interesting to investigate further whether one can identify physically interesting scales associated with the distribution of cosmic rays and free electrons, and the properties of the Galactic magnetic field.
\subsection{Scalar Minkowski functionals for the Haslam map}
\label{sec:mt}
We compute the scalar MFs using methods 1 and 2 described in sections~\ref{sec:method1} and \ref{sec:method2}, for the Haslam and the simulated Gaussian isotropic maps. We refer to the results of these calculations as `exact numerical results'. We use the threshold range $-4\le \nu\le 4$ with a bin size of $\Delta\nu=0.5$. We show our results for the mask boundary threshold value $s_m=0.9$, as discussed in section~\ref{sec:cumulants}.
The results for $u_c=60$ K and 25 K, for the intermediate scale $\ell_c=50$ are shown in figure~\ref{fig:scalarsMFs}. The deviations of $V_k^{\rm Haslam}$ from the Gaussian mean values are easily discerned by eye.
\begin{figure}
\includegraphics[scale=0.69]{ScalarMF_wtcrrctd_v1.png}
\caption{\small Scalar MFs of the Haslam map for $u_c=60$ K (red diamonds) and $u_c=25$ K (green circles), for $\ell_{c}=50$. The ensemble mean and 1$\sigma$ width obtained from 1000 simulated maps are also plotted to show the deviation.}
\label{fig:scalarsMFs}
\end{figure}
In order to quantify the difference of the MFs between the Haslam map and the Gaussian simulations, we define
\begin{equation}
\Delta V_k \equiv V_k^{\rm Haslam} - V^{\rm (G)}_k,
\end{equation}
where the superscript `Haslam' refers to the Haslam map and `G' stands for Gaussian simulation. At each $k$, we compute $\Delta V_k$, normalized by the amplitude of $V_k^{\rm (G)}(\nu)$ (indicated by superscript `max'), for each Gaussian isotropic realization.
\begin{figure}
\includegraphics[height=7.2in,width=6.5in]{ScalarDelta_wtcrrctd_v2.png}
\caption{\small The deviations, $\Delta V_{k}/V^{\rm {G,max}}_k$, of the three MFs for Haslam data from Gaussian expectation for $u_c=60$\,K (red solid lines) and $u_c=25$\,K (green solid lines) are shown for $\ell_{c}=50,70,90$. We use $s_m =0.9$ for these results. The black lines correspond to the results obtained using perturbative expansion of MFs with only first-order terms (dotted lines), only second-order terms (dashed lines), and the sum of first- and second-order (solid lines). The dashed and solid black lines almost overlap since the contributions from the first-order terms are small.}
\label{fig:scalars}
\end{figure}
Figure~\ref{fig:scalars} shows the ensemble mean and 1$\sigma$ error bars of the normalized $\Delta V_k$ for $u_{c}=60$ K (red solid lines) and $u_{c}=25$ K (green solid lines), and for $\ell_{c}=50, 70, 90$ (top to bottom rows). For $u_c=60$ K, the error bars are relatively smaller and, hence, hard to see by eye. All the plots shown in figure~\ref{fig:scalars} are obtained using method 1. We obtain almost identical results from calculations using method 2.
We summarize our findings from the exact numerical calculations as follows:
\begin{itemize}
\item The deviations have a characteristic shape as functions of the threshold. The overall amplitude of the deviations decreases as $u_c$ is decreased, while the shape is approximately maintained. This indicates that masking out very high-intensity regions, which correspond to values on the positive tail of the PDF of the field, makes it tend towards Gaussian nature. The nature of the non-Gaussian deviation of the field approximately remains the same even as we mask more high-temperature regions (decreasing $u_c$), and as we probe down to smaller angular scales (increasing $\ell_c$).
\item As we increase $\ell_c$, the number of structures (equivalently, fluctuations of the field per unit area on the sphere) increases. As a consequence, the error bars on $\Delta V_{k}$ decrease with increasing $\ell_c$. Therefore, even though the amplitude of the deviations decrease with increasing $\ell_c$, the statistical significance of the deviations does not decrease proportionately and can remain high. This is particularly evident for the case of $u_c=60$. At each $\ell_c$ and each $\nu$, the error bar for $u_c=25$ is generally higher than $60$ because of lower sky fraction.
\item Lastly, we compare $\Delta V_k$ obtained from method 1 and 2. As mentioned earlier, method 1 contains small numerical inaccuracies due to the discretization of the $\delta$ function. However, when subtracting between the MFs obtained from the Haslam map and the Gaussian simulations, these numerical errors will mostly cancel out. A small part can still remain because the Haslam map is non-Gaussian, particularly for higher $u_c$ and lower $\ell_c$ values. In comparison, method 2 is free of these errors. We obtain very similar results for $\Delta V_k$ from method 2, indicating that the residual numerical errors for method 1 are insignificant and can be ignored.
Another important point to mention is that we obtain marginally higher error bars from method 1, compared to method 2. The reason for this is the shot noise arising from the discrete harmonic transform associated with calculating field derivatives.
\end{itemize}
Next, we discuss the results obtained using the perturbative formulae of MFs given in section \ref{sec:ana}, and compare with the exact numerical results.
To do so, we define
\begin{eqnarray}
\Delta V_k^{(1),\rm pert} &=& A_k v_k^{(1)}, \\
\Delta V_k^{(2),\rm pert} &=& A_k\,v_k^{(2)}, \\
\Delta V_k^{\rm total, pert} &=& A_k\,\left( v_k^{(1)} + v_k^{(2)}\right),
\end{eqnarray}
where $k=0,1,2$, and $A_k$ is the amplitude of the analytic expressions for MFs for the Gaussian case. The superscript `pert' refers to the perturbative expansion described in section~\ref{sec:ana}. For consistency with the exact numerical case, we normalize them by $V_k^{\rm{G,max}}$ (which is not always the same as $A_k$).
In figure~\ref{fig:scalars}, the first-order results are shown by dotted black lines, second-order by dashed black lines, and the total by solid black lines.
First, for $u_c=60$\,K (top panels accompanying the red plots), we can see that
the first-order deviations for which skewness cumulants contribute are much smaller than the second-order deviations for which kurtosis cumulants contribute. As a consequence, the plots for the second-order and total deviations nearly overlap.
Secondly, the total deviations upto second-order overestimate the amplitude of the deviations of all three MFs by over a factor of two, but the shape roughly agrees (as indicated by the location of zeros, peaks and troughs). This remains so even at high $\ell_c$. Therefore, we conclude that for $u_c=60$\,K, the Haslam field is highly non-Gaussian even at the smallest scales probed here. Hence, it is not meaningful to consider it as a Gaussian field plus a small non-Gaussian component.
In the lower panels of figure~\ref{fig:scalars}, we show the case of $u_c=25$\ K. We again
find that
the first-order deviations are smaller than the second-order for all MFs and all $\ell_c$ values considered here. So the main contribution to the non-Gaussian behaviour of the relatively cooler signals of the Haslam map comes from the four kurtosis cumulants. Secondly, we find very good agreement between the deviations of the MFs given by the analytic and exact numerical calculations. The amplitude of the non-Gaussian deviations decreases as $\ell_c$ increases, indicating that the field approaches Gaussian behaviour at smaller scales.
Therefore, we conclude that the cooler regions of the Haslam map can be well approximated as a mildly non-Gaussian field. The nature of the mild non-Gaussianity, however, does not significantly vary with angular scale, as implied by the shape of the deviations of the MFs. Our analysis with other temperature cuts for the cooler regions, such as $u_c=22$ K and $u_c=30$ K, shows trends similar to what is observed with $u_c=25$ K. We are planning to do a detailed study on these regions, in our future works, to understand more on the nature of synchrotron non-Gaussianity.
A visual comparison of figure~\ref{fig:scalars} with the plots in figure~\ref{fig:comparefnlgnl} shows that the non-Gaussian nature of the Haslam map is similar to the local type $g_{\rm NL}$ non-Gaussianity of primordial inflationary fluctuations. This indicates the presence of an approximate parity symmetry in the fluctuations of synchrotron radiation.
\subsubsection{Quantifying the level of non-Gaussianity}
\label{sec:D}
To quantify the statistical significance of the non-Gaussian deviations for $V_k$, we compute the difference between each statistic computed for Haslam data and its mean value obtained from Gaussian isotropic simulations in units of the standard deviation. This is encapsulated by $\chi^{2}$ which is defined, at each threshold $\nu$, as follows,
\begin{equation}
\chi^2_{V_k}(\nu) = \frac{\left(V_k^{\rm Haslam}(\nu)-\overline{V}_k^{\rm (G)}(\nu)\right)^{2}}{\sigma^{2}_{V_k^{\rm (G)}}(\nu)}
\end{equation}
We compute $\chi^2_{V_k}$ for all the values of $u_c$ and $\ell_c$ that we consider here. We will not show $\chi^2$ for $u_c=60$ K since there is a high level of non-Gaussianity, and it is not meaningful to compute deviations from Gaussian expectation.
\begin{figure}
\begin{center}
\includegraphics[scale=0.62]{ChiSqr_wtcrrctd_v7.png}
\end{center}
\caption{\small $\chi^2_{V_k}$ is shown as a function of threshold for each scalar MFs for $u_c=25$ K, for different $\ell_c$. It is seen that $\chi^2_{V_k}$ gets close to 3-$\sigma$ for all thresholds as we increase $\ell_c$. This indicates that the level of non-Gaussianity decreases as we remove more bright regions as well as large-scale structures in the Haslam map.}
\label{fig:ChiSqr}
\end{figure}
For each of the three scalar MFs, $\chi^2$ for the case of $u_c=25$ K are shown in figure \ref{fig:ChiSqr}. The line for $\chi^2=9$ which corresponds to $3\sigma$ is shown by the black dotted line for reference. Note that except for the case of $V_0$, the $y$-axis scales for the top panels showing $\ell_c=50$ are different from the lower panels.
We observe that for all three MFs, $\chi^2$ values decrease towards $\ell_c=120$. The rate of decrease, however, varies.
For $V_0$, the $\chi^2$ values are higher than 9 for most threshold values, at all $\ell_c$. For both $V_1$ and $V_2$, the values of $\chi^2$ decrease as $\ell_c$ increases, and for $\ell_c=120$, are smaller than 3$\sigma$ for all threshold values (except at $\nu=-1.5$ where it is higher than 9 for $V_2$).
We get the value of $\chi^2$ for $V_0$ averaged over all threshold values for $\ell_c=120$ is 11.08, corresponding to statistical significance of 3.3$\sigma$. Therefore, from the behaviour of $V_0$, we conclude that the Haslam map for $u_c=25$ K is mildly non-Gaussian with statistical significance 3.3$\sigma$ at the smallest scale probed in this work. The nature of the non-Gaussianity is of the kurtosis type given by the cumulant $K_0$ since the non-Gaussian deviation of $V_0$ is determined by $K_0$.
\subsection{Statistical isotropy of the Haslam map}
\label{sec:iso}
Next, we discuss the results for $\mathcal{W}_1$. We again quantify the difference between the Haslam map and the Gaussian simulations as:
\begin{eqnarray}
\Delta\mathcal{W}_1 &\equiv& \mathcal{W}_1^{\rm Haslam} - \mathcal{W}_1^{\rm (G)}, \\
\Delta\alpha &\equiv& \alpha^{\rm Haslam} - \alpha^{\rm (G)},
\end{eqnarray}
where $\mathcal{W}_1^{\rm (G)}$ and $\alpha^{\rm (G)}$ are the values obtained from the Gaussian simulations, while the superscipt `Haslam' refers to the values for the Haslam map. As in the previous case, the deviations $\Delta\mathcal{W}_1$ and $\Delta\alpha$ are normalized with $\mathcal{W}_1^{\rm G,max}$ and $\alpha^{\rm G,max}$, respectively. We compute them for each Gaussian isotropic simulation.
The top row of figure~\ref{fig:TMFs} shows the diagonal elements of $\mathcal{W}_1$ (left and middle) and $\alpha$ for $u_c=60$ and $25$ K, for $\ell_c=50$ K. The colour coding is the same as in figure~\ref{fig:scalars}. The mean values obtained from the 1000 Gaussian isotropic simulations corresponding to each $u_c$ are shown by the solid lines, along with the 1$\sigma$ regions.
The ensemble mean of the diagonal elements of $\Delta\mathcal{W}_1$, along with 1$\sigma$ error bars are shown in columns one and two of the lower panels,
for the same values of $u_{c}$ and for $\ell_{c}=50, 70, 90$. The physical information that can be deciphered from the elements of $\Delta\mathcal{W}_1$ is similar, up to statistical fluctuations, as $\Delta V_1$, and we find that the behaviour is the same, as expected.
Ensemble mean and $1\sigma$ error bars of $\Delta\alpha$ are shown in the third column of figure~\ref{fig:TMFs} for the same values of $u_c$ and $\ell_c$. We observe that $\Delta\alpha$ is smaller for smaller $u_c$ implying that the field becomes more isotropic when the warmer regions are excluded. This corroborates what we infer from visual inspection that high-intensity regions
have large scale correlations that appear to be direction-dependent.
\begin{figure}{t}
\begin{center}
\includegraphics[scale=0.655]{Tensor_wtcrrctd_v2.png}
\end{center}
\caption{\small The first row shows the two diagonal components of tensor MF, $\mathcal{W}_{1}$ and the anisotropy parameter, $\alpha$ for two temperature thresholds $u_c=60$ K and $u_c=25$ K (red diamonds and green circles, respectively) for $\ell_{c}=50$. The ensemble mean and $1\sigma$ width from 1000 simulated maps are also plotted to show the deviation. Note that, for $\alpha$, the threshold range is (-3:3). The remaining rows represent the ensemble mean and $1\sigma$ width of the deviations, $\Delta \mathcal{W}_{1}$ and $\Delta \alpha$ with respective normalizations, for $u_c=60$\,K (red solid lines) and $u_c=25$\,K (green solid lines), for $\ell_{c}=50,70,90$.
}
\label{fig:TMFs}
\end{figure}
Next, to proceed with the quantification of the statistical significance of any deviation from SI of the Haslam map, we take into consideration the fact that the $\alpha$ statistic follows the Beta probability distribution given by
\begin{equation}
P(\alpha)= \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}\alpha^{a-1} (1-\alpha)^{b-1}
\end{equation}
where $a > 0,\ b> 0$ are parameters that depend on the cosmological model~\cite{Prava:2021}.
Due to this reason,
for accurate quantification of the statistical significance of deviation from SI, we use the median value of $\alpha$, denoted by $\widetilde\alpha^{\,\rm (G)}$ obtained from the 1000 simulations along with the 95\% confidence interval. We find that the mean and median values differ by less than 1\% at all threshold values. Let us denote the 95\% confidence interval about the median by $[\delta_1, \delta_2]$. For each threshold, we determine $\delta_1$ and $\delta_2$ such that they satisfy
\begin{equation}
\int_{\widetilde\alpha^{\,\rm (G)}-\delta_1}^{\widetilde\alpha^{\,\rm (G)}} {\rm d\alpha}\,P(\alpha)= \int_{\widetilde\alpha^{\,\rm (G)}}^{\widetilde\alpha^{\,\rm (G)}+\delta_2} {\rm d\alpha}\,P(\alpha)=0.475.
\end{equation}
Let $\Delta\widetilde\alpha \equiv \alpha^{\rm Haslam} - \widetilde\alpha^{\rm (G)}$. Then, to quantify the statistical significance of $\Delta\widetilde\alpha $, we use
the variable $\widetilde\chi$ which is defined as follows:
{\renewcommand{\arraystretch}{1.5}
\begin{equation}
\widetilde \chi = \left\{
\begin{array}{c}
\frac{\Delta\widetilde\alpha}{\delta_1}, \quad {\rm if} \ \Delta\widetilde\alpha<0, \\
\frac{ \Delta\widetilde\alpha}{\delta_2}, \quad {\rm if} \ \Delta\widetilde\alpha>0.
\end{array} \right.
\end{equation}
$\widetilde\chi$ reduces to the square root of the standard chi-squared statistic for the Gaussian case. $|\widetilde\chi|>1$ implies $\alpha^{\rm Haslam}$ is outside the 95\% confidence interval and, hence, exhibits statistically significant deviation from the simulations. The sign of $\widetilde\chi$ contains useful information \textendash~if it is negative, it means more anisotropic, while positive values means more isotropic than the median value.
$\alpha$ at neighbouring thresholds are uncorrelated if the threshold bin size is sufficiently large, and we have seen that our choice of $\Delta\nu=0.5$ is large enough.
\begin{figure}{H}
\begin{center}
\includegraphics[scale=0.6]{ChiSqr_alpha_median_2sigma_v2.png}
\end{center}
\caption{\small $\widetilde\chi$ values of $\Delta\widetilde{\alpha}$ at each threshold values for $u_c=60$\,K (top panel) and $u_c=25$\,K (bottom panel), and for $\ell_c=50,90,120$. Lines corresponding to $|\widetilde\chi| = 1$ (95\% confidence interval) are marked for reference.
}
\label{fig:ChiSqr_alpha}
\end{figure}
Figure~\ref{fig:ChiSqr_alpha} shows $\widetilde\chi$ versus threshold values, for different $u_c$ and $\ell_c$. Lines corresponding to $|\widetilde\chi| = 1$ are marked for reference.
For $u_c=60$ K, we find that $\widetilde\chi$ is negative for almost all threshold values for all $\ell_c$, which is due to $\alpha^{\rm Haslam}$ being smaller than $\widetilde\alpha^{\rm (G)}$. This implies that the Haslam map is genuinely anisotropic in comparison to the isotropic simulations. Further, we observe that $\widetilde\chi$ becomes smaller as $\ell_c$ increases, indicating that the statistical significance of the anisotropy decreases at smaller angular scales. Hence, the smaller scale fluctuations of the field tend to follow isotropic distribution.
For the case of $u_c=25$K, we see that $|\widetilde\chi| \le 1$ for most thresholds and the values fluctuate between positive and negative values for all $\ell_c$.
Therefore, after excluding the warmer regions of the field (decreasing $u_c$), we find that the Haslam map exhibits isotropic behaviour even at relatively large scales.
\section{Summary of results and their implications}
\label{sec:sec6}
Using scalar Minkowski functionals and Minkowski tensors, we have carried out careful investigation of the statistical properties of one of the major foreground components, namely the Galactic synchrotron given by the full sky 408 MHz Haslam map.
The results are summarized as follows.
\begin{itemize}
\item Firstly, we find that the overall level of non-Gaussian deviations does decrease as more high emission regions are masked, and as we go down to smaller scales. This is not a new result and corroborates findings in earlier works.
\item Our analysis reveals that the leading source of non-Gaussianity of the Haslam map, at all scales, arises from kurtosis terms, with skewness being sub-dominant. We demonstrate that in the cooler regions of the Haslam map, the non-Gaussian deviations of MFs agree very well with analytic perturbative expressions keeping up to kurtosis terms or second-order in the standard deviation of the field.
\item The level of non-Gaussianity at the smallest angular scales of $\sim 1.5^{\circ}$ corresponding to $\ell_c=120$ probed by the Haslam map has a statistical significance of 3.3$\sigma$. This is determined by the area fraction, $V_0$, which has dependence only on one kurtosis cumulant, $K_0$. Hence, we conclude that the assumption of Gaussian fluctuations in the synchrotron simulations is not appropriate at this scale. It is therefore important to analyse higher resolution synchrotron maps to determine the validity of the Gaussian approximation at scales smaller than the Haslam scale.
\item Lastly, we test the statistical isotropy of the Haslam map and find that it becomes increasingly more isotropic in the cooler regions of the map as well as at smaller angular scales. This implies that the usual assumption of statistical isotropy at small scales in component separation methods is supported by the properties of the Haslam map.
\end{itemize}
It is interesting to note that the shape of non-Gaussian deviations of the MFs for the Haslam map is reminiscent of curvaton models of inflation where the leading contribution for non-Gaussianity comes from terms containing cubic self-coupling of perturbations with coupling parameter $g_{\rm NL}$ (see for example,~\cite{Enqvist:2008}). As a consequence, we can expect that any residual Galactic synchrotron contamination in the CMB will predominantly bias constraints on $g_{\rm NL}$. Our results indicate that it may be possible to model the Galactic synchrotron fluctuations in the cooler regions, along the lines of inflationary perturbations, as an effective field that can be expanded as a Gaussian component plus a small perturbation of the type $\delta I(\vec x) \simeq \delta I^{\rm (G)}(\vec x)+g_{\rm NL}\left(\delta I^{\rm (G)}(\vec x)\right)^3$. Here, `G' stands for Gaussian component.
We expect that $g_{\rm NL}$ can be related to small scale fluctuations of the Galactic magnetic field and the distribution of relativistic cosmic ray electron and, hence, will be useful in constraining them. We will address this issue in the near future.
Our results also imply that any residual synchrotron component that contaminates the CMB will most likely not be captured by estimators of non-Gaussianity such as the bispectrum. Instead, it can be revealed by trispectrum or real space statistics such as MFs. Therefore, it is necessary to analyze foregrounds using a multitude of complementary statistics to uncover their true statistical nature.
Further, it is important to probe non-Gaussianity and statistical isotropy of foreground fields at scales smaller than the resolution of the Haslam map. It is also important to probe different Galactic components at frequencies ranging from radio to infra-red, such as done recently by Coulton \& Spergel~\cite{Coulton:2019bnz} using the bispectrum. We plan to carry out a detailed investigation of the non-Gaussian nature and SI of different foreground components at different frequencies relevant for the CMB, EoR and line intensity mappings using Minkowski tensors and trispectrum.
\acknowledgments
{We acknowledge the use of the \texttt{Nova} cluster at the Indian Institute of Astrophysics, Bangalore.
We have used \texttt{HEALPIX}~\cite{Gorski:2005,Healpix} and \texttt{Polspice}~\cite{Polspice,Chon:2004} packages to produce the results in this paper. The plots in this work are generated using \texttt{Matplotlib} library~\cite{Hunter:2007}. We thank A. Ducout and D. Pogosyan for giving us their code for the calculation of scalar Minkowski functionals. We would like to thank T. Matsubara for useful communication. F.R. acknowledges support from the Department of Atomic Energy, Government of India, for visiting NISER, Bhubaneshwar, where a part of this work was carried out. F.R. would like to thank P. Goyal for helping out with the testing and analysis of Minkowski functionals. P.C. would like to thank K.~P.~Yogendran for useful discussion on the non-Gaussian nature of random fields. The work of P.C is supported by the Science and Engineering Research Board of the Department of Science and Technology, India, under the \texttt{MATRICS} scheme, bearing project reference no \texttt{MTR/2018/000896}. TG acknowledges support from the Science and Engineering Research Board of the Department of Science and Technology, Govt. of India, grant number \texttt{SERB/ECR/2018/000826}. We thank the anonymous referee for the helpful comments and suggestions.}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,467 |
I ghiacciai delle Alpi sono le formazioni che interessano la catena montuosa delle Alpi. Le Alpi, per la loro collocazione nella zona temperata dell'emisfero terrestre e per la loro altezza presentano molti ghiacciai, situati principalmente in Italia, Svizzera, Francia e Austria.
Descrizione
Generalmente sono di tipo alpino, ovvero con un bacino collettore ed una lingua glaciale che scende verso valle. Nei casi dei ghiacciai più piccoli sono di forma circolare o semicircolare senza lingua glaciale evidente. Sono talvolta molto grandi sia per volume che per estensione. Altre volte sono di dimensioni molto più ridotte. I ghiacciai si trovano a ridosso delle montagne che superano i 4000 metri, ma si trovano addossati anche alle montagne che superano i 3.000 metri. Alcuni nevai perenni si trovano a quote inferiori.
Quelli più grandi sono collocati nei grandi massicci alpini: nel massiccio del Monte Bianco, nel massiccio del Monte Rosa, nel massiccio del Gran Paradiso, nelle Alpi Bernesi, nel massiccio del Bernina. Per la maggiore altitudine delle montagne i ghiacciai sono più presenti nelle Alpi Occidentali e nelle Alpi Centrali; nelle Alpi Orientali se ne trovano, ma di minore entità. Il ghiacciaio più grande delle Alpi è il ghiacciaio dell'Aletsch nelle Alpi Bernesi. Tre piccoli ghiacciai sono situati nel massiccio dello Zugspitze, nelle Alpi Bavaresi.
In rapporto ai ghiacciai di tutto il mondo i ghiacciai delle Alpi coprono meno dello 0,02%, ma rivestono un'importanza particolare perché qui sono nati i primi studi di glaciologia. Nel 1989 sono stati censiti sulle Alpi 5.154 ghiacciai e per una superficie interessata di circa 3.000 km². Dopo la fine della piccola era glaciale, dal 1850 ad oggi i ghiacciai delle Alpi si sono fortemente ritirati.
Italia
:Categoria:Ghiacciai d'Italia
Francia
:Categoria:Ghiacciai della Francia
Svizzera
:Categoria:Ghiacciai della Svizzera
Austria
:Categoria:Ghiacciai dell'Austria
Galleria d'immagini
Note | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,922 |
Selected Reference and Reading Materials compiled by Dan Villanueva
Total records: 676 | Select no. of records per page: 10 | 20 | 30 | 50 | 100 | Show all | Search
Select a Page: << Previous 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 Next >>
276 [ Page 41 of 68, No. 1 ]
Armand Fouejieu and Scott Roger
l'Université d'Orléans and International Monetary Fund
Inflation Targeting and Country Risk: an Empirical Investigation
Summary /
The sovereign debt crisis in Europe has highlighted the role of country risk premia as a link between countries' fiscal and external balances, financial conditions and monetary policy. The purpose of this paper is to estimate how adoption of inflation targeting (IT) affects spreads. It is hypothesized that country risk premia for IT countries (especially among emerging market economies) may be lower than for other countries owing to greater policy predictability and more stable long-term inflation. The findings suggest that IT reduces the risk premium, both through adoption of the IT regime, and through the observed track record in stabilizing inflation.
Inflation targeting, risk premium, external debt
http://www.imf.org/external/pubs/ft/wp/2013/wp1321.pdf
Pelin Ilbas, Øistein Røisland, and Tommy Sveen
National Bank of Belgium, Norges Bank, BI Norwegian Business School
Robustifying optimal monetary policy using simple rules as cross-checks
There are two main approaches to modelling monetary policy; simple instrument rules and optimal policy. We propose an alternative that combines the two by extending the loss function with a term penalizing deviations from a simple rule. We analyze the properties of the modified loss function by considering three different models for the US economy. The choice of the weight on the simple rule determines the trade-off between optimality and robustness. We show that by placing some weight on a simple Taylor-type rule in the loss function, one can prevent disastrous outcomes if the model is not a correct representation of the underlying economy.
Model uncertainty, optimal control, simple rules
http://www.norges-bank.no/pages/92245/Norges_Bank_Working_Paper_2012_22.pdf
Abdul Abiad, John Bluedorn, Jaime Guajardo, and Petia Topalova
Research Department, IMF
The Rising Resilience of Emerging Market and Developing Economies
Economic performance in many emerging market and developing economies (EMDEs) improved substantially over the past twenty years. The past decade was particularly good—for the first time EMDEs spent more time in expansion and had smaller downturns than advanced economies. In this paper we document the history of EMDEs' resilience over the past sixty years, and investigate what factors have been associated with it. We find that their improved performance in recent years is accounted for by both good policies and a lower incidence of external and domestic shocks—better policies account for about three-fifths of their improved resilience, while less frequent shocks account for the remainder.
Emerging markets, low-income countries, developing countries, growth, development, expansion, recovery
http://www.imf.org/external/pubs/ft/wp/2012/wp12300.pdf
The Philippines is included in this study.
Independent Evaluation Office
International Reserves: IMF Concerns and Country Perspectives
This evaluation focuses on two aspects of the IMF's concerns and advice related to international reserves. First, it examines the origin, rationale, and robustness of the IMF's concerns about the effects of excessive reserve accumulation on the stability of the international monetary system. Second, it assesses the conceptual underpinnings and quality of the advice on reserve adequacy in the context of bilateral surveillance. In 2009, IMF Management and some senior staff began to emphasize the potential for large reserve accumulation to threaten the stability of the international monetary system. The evaluation argues that the focus on reserve accumulation as a risk for the international monetary system was not helpful in that it stressed the symptom of problems rather than the underlying causes, and it did not appear to be different from the longer-standing concerns about risks from global imbalances. Many country officials also felt that the IMF should have placed greater emphasis on other developments relating to the evolution and stability of the international monetary system—in particular the causes and consequences of fluctuations of global liquidity and international capital flows—that they considered to be of more pressing concern than reserves. The evaluation found a broadly held view that Management's emphasis on excessive reserve accumulation was a response to frustration among some member countries with the IMF's inability to achieve exchange rate adjustments in Asian countries with persistently large current account surpluses. In parallel with the aforementioned concerns about excessive reserve accumulation, IMF staff developed a new indicator to assess reserve adequacy in emerging-market economies. The new indicator defined upper and lower bounds for precautionary reserves. A number of country officials became worried that its use would engender pressures on countries to reduce their reserves at a time of heightened uncertainty in the global economy. With respect to reserve adequacy assessments in the context of bilateral surveillance, the evaluation centered on a sample of 43 economies that had accumulated the bulk of global reserves during the 2000–11 period. The country sample reflects the evaluation's focus on the possible implications of excess reserves. The evaluation concludes that the IMF's assessments and discussions of international reserves were often pro forma, emphasizing a few traditional indicators and insufficiently incorporating country-specific circumstances. It also identifies cases where the Fund's analysis and advice could have been improved, notably by embedding the assessment of reserve adequacy in a broader analysis of countries' internal and external stability.
The evaluation recommends that:
(1) Policy initiatives should target distortions and their causes rather than symptoms such as excessive reserves. Discussion of reserve accumulation in the multilateral context should be imbedded in a comprehensive treatment of threats to global financial stability, one that is informed by developments in global liquidity and financial markets; (2) Policy initiatives that are meant to deal with systemic externalities must take into account the relative size of countries' contributions to the externality; (3) Reserve adequacy indicators should be applied flexibly and reflect country-specific circumstances; and (4) The multiple tradeoffs involved in decisions on reserve accumulation and reserve adequacy at the country level need to be recognized, and advice on reserves should be integrated with advice in related policy areas. Advice should not be directed only to emerging markets but, when necessary, take into account the concerns in advanced economies that have arisen since the financial crisis.
International reserves; reserve adequacy assessments
http://www.ieo-imf.org/ieo/files/completedevaluations/IR_Main_Report.pdf
Medina, Leandro
Middle East and Central Asia Department, IMF
Spring Forward or Fall Back? The Post-Crisis Recovery of Firms
This paper studies corporate performance in the aftermath of the global crisis by examining 6,581 manufacturing firms in 48 developed and developing countries in 2010, identifying factors of resilience as well as vulnerability. Based on a cross-sectional analysis, the results show that pre-crisis leverage and short-term debt have had negative effects on the speed of the recovery, while asset tangibility has had positive effects. The negative effect of leverage is non-linear, being particularly strong in firms with high pre-crisis leverage. Furthermore, the effects are different for advanced and emerging market economies. The paper also shows that the macroeconomic framework critically matters for firm growth. In particular, in countries that have allowed the exchange rate to depreciate, firms have had a faster recovery in sectors highly dependent on trade.
There are 17 Philippine firms included in this empirical study.
Andrew G. Berg and Jonathan D. Ostry
Inequality and Unsustainable Growth: Two Sides of the Same Coin?
The relationship between income inequality and economic growth is complex. Some inequality is integral to the effective functioning of a market economy and the incentives needed for investment and growth. But inequality can also be destructive to growth, for example, by amplifying the risk of crisis or making it difficult for the poor to invest in education. The evidence has also been mixed: some find that average growth over long periods of time is higher with more initial equality; others find that an increase in equality today tends to lower growth in the near term. The empirical literature on growth and inequality, however, has missed a key feature of the growth process in developing countries: namely, its lack of persistence. Per capita incomes do not typically grow steadily for decades. Rather, periods of rapid growth are punctuated by collapses and sometimes stagnation—the hills, valleys, and plateaus of growth. Relating income distribution to long-run average growth may thus miss the point. The more relevant issue for many countries is: how is income distribution related to these sharp growth breaks?
This note focuses on the duration of growth spells—defined as the interval starting with a growth upbreak and ending with a downbreak—and on the links between duration and various policies and country characteristics, including income distribution. It turns out that many of even the poorest countries have succeeded in initiating growth at high rates for a few years. What is rarer—and what separates growth miracles from laggards—is the ability to sustain growth. The question then becomes: what determines the length of growth spells, and what is the role of income inequality in duration?
We find that longer growth spells are robustly associated with more equality in the income distribution. For example, closing, say, half the inequality gap between Latin America and emerging Asia would, according to our central estimates, more than double the expected duration of a growth spell. Inequality typically changes only slowly, but a number of countries in our sample have experienced improvements in income distribution of this magnitude in the course of a growth spell. Inequality still matters, moreover, even when other determinants of growth duration—external shocks, initial income, institutional quality, openness to trade, and macroeconomic stability—are taken into account.
A key implication of these results is that it is difficult to separate analyses of growth and income distribution. The immediate role for policy, however, is less clear. Increased inequality may shorten growth duration, but poorly designed efforts to lower inequality could grossly distort incentives and thereby undermine growth, hurting even the poor. There nevertheless may be some "win-win" policies, such as better-targeted subsidies, improvements in economic opportunities for the poor, and active labor market policies that promote employment. When there are trade-offs between potential short-run effects of policies on growth and income distribution, the evidence presented in this note is not decisive. But the analysis below does perhaps tilt the balance towards the notion that attention to inequality can bring significant longer-run benefits for growth. Over longer horizons, reduced inequality and sustained growth may thus be two sides of the same coin.
Income distribution; sustainable growth.
http://www.imf.org/external/pubs/ft/sdn/2011/sdn1108.pdf
The authors thank Olivier Blanchard and other IMF colleagues for useful discussions on this IMF Staff Discussion Note.
Jonathan D. Ostry, Atish R. Ghosh, Karl Habermeier, Luc Laeven, Marcos Chamon, Mahvash S. Qureshi, and Annamaria Kokenyne
Managing Capital Inflows: What Tools to Use?
Emerging market economies are facing increasing challenges in managing the current wave of capital inflows. In an earlier note (Ostry et al., 2010), we laid out a set of circumstances under which capital controls could usefully form part of the policy response to inflow surges. For countries whose currencies were on the strong side, where reserves were adequate, where overheating concerns precluded easier monetary policy, and where the fiscal balance was consistent with macroeconomic and public debt considerations, capital controls were a useful part of the policy toolkit to address inflow surges. Beyond macroeconomic considerations, capital controls could also help to address financial-stability concerns when prudential tools were insufficient or could not be made effective in a timely manner. We also stressed that the use of capital controls needs to take account of multilateral considerations, as well as their costs and the mixed evidence on their effectiveness in restraining aggregate flows.
This note elaborates on how the macro and financial-stability rationales for capital controls fit together; how prudential and capital control measures should be deployed against various risks that inflow surges may bring; and specifically, how capital controls should be designed to best meet the goals of efficiency and effectiveness. Four broad conclusions emerge. First, capital controls may be useful in addressing both macroeconomic and financial stability concerns in the face of inflow surges, but before imposing capital controls, countries need first to exhaust their macroeconomic-cum-exchange-rate policy options. The macro policy response needs to have primacy both because of its importance in helping to abate the inflow surge, and because it ensures that countries act in a multilaterally-consistent manner and do not impose controls merely to avoid necessary external and macro-policy adjustment. Second, while prudential regulations and capital controls can help reduce the buildup of vulnerabilities on domestic balance sheets, they both inevitably create distortions—reducing some "good" financial flows alongside "bad" ones—and may be circumvented. Thus, there is no unambiguous welfare ranking of policy instruments (though non-discriminatory prudential measures are always appropriate), and a pragmatic approach taking account of the economy's most pertinent risks and distortions needs to be adopted. Third, measures need to be targeted to the risks at hand. When inflows are intermediated through the regulated financial system, prudential regulation will be the main instrument. When inflows bypass regulated markets and institutions, capital controls may be the best option if the perimeter of regulation cannot be widened sufficiently quickly or effectively. Fourth, the design of capital controls needs to be tailored to country circumstances. Where inflows raise macro concerns, controls will need to be broad, usually price-based, and temporary (though institutional arrangements to implement controls could be maintained). To address financial-stability concerns, controls could be targeted on the riskiest flows, might include administrative measures, and could be used even against more persistent inflows.
Capital inflows, capital controls, prudential tools
This research paper was approved by Olivier Blanchard.
Jain-Chandra, Sonali ; Unsal, D. Filiz
Asia and Pacific Department, IMF
The Effectiveness of Monetary Policy Transmission Under Capital Inflows: Evidence from Asia
The effectiveness of the monetary policy transmission mechanism in open economies could be impaired if interest rates are driven primarily by global factors, especially during periods of large capital inflows. The main objective of this paper is to assess whether this is true for emerging Asia's economies. Using a dynamic factor model and a structural vector auto-regression model, we show that long-term interest rates in Asia are indeed predominantly driven by global factors. However, monetary policy transmission mechanism remains effective in the region, as it operates predominantly through short-term interest rates. Nevertheless, the monetary transmission mechanism, though effective, is somewhat weaker in Asia during the periods of surges in capital inflows.
Monetary policy transmission, capital flows, dynamic factor model, structural VAR
Giovanni Dell'Ariccia, Deniz Igan, Luc Laeven, and Hui Tong
Policies for Macrofinancial Stability: How to Deal with Credit Booms
Credit booms buttress investment and consumption and can contribute to long-term financial deepening. But they often end up in costly balance sheet dislocations, and, more often than acceptable, in devastating financial crises whose cost can exceed the benefits associated with the boom. These risks have long been recognized. But, until the global financial crisis in 2008, policy paid limited attention to the problem. The crisis—preceded by booms in many of the hardest-hit countries—has led to a more activist stance. Yet, there is little consensus about how and when policy should intervene. This note explores past credit booms with the objective of assessing the effectiveness of macroeconomic and macroprudential policies in reducing the risk of a crisis or, at least, limiting its consequences. It should be recognized at the onset that a more interventionist policy will inevitably imply some trade-offs. No policy tool is a panacea for the ills stemming from credit booms, and any form of intervention will entail costs and distortions, the relevance of which will depend on the characteristics and institutions of individual countries. With these caveats in mind, the analysis in this note brings the following insights. First, credit booms are often triggered by financial reform, capital inflow surges associated with capital account liberalizations, and periods of strong economic growth. They tend to be more frequent in fixed exchange rate regimes, when banking supervision is weak, and when macroeconomic policies are loose. Second, not all booms are bad. About a third of boom cases end up in financial crises. Others do not lead to busts but are followed by extended periods of below-trend economic growth. Yet many result in permanent financial deepening and benefit long-term economic growth. Third, it is difficult to tell "bad" from "good" booms in real time. But there are useful telltales. Bad booms tend to be larger and last longer (roughly half of the booms lasting longer than six years end up in a crisis). Fourth, monetary policy is in principle the natural lever to contain a credit boom. In practice, however, capital flows (and related concerns about exchange rate volatility) and currency substitution limit its effectiveness in small open economies. In addition, since booms can occur in low-inflation environments, a conflict may emerge with its primary objective. Fifth, given its time lags, fiscal policy is ill-equipped to timely stop a boom. But consolidation during the boom years can help create fiscal room to support the financial sector or stimulate the economy if and when a bust arrives. Finally, macroprudential tools have at times proven effective in containing booms, and more often in limiting the consequences of busts, thanks to the buffers they helped to build. Their more targeted nature limits their costs, although their associated distortions, should these tools be abused, can be severe. Moreover, circumvention has often been a major issue, underscoring the importance of careful design, coordination with other policies (including across borders), and close supervision to ensure the efficacy of these tools.
Credit booms; financial stability; macroprudential regulation; macroeconomic policy
267 [ Page 41 of 68, No. 10 ]
Paolo Gelain, Kevin J. Lansing, and Caterina Mendicino
Norges Bank, FRB San Francisco, and Bank of Portugal
House Prices, Credit Growth, and Excess Volatility: Implications for Monetary and Macro-prudential Policy
Progress on the question of whether policymakers should respond directly to financial variables requires a realistic economic model that captures the links between asset prices, credit expansion, and real economic activity. Standard DSGE models with fully-rational expectations have difficulty producing large swings in house prices and household debt that resemble the patterns observed in many developed countries over the past decade. We introduce excess volatility into an otherwise standard DSGE model by allowing a fraction of households to depart from fully-rational expectations. Specifically, we show that the introduction of simple moving-average forecast rules for a subset of households can significantly magnify the volatility and persistence of house prices and household debt relative to otherwise similar model with fully-rational expectations. We evaluate various policy actions that might be used to dampen the resulting excess volatility, including a direct response to house price growth or credit growth in the central bank's interest rate rule, the imposition of more restrictive loan-to-value ratios, and the use of a modified collateral constraint that takes into account the borrower's loan- to-income ratio. Of these, we find that a loan-to-income constraint is the most effective tool for dampening overall excess volatility in the model economy. We find that while an interest-rate response to house price growth or credit growth can stabilize some economic variables, it can significantly magnify the volatility of others, particularly inflation.
Asset Pricing, Excess Volatility, Credit Cycles, Housing Bubbles, Monetary policy, Macroprudential policy.
http://www.norges-bank.no/Upload/English/Publications/Working%20Papers/2012/wp_2012_08.pdf
Copyright ©2010-2013 Web development and maintenance by Ferdinand S. Co | Updated by: Dan Villanueva | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,798 |
\section{Introduction}
Cell selection is a fundamental functionality in wireless networks, and involves
choosing which base station (BS) the user equipment (UE) should be connected to.
Current cellular networks that operate in the microwave bands (around 2 GHz) use simple
heuristics to perform cell selection, usually choosing the BS that provides the
highest long-term signal to noise ratio (SNR) \cite{dahlman20134g}.
In this paper, we revisit the cell selection problem in the context of
next-generation cellular networks. These networks are expected to use
millimeter wave (mmWave) technology, that operates at frequencies above 28~GHz,
thereby exploiting the enormous amount
of spectrum available in these bands. At these frequencies, the radio
propagation characteristics are starkly different from their microwave counterparts.
First, according to the Friis transmission
equation~\cite{Rappaport:Book}, the path loss can easily exhibit 30-40~dB more
attenuation. This higher path loss necessitates the
use of fairly narrow and very directional beams, that can be realized through phased antenna
arrays, whose implementation is made possible thanks to the smaller wavelengths
that correspond to these
frequencies. Furthermore, due to the exacerbated blockage and shadowing effects~\cite{shadowing},
the wireless links will exhibit rapid variations in quality, thereby leading to
severe intermittency in link connectivity between the UE and the BS.
To address these challenges, and in particular to
maintain an acceptable level of service despite this intermittency,
the density of BSs in mmWave cellular networks is expected to be an order
of magnitude higher than in current systems~\cite{bsdensity}. The UEs will track several BSs
simultaneously and rapidly switch between them in response to the fast-varying
link qualities~\cite{michele:mac}. A simple approach to cell selection would
be for each UE to greedily pick the BS that is instantaneously the best,
thereby attempting to keep an optimal
state for itself. Unfortunately, these approaches may lead to degraded performance
for other UEs~\cite{mitrl, andrews:load}, or even to instability. In addition,
they entail significant overhead because of
frequent signaling in the control plane due to the large number of BS handovers that would result under such a policy.
Therefore, a better approach would need to consider the network behavior
and to look for solutions where all relevant information (including
channel conditions and BS load) is explicitly included in the optimization.
The problem of cell selection in mmWave networks, as well as in macrocellular networks
with high mobility~\cite{vtc:train}, has received considerable attention over
the past few years. In~\cite{nsn:amitava}, Talukdar et al. conclude that in mmWave
the UE will remain associated with a BS for just a few seconds and, in some
cases, for as little as 0.75 s. In~\cite{michele:mac}, Shokri-Ghadikolaei et al. study the
implications of the mmWave PHY on the MAC layer and argue that, if simple
cell selection techniques based on SNR were used, the handovers would become
too frequent. Further, loss of channel information and outdated beamforming
vectors will also lead to more frequent outages and expensive cell discovery
searches. The impact of network load on cell selection in dense pico-cell
environments was studied by Ye et al. in~\cite{andrews:load}. They argue
that considering SINR alone leads to sub-optimal assignments, and the optimal
approach is therefore to solve cell selection and resource allocation jointly.
One of the most popular techniques to study the problem of cell selection as
well as possible handoff strategies is through Markov Decision Processes
(MDPs)~\cite{mdp1, mdp2, mdp3}, which provide a useful mathematical framework
for studying the properties and performance of proposed cell selection
strategies. However, in order to be useful, MDPs need to be carefully applied.
In particular, it is important that all factors that play a key role in
determining the goodness of a cell selection solution be included in the model.
Previous studies that only use partial information may lead to sub-optimal results.
For example, Dang et al. in~\cite{mdp2} and Pan et al. in~\cite{mdp3} do
not consider dynamic variations in the network load to be an input to the cell
selection algorithm. Furthermore,~\cite{mdp2} considers a network with just one
UE, and therefore does not capture the global network-level performance effects of
the proposed technique. In~\cite{mdp1} Stevens-Navarro et al. consider a network with
just one BS, but with multiple relay nodes.
A more comprehensive study of the cell association problem will need to (i) consider a network with multiple BSs, where the network load can vary dynamically, and (ii) explicitly include in the optimization problem the key parameters that affect the performance (at both the network and the user level) in a multi-cell multi-user scenario, including cell load and channel conditions. Our contribution in this paper is to develop
such an approach and compare its performance to schemes that use only partial information.
The paper is organized as follows. In Sec. \ref{sec:model}, we introduce our model formulation. In Sec. \ref{sec:mdp}, we describe our decision algorithm and the iterative process applied to solve the multi-agent nature of the problem. In Sec. \ref{sec:results}, we discuss some simulation results. In Sec. \ref{sec:states}, we analytically derive the number of states for varying configurations. Finally, we conclude the paper and propose some future work in Sec. \ref{sec:conclu}.
\section{Model formulation}
\label{sec:model}
In our cell association problem, each UE can connect to a set of $L$ surrounding BSs. The time evolution of the quality of each link is described by a Markov process with $K$ states. $N$ represents the total number of UEs in the system.
As a first step towards more general scenarios, we consider the situation in which
all links have the same statistics. This can be
justified in mmWave scenarios where the channel can be assumed to alternate between well-defined states
(e.g., line-of-sight (LOS) and non-LOS) and all LOS links (non-LOS links) can be considered to be
equally good (equally bad) on average. More general models where different statistics may be associated
to different links will be left for future work.
Although the framework is general, we will illustrate the methodology using
a simplified version of the mmWave channel model described in \cite{mustafa}.
In this model, each link is characterized by three possible states:
\begin{itemize}
\item \emph{outage}, where no mmWave link is available;
\item \emph{LOS}, where a direct LOS mmWave link is available;
\item \emph{NLOS}, where only a non-LOS mmWave link is available.
\end{itemize}
The presence of the outage state, which occurs due to blockage, and the highly dynamic behavior of the channel, which can move in and out of the outage state on a very short time scale, are unique to the mmWave model. In practice, the rate that a mobile experiences in
any state depends on several conditions, including interference and SNR.
However, to simplify the study, we will assume that the rate is uniquely determined
by the state. A more complex model, which includes the SNR or other variations within each
state, can also be included. The transmission rates in the LOS and NLOS states are based approximately on the average spectral efficiencies
in those states, as presented in \cite{mustafa}.
More specifically, the statistical model provided in \cite{mustafa} gives the probability that a UE is in each of the three states based on its distance from the BS. Assuming the UE is randomly dropped in each cell with a radius of 200 m (a typical cell radius in the mmWave range), we computed the steady-state probability of each state, $\pi$. Hence, via quadratic programming optimization, we obtain matrix $\mathbf{P}$ such that $diag(\mathbf{P})$ is close to $1-\frac{1}{T_{avg}}$, where $T_{avg}=[t_{LOS},t_{NLOS},t_{out}]$ is the average time spent in each state before leaving it. Also, this matrix is consistent with the steady-state equation, $\pi P = \pi$.
Following this approach, we model the channel conditions seen by each UE towards the $L$ BSs as $NL$ i.i.d. Markov processes with common transition probability matrix,
\begin{equation}
\mathbf{P}=\begin{bmatrix}
p_{out-out} & p_{out-NLOS} & p_{out-LOS} \\
p_{NLOS-out} & p_{NLOS-NLOS} & p_{NLOS-LOS} \\
p_{LOS-out} & p_{LOS-NLOS} & p_{LOS-LOS}
\end{bmatrix}.
\end{equation}
Each connection is defined as
\begin{equation}
C^i=\{K_i,U_i\},
\end{equation}
where $K_i$ and $U_i$ represent the $K-$quantized channel state characterizing the link between a generic UE, $k$, and BS $i$ and the number of UEs connected to BS $i$, respectively.
The state space is defined as a subset of
\begin{equation}
S=[C^1 \times \mathbf{C^{L-1}]},
\end{equation}
constrained by \begin{equation}
\sum_{i=1}^{L}U_i=N,
\end{equation}
and where
\begin{equation}
\mathbf{C^{L-1}} = [C^2 \times \ldots \times C^L].
\end{equation}
In a state, $C^1$ describes the primary connection, i.e., the BS serving UE $k$, and $\mathbf{C^{L-1}}$ represents the characterization of the $L-1$ surrounding links (between UE $k$ and the non-serving BSs). The state space $S$ contains all possible combinations of channel conditions towards the different BSs and load occupancy at each BS. Due to the symmetry of the system model, a single state can represent multiple situations (according to all possible permutations of a given scenario), which leads to a significant reduction of the number of states needed to represent the possible system configurations, and therefore to a better scalability of the model. To assess the complexity of these models, we analytically derive the number of those states in Section \ref{sec:states}.
The action is defined as the identifier of the cell that the UE will join at the next step, i.e.,
\begin{equation} \label{eq:actions}
a \in A_s, \quad A_s=\{1, \ldots, L\},
\end{equation}
which corresponds to a handover if $a$ is different from the current serving cell. Here, $A_s$ represents the set of all BSs.
In an MDP, the statistics of the next state depends only on the current state and on the decision made. Therefore, we need to define the transition probabilities, $p(s_j|s_i,a)$, i.e., the probabilities of moving to state $s_j$ given the current state $s_i$ and under action $a$, where $s_i, s_j \in S$.
The transition probabilities must satisfy the condition
\begin{equation}
\sum_{s_j\in S}p (s_j|s_i,a)=1, \forall s_i \in S, a \in A_s.
\end{equation}
\begin{algorithm}[t!]
\caption{MDP-based Handover}\label{euclid}
\begin{algorithmic}[1]
\State Intialization: Initial Policy $\mathcal{D}_{0}^{i}, \forall i \in [1,N]$
\State For each iteration ($n > 0$)
\hspace{-0.8cm}
Select a UE: $k = mod(N, n) + 1$
\hspace{-0.8cm}
Update the Policies:
For UE $k$
~~~~$p(s_j|s_i,a) = f(\mathcal{D}_{n-1}^{-\mathbf{k}}, r(s_i,s_j,a))$
~~~~~~~~~~~~~~~~~~~~~~~~~~~$\forall s_i,s_j \in S, \forall a$
~~~~$\mathcal{D}_{n}^{k} =$ VIA$(\bold{p}, \bold{r})$
For other UEs $m\in \{1,,2,\dots,N\}\setminus{k}$
~~~~$\mathcal{D}_{n}^{m} = \mathcal{D}_{n-1}^{m}$
\hspace{-0.8cm}
$n$ = $n+1$
\hspace{-0.8cm}
Until convergence
\end{algorithmic}
\label{algo1}
\end{algorithm}
Our link reward function $r(s_i,a)$ depends on the average reward over all possible destinations. Thus, we let $r_t(s_i,a,s_j)$ denote the value at time $t$ of the instantaneous reward received given that the state of the system at decision epoch $t$ is $s_i$, action $a \in A_s$ is selected, and the system is in state $s_j$ at decision epoch $t+1$. Its expected value at decision epoch $t$ can be evaluated by computing
\begin{equation}
r(s_i,a)=\sum_{s_j\in S}r_t(s_i,a,s_j) p_t(s_j|s_i,a),
\end{equation}
where
\begin{equation}
r_t(s_i,a,s_j)=(1-c(s_i,s_j,a)) \frac{R_{s_j}}{U_{a}+1},
\end{equation}
$R_{s_j}$ is the achievable rate the UE would enjoy if it were the only UE in its cell, and only depends on the channel quality of state $s_j$, whereas $\frac{R_{s_j}}{U_{a}+1}$ is the rate actually available when the cell load $U_{a}$ on the target BS $a$ is taken into account.\footnote{Note that in this formulation the cell load does not include the incoming user (which instead accounts for the "+1" in the denominator). Also, $U_a+1$ is an estimate based on the status of the BS occupancy in the previous slot, and does not necessarily represent the true state, which depends on the decisions being made in the current slot (i.e., other users leaving or joining that BS).} $c(s_i,s_ja)$ is the handover cost function, which is equal to $OH$ if the UE moves from the associated BS in state $s_i$ to a different BS in state $s_j$, and is otherwise equal to zero. We define the value of $OH$ as a percentage of the spectrum that needs to be used for signaling.
\section{MDP-based handover decision}
\label{sec:mdp}
In this section, we describe our algorithm to obtain the optimal cell selection strategy for each UE. We use a distributed iterative approach in which each UE finds its optimal deterministic policy when assuming that all other UEs make handover decisions based on current BS occupancy but assuming steady-state channel conditions, which results in an approximated cell occupancy evolution\footnote{We note that a precise model would need to keep track of the channel conditions from all UEs to all BSs, which is clearly an impossible task.}.
The proposed algorithm is described in Algorithm~\ref{algo1}. It initializes the system with a random policy assignment to each UE, $\mathcal{D}_{0}^{i}, \forall i \in \{1,2,\dots,N\}$, where $\mathcal{D}_{n}^{i} = (d^n_i(s_1),d^n_i(s_2),\cdots,d^n_i(s_j),\cdots)$ contains the set of actions for all states $s_j \in S$ for UE $i$ at iteration $n$. This algorithm runs for multiple iterations. In each iteration, a UE $k$ is selected sequentially among the given set of UEs. For the selected UE, the policy is updated based on the policies of the other UEs at the previous iteration, denoted by $\mathcal{D}_{n-1}^{-\mathbf{k}}$. We introduce the following definitions.
\begin{equation}
s(t)=[(K_1(t),U_1(t)), \cdots, (K_L(t),U_L(t))]
\end{equation}
is the state seen by the selected UE, i.e., the UE that is updating its policy. On the other hand,
\begin{equation}
s^{\star}(t)=[(.,U_1(t)), \cdots, (.,U_L(t))],
\end{equation}
is the approximate description of the state associated with all the other UEs, which refers to the fact that for those UEs we define a decision strategy that only refers to the cell occupancy, thereby avoiding the need to track instantaneous channel conditions for everyone. That being said, we can define the probability for any UE (say UE $x$) to select BS~$i$ starting from any state $s^{\star}(t)$ as
\begin{algorithm}[t!]
\caption{Value Iteration Algorithm (VIA($\bold{p}, \bold{r}$))}\label{euclid}
\begin{algorithmic}[1]
\State Select $v^0 \in V$, specify $\epsilon, \omega> 0$, and set $n=0$
\State For each $s_i \in S$, compute $v^{(n+1)}(s_i)$ by
\hspace{-0.8cm}
{\footnotesize $v^{(n+1)}(s_i)=\max_{a \in A_s}\left \{ r(s_i,a)+\sum_{s_j \in S} \omega~p(s_j|s_i,a)~v^{n}(j) \right \}$}
\If {$\begin{Vmatrix}
v^{n+1}-v^n
\end{Vmatrix}<\epsilon (1- \omega)/2 \omega$}
\textbf{goto} step $\mathbf{6}$
\Else
$n \gets n+1$
\textbf{goto} step $\mathbf{2}$
\EndIf\\
For each $s_i$, choose
\hspace{-0.8cm}
{\footnotesize $d_k(s_i) = \argmax_{a \in A_s} \left \{ r(s_i,a)+\sum_{s_j \in S} \omega~p(s_j|s_i,a)~v^{n}(j) \right \}$}
\end{algorithmic}
\label{algo2}
\end{algorithm}
\begin{equation}
P[s^{\star}(t) \rightarrow i]= \sum_{m=1}^{K^L}\pi(s_{m}(t))~\delta_{id_{x}(s_m(t))},
\end{equation}
where $K^L$ is the total number of channel states' combinations, and $\delta_{id_{x}(s_m(t))}$ is calculated from the policy of the corresponding UE.
\begin{equation}
\delta_{id_x(s_m(t))}=\left\{\begin{matrix}
1, \quad i = d_{x}(s_m(t))\\
0, \quad i \neq d_{x}(s_m(t))
\end{matrix}\right..
\end{equation}
\begin{figure}[t]
\centering
\includegraphics[trim = 0mm 0mm 0mm 7mm, clip, width=1\columnwidth]{fig1_updated.eps}
\caption{Average Spectral Efficiency (bits/s/Hz) for different schemes with 3 BSs, handover cost = 10\%.}
\label{ase}
\end{figure}
Here, $\pi(s_{m}(t))$ represents the steady-state distribution of the channel. Now, because we have introduced a probabilistic evolution of each UE, we can update the transition matrix accordingly. Then, based on the updated transition probability matrix ($\bold{P}$), the Value Iteration Algorithm (VIA) described in Algorithm \ref{algo2} is used to solve the MDP, which gives the optimal deterministic policy of the selected UE. This way, the load occupancy dynamics will be captured, thus allowing us to evaluate the overall performance of a fully characterized multi user system. In our VIA algorithm, $v(\mathbf{s})$ denotes the maximum expected total reward, $\omega$ represents the discount factor, i.e., the length of the analyzed horizon, whereas $\bold{r}$ is the vector containing the reward values.
For other UEs, the policy is retained from the previous iteration. The reason behind solving the MDP for one UE per iteration is to reach convergence. If multiple UEs change their policy simultaneously, we observed that the algorithm does not converge and instead oscillates indefinitely. This is a very well known property of multi-user distributed solutions, where the performance of a user is strongly coupled with the performance of the other users. For example, this issue is discussed in the context of distributed power control in a multi-cell 4G network \cite{zhang2011weighted}. In this paper, we do not provide a formal proof of the convergence of the proposed algorithm, which is left for future work.
In summary, (i) we derive the optimal policy at each UE as a function of its detailed state (i.e., channel state plus occupancy), and find the related steady-state distribution; (ii) we converge to an optimal equilibrium through an iterative process by averaging the previous policies of all users over the conditional channel distribution at each iteration.
\begin{figure}[t]
\centering
\includegraphics[trim = 0mm 0mm 0mm 7mm, clip, width=1\columnwidth]{fig2_updated.eps}
\caption{Number of Handovers for all different schemes with 3 BSs, handover cost = 10\%.}
\label{hos}
\end{figure}
\section{Simulation results}
\label{sec:results}
In this section, we present some simulation results obtained by applying the proposed MDP-based handover algorithm for varying system configurations. Specifically, we studied simple scenarios where the number of BSs is fixed to $3$, while the number of UEs varies between $3$ and $6$. Moreover, to better assess the performance of the proposed model, we generate the results for different handover costs, defined as the percentage of resources spent for signaling and flow rerouting, as defined in Section~\ref{sec:model}.
The channel matrix shown in (\ref{channel_matrix}) is obtained as per the description given in Section~\ref{sec:model}, where $T_{avg}=[t_{LOS},t_{NLOS},t_{out}]=[5,25,3]$, which characterizes an urban scenario where the dominant link is NLOS:
\begin{equation}
\mathbf{P}=\begin{bmatrix}
0.55 & 0.3 & 0.15 \\
0.01 & 0.8 & 0.19 \\
0.38 & 0.40 & 0.22
\end{bmatrix}.
\label{channel_matrix}
\end{equation}
In addition, we consider a 28~GHz carrier frequency with 1~GHz bandwidth, a slot duration equal to 125 $\mu$s and $30$ OFDM symbols per slot ($6$ for control, $24$ for data).
We use the optimal policy obtained with our algorithm, and compare its performance against other cell selection approaches, namely: \begin{itemize}
\item \textbf{Load:} Each UE connects to the least loaded BS. If two or more BSs show the same occupancy level, UEs randomly select one of them;
\item \textbf{Rate:} UEs associate with the BS that can offer the best instantaneous rate, which depends on both channel and load information;
\item \textbf{Channel:} Traditional approach where UEs select the BS offering the best channel (SNR-based);
\item \textbf{Upper Bound:} Centralized exhaustive search method; it requires global information about link qualities along with cell occupancy, and exploits UE coordination, which is unavailable in distributed schemes. Hence, this approach represents an upper bound.
\end{itemize}
In Figs. \ref{ase} and \ref{hos}, we report the results for the case of $3$ UEs with $3$ BSs and handover cost 10\%. We plot the average spectral efficiency (bits/s/Hz) and the average number of handovers. We can observe how the optimal policy obtained by solving the MDP described in Section \ref{sec:mdp} outperforms other approaches. In particular, we can note that the \emph{Load}-based scheme, which relies solely on occupancy information, is very inefficient and results in biasing all the UEs towards unloaded cells. As a consequence, BSs will be overloaded, thus explaining the low rate observed in Fig. \ref{ase}. On the other hand, \emph{Channel}- and \emph{Rate}-based schemes show better performance but, because of the channel variations that characterize mmWave links, instantaneous actions are highly inefficient.
Instead our MDP model, where the dynamics of the links are fully captured, can be seen to provide significantly better performance. This not only results in increased sum-rate, but also provides a greatly reduced number of handovers, as shown in Fig. \ref{hos}, thus representing a more energy-efficient solution. The \emph{Upper Bound} refers to a centralized scheme, which compared to our distributed scheme has the advantage of full knowledge and of coordinated decisions, thereby resulting in significantly better performance in general. Nevertheless, it can be observed that despite such big advantages the performance gap between our solution and the centralized upper bound is not very wide, showing that our solution (which is not necessarily the distributed optimum because the problem is non-convex) still achieves a fairly good performance
\begin {table}
\caption {Average Spectral Efficiency Gain (bits/s/Hz)} \label{tab:tab3}
\label{results}
\begin{center}
\begin{tabular}{| l | l | l | l | l | l |}
\hline
& \textbf{3\% OH} & \textbf{6\% OH} & \textbf{10\% OH} & \textbf{30\% OH} \\ \hline
\textbf{3 UEs} & 37\% & 39\% & 42\% & 51\% \\ \hline
\textbf{4 UEs} & 33\% & 35\% & 39\% & 50\% \\ \hline
\textbf{5 UEs} & 30\% & 32\% & 36\% & 50\% \\ \hline
\textbf{6 UEs} & 26\% & 28\% & 33\% & 50\% \\ \hline
\end{tabular}
\end{center}
\end{table}
In Table \ref{results}, we report a more detailed sum-rate comparison of our \emph{MDP}-based model against a traditional \emph{Channel}-based association scheme in terms of average spectral efficiency gain (\%). We can observe significant gains in the \emph{MDP}-based approach, which increase as the HO cost increases. The ability to capture optimal solutions for more complex scenarios may lead us to draw some important conclusions about the shape of effective policies, and to find heuristics to better address a number of critical issues related to mmWave cellular networks.
\section{Complexity analysis}
\label{sec:states}
In this section, we aim at analyzing the complexity of our MDP model in terms of number of states required as a function of the number of UEs and BSs.
First of all, we will analytically derive the number of load occupancy combinations, for at most $5$ BSs,\footnote{A reasonable maximum number of surrounding BSs.}.
Let us introduce $q(\cdot)$, expressed as
\begin{equation}
q(x)=\max\{x,0\}.
\end{equation}
Now, we can count the possible occupancy combinations for $1, 2, 3, 4$ BSs as a function of the number of UEs $N$, i.e.,
\begin{equation}
c_{1}(N)=N+1 ,
\end{equation}
\begin{equation}
c_{2}(N)=\left \lfloor \frac{N}{2} \right \rfloor,
\end{equation}
\begin{equation}
c_{3}(N)=\sum_{i=0}^{N-1} q\left ( \left \lfloor \frac{N-1-i}{2} \right \rfloor - i \right ),
\end{equation}
\begin{equation}
\begin{split}
c_{4}(N) &= \sum_{i=0}^{N-1}\sum_{j=0}^{N-1} q\left ( \left \lfloor \frac{N-1-j}{2} \right \rfloor - j\right ) - \\
& - \sum_{k=0}^{i-1} q\left ( \left \lfloor \frac{N-2-i-k}{2} \right \rfloor - k\right ),
\end{split}
\end{equation}
and derive the number of load occupancy combinations at varying number of BSs, $L$, as follows,
\begin{equation}
C_L(N)=c_1(N)+\sum_{i=0}^{N-1}\sum_{k=2}^{L-1} c_k(N-i).
\end{equation}
As stated above the number of possible channel states' combinations is equal to $K^L$.
Therefore, the total number of states, as shown in Fig. \ref{ues}, will be as follows:
\begin{equation}
|S(L,K,N)|=K^LC_L(N).
\end{equation}
\begin{figure}[t!]
\centering
\includegraphics[trim = 0mm 0mm 15mm 0mm, clip, width=1\columnwidth]{UES.eps}
\caption{Number of states at varying number of BSs, $L$, and UEs, $N$.}
\label{ues}
\end{figure}
In terms of run time, the computational complexity (convergence time) of the proposed MDP approach increases exponentially with
the number of UEs. However, the proposed algorithm can be executed offline within specific clusters of mmWave cells, at varying number of associated users.
Each BS will disseminate the optimal policies for various numbers of instantaneous connected UEs, thus quickly adapting to topology changes, i.e., a new UE coming or leaving.
\section{Conclusions}
\label{sec:conclu}
In this paper, we have argued why harnessing the potential of mmWave cellular
networks requires revisiting the problem of cell selection. Judicious choices
in cell selection serve to improve the quality of service and increase network
capacity, while minimizing the signaling overhead caused by sub-optimal cell
selections and subsequent re-associations. We have made the case in favor of
using MDPs to design and analyze association techniques. Through numerical
analysis and simulations, we have demonstrated the ability of our proposed
technique to achieve these goals. In the future, we plan to extend this work in several ways: $i)$ evaluate over more complex networks to derive procedural guidelines to design heuristics; $ii)$ investigate whether finer-grained SNR measurements can improve
outcomes; $iii)$ examine the effectiveness of these techniques in heterogeneous
networks. In conclusion, although mmWave technology holds the promise to revolutionize
cellular networks, realizing this potential will
require revisiting and potentially redesigning several components of the
communication stack. This paper makes an important step in this direction with focus on the problem of cell selection in mmWave cellular networks.
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,872 |
#include "e.h"
#include "e_mod_main.h"
/* actual module specifics */
static E_Module *conf_module = NULL;
/* module setup */
EAPI E_Module_Api e_modapi =
{
E_MODULE_API_VERSION,
"Settings - Screen"
};
EAPI void *
e_modapi_init(E_Module *m)
{
e_configure_registry_category_add("screen", 30, _("Screen"), NULL,
"preferences-desktop-display");
e_configure_registry_item_add("screen/virtual_desktops", 10,
_("Virtual Desktops"), NULL,
"preferences-desktop", e_int_config_desks);
// e_configure_registry_item_add("screen/screen_resolution", 20,
// _("Screen Resolution"), NULL,
// "preferences-system-screen-resolution",
// e_int_config_display);
e_configure_registry_item_add("screen/screen_lock", 30,
_("Screen Lock"), NULL,
"preferences-system-lock-screen",
e_int_config_desklock);
e_configure_registry_item_add("screen/screen_saver", 40,
_("Blanking"), NULL,
"preferences-desktop-screensaver",
e_int_config_screensaver);
e_configure_registry_item_add("screen/power_management", 50,
_("Backlight"), NULL,
"preferences-system-power-management",
e_int_config_dpms);
e_configure_registry_category_add("internal", -1, _("Internal"), NULL,
"enlightenment/internal");
e_configure_registry_item_add("internal/desk", -1,
_("Desk"), NULL,
"preferences-system-windows",
e_int_config_desk);
conf_module = m;
e_module_delayed_set(m, 1);
return m;
}
EAPI int
e_modapi_shutdown(E_Module *m __UNUSED__)
{
E_Config_Dialog *cfd;
while ((cfd = e_config_dialog_get("E", "internal/desk")))
e_object_del(E_OBJECT(cfd));
e_configure_registry_item_del("internal/desk");
e_configure_registry_category_del("internal");
while ((cfd = e_config_dialog_get("E", "screen/power_management")))
e_object_del(E_OBJECT(cfd));
while ((cfd = e_config_dialog_get("E", "screen/screen_saver")))
e_object_del(E_OBJECT(cfd));
while ((cfd = e_config_dialog_get("E", "screen/screen_lock")))
e_object_del(E_OBJECT(cfd));
// while ((cfd = e_config_dialog_get("E", "screen/screen_resolution")))
// e_object_del(E_OBJECT(cfd));
while ((cfd = e_config_dialog_get("E", "screen/virtual_desktops")))
e_object_del(E_OBJECT(cfd));
e_configure_registry_item_del("screen/power_management");
e_configure_registry_item_del("screen/screen_saver");
e_configure_registry_item_del("screen/screen_lock");
// e_configure_registry_item_del("screen/screen_resolution");
e_configure_registry_item_del("screen/virtual_desktops");
e_configure_registry_category_del("screen");
conf_module = NULL;
return 1;
}
EAPI int
e_modapi_save(E_Module *m __UNUSED__)
{
return 1;
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,688 |
{"url":"https:\/\/tailieu.vn\/doc\/mot-cach-tiep-can-mo-rong-mo-hinh-co-so-du-lieu-quan-he-de-xu-ly-thong-tin-khong-day-du-va-cac-phu-t-1554931.html","text":"# M\u1ed9t c\u00e1ch ti\u1ebfp c\u1eadn m\u1edf r\u1ed9ng m\u00f4 h\u00ecnh c\u01a1 s\u1edf d\u1eef li\u1ec7u quan h\u1ec7 \u0111\u1ec3 x\u1eed l\u00fd th\u00f4ng tin kh\u00f4ng \u0111\u1ea7y \u0111\u1ee7 v\u00e0 c\u00e1c ph\u1ee5 thu\u1ed9c d\u1eef li\u1ec7u.\n\nChia s\u1ebb: B\u00fat M\u00e0u | Ng\u00e0y: | Lo\u1ea1i File: PDF | S\u1ed1 trang:7\n\n70\nl\u01b0\u1ee3t xem\n2\n\nM\u1ed9t c\u00e1ch ti\u1ebfp c\u1eadn m\u1edf r\u1ed9ng m\u00f4 h\u00ecnh c\u01a1 s\u1edf d\u1eef li\u1ec7u quan h\u1ec7 \u0111\u1ec3 x\u1eed l\u00fd th\u00f4ng tin kh\u00f4ng \u0111\u1ea7y \u0111\u1ee7 v\u00e0 c\u00e1c ph\u1ee5 thu\u1ed9c d\u1eef li\u1ec7u. Do v\u1eady, c\u00e1ch ti\u1ebfp c\u1eadn h\u1ec7 th\u1ed1ng \u0111\u00e3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong l\u00fd thuy\u1ebft mang t\u00ednh ch\u1ea5t li\u00ean ng\u00e0nh, t\u1ea1o ra c\u01a1 h\u1ed9i \u0111em nh\u1eefng quy lu\u1eadt v\u00e0 nh\u1eefng kh\u00e1i ni\u1ec7m t\u1eeb m\u1ed9t l\u0129nh v\u1ef1c nh\u1eadn th\u1ee9c n\u00e0y sang m\u1ed9t l\u0129nh v\u1ef1c kh\u00e1c. 2. \u0110i\u1ec1u khi\u1ec3n h\u1ecdc th\u1ebf h\u1ec7 th\u1ee9 hai\n\nCh\u1ee7 \u0111\u1ec1:\n\nB\u00ecnh lu\u1eadn(0)\n\nL\u01b0u\n\n## N\u1ed9i dung Text: M\u1ed9t c\u00e1ch ti\u1ebfp c\u1eadn m\u1edf r\u1ed9ng m\u00f4 h\u00ecnh c\u01a1 s\u1edf d\u1eef li\u1ec7u quan h\u1ec7 \u0111\u1ec3 x\u1eed l\u00fd th\u00f4ng tin kh\u00f4ng \u0111\u1ea7y \u0111\u1ee7 v\u00e0 c\u00e1c ph\u1ee5 thu\u1ed9c d\u1eef li\u1ec7u.\n\n1. Ti!p chi Tin hoc va Dieu khie'n hoc, T.17, S.3 (2001), 41-47 AN APPROACH TO EXTENDING THE RELATIONAL DATABASE MODEL FOR HANDLING INCOMPLETE INFORMATION AND DATA DEPENDENCIES HO THUAN, HO CAM HA Abstract. In this paper we propose a new approach to extending the relational database model. This approach is based on the concept of similarity based fuzzy relational database and somewhat of new viewpoint on redundancy. It is shown that, in such an extended database model, we can capture imprecise, uncertain information. The formal definition of fuzzy functional and multivalued dependencies in this study allows a sound and complete set of inference rules. This paper describes an ongoing work. We state some open problems to be solved in order to render our approach more operational. T6m t~t. Bai bao de xuat mi?t each tiep c~n m&i M m& ri?ng me hlnh err s& dir li~u quan h~. Cach tiep c~n nay du-a tren khii niern err s& dir li~u mer tircng t~\u00b7 va mi?t quan die'm mo-i ve duo th ira dir li~u. V &i me hlnh err S6-dir li~u nhir v~y co the' nitm bitt dtro'c nhirng thong tin khong chinh xac, khOng chltc chan. Dinh nghia ve phu thuoc ham mer va phu thuoc da tri mer trong bai bao cho m9t t~p cac lu~t suy din xac ding va diy dii. 1. INTRODUCTION Database systems have been extensively studied since Codd [3] proposed the relational data model. Such database systems do not accept uncertain and imprecise data. In fact, the value of an object's attribute may be completely unknown, incompletely known (i.e., only a subset of possible values of the attribute is known)' or uncertain (e.g. a probability or possibility distribution for its value is known). In addition, the attribute may not be applicable to some of the objects being considered and, in certain cases, we may not known whether the value even exists, or not. Many approaches to that problem have been proposed. One of them is \"A fuzzy representation of data for relational database\" [2], which is suggested by P. Buckles and E. Petry. In [2] a structure for representing inexact information in the form of a relational database is presented. The structure differs from ordinary relational database in two important respects: value of an attribute of an object need not be single value and a similarity relation is required for each domain set of the database. In a fuzzy database proposed by these authors, a tuple is redundant if it can be merged with another through the set union of corresponding domain values. The merging of tuple, however, is subject to constraints on some similar thresholds. Within this conception, in a fuzzy relation with no redundant tuples and each domain similarity relation formulated according to Tl transitivity, each tuple represents information of an object, and each value of an attribute (called domain value) consists of one or more elements from the domain base set. At this point, there is an emphatic notice that elements of each domain value must be similar enough to each other (i.e. similarity degree of every couple of elements is not less than the given threshold). The work reported here is quite distinct from that of P. Buckles and E. Petry in that the elements of each domain value are not required to be similar enough according to the threshold. This idea allows each domain value to contain elements, which even are not very similar and represent the possibilities that can be happened. Therefore, to model a relational database by using this approach will preserve not only the exact information but also the nuances of fuzzy uncertainty. This paper is organized as follows. Notations and basic definitions related to fuzzy relational data model and similarity relation, are reviewed in Section 2 to get an identical understanding of terminology. A new definition about tuple redundant is presented in Section 3. Section 4 contains\n2. 42 HO THUAN, HO CAM HA definition of functional dependency in this scene. The soundness and completeness of the set of axioms, which is similar with Amstrong's axioms in the traditional relational database, will be proved in this section. In Section 5, we propose a formal definition of fuzzy multivalued dependency and the inference rules. 2. BACKGROUND First, similarity relations are described as defined by Zadeh [9]. Then the basic concepts of fuzzy relational database model are reviewed. Similarity relations are useful for describing how similar two elements from the same domain are. Definition 2.1. ([5]) A similarity relation, SD (x, y), for a given domain D, is a mapping of every pair of elements in the domain onto the unit interval [0,1] with the three following properties, \"Ix, y, zED: 1. Reflexivity SD(X,X) = 1 2. Symmetry SD(X,y) = SD(Y,X) 3. Transitivity SD(X,Z) ~ Max(Min[SD(x,y),SD(Y'z)]) (T1) Y or 3'. Transitivity SD (x, z) = Max([SD (x, y) * SD (y, z)]) (T2) Y where * is arithmetic multiplication) For each domain j in a relational database, a domain base set Dj is understood. Domains for fuzzy relational databases will be either discrete scalars or discrete numbers drawn from either a finite or infinite set. A domain value dij, where i is the tuple index, is defined to be a subset (not empty) of its domain base set Dj. Let 2Dj denote a set of any non-null member of the powerset of Dj. Definition 2.2. ([2]) A fuzzy relation, r, is a subset of the set cross product 2Dl X \"\" \" X 2Dm. Definition 2.3. ([2]) A fuzzy relation tuple, t, is any member of 2Dl x .. \" X 2Dm. An arbitrary tuple is of the form ti E r, ti = (di1, di2, ... ,dim), dij ~ Dj . For example: Name Car.color Job {John} {green, blue, pink} {doctor, physician, dentist, farmer} 3. REDUNDANCY AND DETERMINANCY PROPERTIES In a nonfuzzy database, a tuple is redundant if it is exactly the same as another tuple. In fuzzy database of P.Buckles and E.Petry [2], a tuple is redundant if it can be merged with another without violating LEVEL(Dj) = THRES(Dj)' J\" = 1,2, ... , m, where THRES(Dj) = mini{minx,YEdij [s(x, y)]} [2] In a given domain Dj, x, Y E Dj, if s(x, y) ~ LEVEL(Dj) then we write down x ~ y. Obviously, ~ is a binary relation on D j . Lemma 3.1. ~ is an equivalence relation. Proof. \"Ix E Dj, s(x, x) = 1, so s(x, x) ~ LEVEL(Dj), we have x ~ x. Symmetry property of ~ relation is easily implied from the symmetry property of a similarity measure. V x, y, z E Dj, if s(x, y) ~ LEVEL(Dj) and s(y, z) ~ LEVEL(Dj), from (T1) transitivity we have s(x, z) ~ LEVEL(Dj). Thus, ~ is an equivalence relation and induces a unique partition in Dj. In a fuzzy relational scheme suggested by Buckles and Petry [2], each domain value may consist of many elements, all of which belong to the same equivalence class partitioned by the ~ relation.\n3. AN APPROACH TO EXTENDING THE RELATIONAL DATABASE MODEL 43 According to these authors, two tuples are redundant to each other if on every attribute, the domain value of each tuple includes representatives of the same equivalence class. To a certain meaning, if we consider an equivalence class (of the ~ relation) as a branch of possibilities that may happen, the model of P. Buckles and E. Petry will allow only to capture information of the objects, of which the known information about each attribute belongs to only one branch of possibilities. The branch of possibilities mentioned here is considered to be shown by values, which are, although not equal to each other, but closed enough to each other according to the measure of a similarity relation. However, in fact there can be uncertain information about an object, on an attribute of that there are many possibilities which are far different to each other. In the above example, John may be a doctor, a physician, a dentist (or any position in medical profession), but John may be also a farmer. John has a green car, or a pink one, but he may have two cars, one is blue and the other is pink. And it is not excluded that John has all the three cars which are green, blue and pink. If a group of possibility branches is considered necessary to keep as it identifies a full information in this case, the model in [2] should be expanded, and we have tried to do this. Suppose that with each Dj there is a LEVEL(Dj) for an identified similarity on this domain, two tuples are said to be redundant to each other if they have the same group of possibilities on each attribute. Definition 3.1. In fuzzy relation r, two tuples ti = (dil, di2, ... , dim) and tk = (dkl, dk2, ... , dkm), i =1= k are redundant if 't\/x E dij 3x' E dkj : x ~ x', VJ = 1,2, , m and vice versa, i.e. 't\/x E dkj 3x' E dij : z ~ x', VJ = 1,2, , m. As t, and tk are equitable in the above definition, the notation ti RJ tk is used to denote that t; and tk are redundant. Lemma 3.2. RJ is an equivalence relation on the fuzzy relation r. Proof. It is clear that, for every tuple ti of r, t, RJ ti from reflexivity of ~ relation. Obviously, if ti RJ tk then tk RJ ti . Suppose that ti RJ tk and tk RJ tho Consider arbitrary domain Dj, if x E dij then 3x' E dkj : x ~ x' (from t, RJ tk). Since x' E dkj, we have 3x\" E dhj : x' ~ z\" (from tk RJ th). We also have z ~ z\" by transitivity of ~ relation. Similarly, if x E dhj we have 3x\" E dij : x ~ z\", Thus, redundant (RJ) is an equivalence relation on R and induces a unique partition in r. An example of a fuzzy relation with similarity relations: r1 Name Car .color Job John green, blue, pink actor, teacher Johan black, magent aconductor, instructor Elina white, pink artist Melia pink, light-milk artist Tom black, red pilot Fig. 1. A fuzzy relation If it is assumed that LEV(Name) = 0.6 then ~ relation partitions Dom (Name) by three equivalence classes: {John, Johan}; {Elina, Melina}; {Tom} It is also assumed that LEV(Car_color) and LEV(Job) are given such that Domj Car.color] and Dom( Job) are partitioned as follow {{green, blue, black}, {pink, magenta, red}, {white, lighLmilk}} {{actor, conductor, artist}, {teacher, instructor}, {pilot}}\n4. 44 HO THUAN, HO CAM HA Thus in r1 above, tl is redundant for tz and t3 is redundant for t4 . John Johan Elina Melina Tom John 1.0 0.6 0.0 0.0 0.0 Johan 0.6 1.0 0.0 0.0 0.0 Elina 0.0 0.0 1.0 0.8 0.0 Melina 0.0 0.0 0.8 1.0 0.0 Tom 0.0 0.0 0.0 0.0 1.0 Fig. 2. Similarity relation for Dom(Name) 4. FUZZY FUNCTIONAL DEPENDENCY AND A SET OF SOUND AND COMPLETE INFERENCE RULES Let r is a fuzzy relation with m attributes, these according to m domains DI, Dz, ... , Dm, we said that r. is an instance of R, which is called a relation scheme on U, U = {AI, Az, ... , Am}. Suppose that X is a set of attributes (X ~ U), two tuples tl, tz E r, tl = (dll, dvz, ... , dIm) and tz = (dZI' dzz, ... , dzm), we said tl, tz are redundant each other on X and write tdX] ~ tz[X] if Vx E dlj :lx' E dZj : x,..., x', and vice versa, i.e. Vx E dZj :lx' E dlj : x,..., x', Vj : Aj E X. Definition 4.1. A fuzzy functional dependency X ~ Y is said to be hold in a fuzzy relation r if for every pairs of tuple tl, tz E r: tdX] ~ tz[X] implies that tdY] ~ tz[Y]. In what follows we assume that we are given a fuzzy relational schema with set of attribute U, the universal set of attributes, and a set of fuzzy functional dependencies F involving only attributes in U. The inference rules, which similar with Amstrong's axioms are: FFD1 : Reflexivity If Y ~ X then X ~ Y FFD2: Augmentation If X ~ Y holds, then XZ ~ YZ holds FFD3: Transitivity If X ~ Y and Y ~ Z hold, then X ~ Z holds Lemma 4.1. The set of FFD axioms (FFD1-FFD3) are sound. That is, if X ~ Y is deduced from F using the axioms, then X ~ Y is true in any relation in which the dependencies of F are true. Proo]. (FFD1) The reflexivity axiom is clear sound. (FFD2) Suppose tl, t2 E r such that tl[XZ] ~ tz[XZ] (1) then by definition of \"~\" we have tdX] ~ tz[X]. From X ~ Y we have tdY] ~ tz[Y] (2) (1) means Vx E dl) :lx' E dz) : x,..., x', and vice versa Vj : Dj E XZ. (2) means Vx E dlj :lx' E dZj : x,..., x', and vice versa VJ' : D) E Y. So we have Vx E dlj :lx' E dz): z >\u00ab x', and vice versa VJ': Dj E YZ. It means XZ ~ YZ. (FFD3) If tl[X] ~ tz[X] then we have tl[Y] ~ tz[Y] from X ~ Y and tdZ] ~ tz[Z] from Y ~ Z. The following inference axioms are infered from the above axioms\n5. AN APPROACH TO EXTENDING THE RELATIONAL DATABASE MODEL 45 FFD4: Union If X ~ Y and X ~ Z hold, then X ~ Y Z holds. FFD5 : Decomposition If X ~ Y Z holds, then X ~ Y and X ~ Z hold. FFD6 : Pseudo transitivity If X ~ Y and YW ~ Z hold, then XW ~ Z holds. Procedure of proof for the completeness of above inference axioms is very similar to the classical case. Theorem 4.1. The set of axioms (FFDI-FFD2) are sound and complete. 5. FUZZY MULTIVALUED DEPENDENCY AND SET OF INFERENCE RULES In the fuzzy paradigm, let R be a relation scheme and let X and Y be subsets of R. In a relation r, an instance of R, for X-value z we define Xr(x) = {x'l::3t E r, such that t[X] = x', x ~ x'}. Yr(x) = {YI::3t E r, such that t[X] E Xr(X), try] = y}. Let Z = R - XY. It is clear that Yr(x) is independent of Z-values. We say that Yr(x) is equivalent to Yr (xz) if for every y of one, there is existing y' of the other such that y ~ y' and vice versa. The fuzzy equivalence of two set Y -value (Yr (x) and Yr (xz)) can be reperesented as Yr (x) ~ Yr (xz). Definition 5.1. A fuzzy multivalued dependency (FMVD) m on a scheme R, is a statement m : X~ Y, where X, Yare subsets of R. Let Z = R - XY. A relation r on the scheme R obeys the FMVD m: X ~ Y if for every XZ-value xz that appears in r we have Yr(x) ~ Yr(xz). Example: r2 X (Degree) Y (Courses) Z (Student) a, b, c g, h zl a', c' s', i z2 a, c' g, i' zl' a', c s', h' z2' Fig. 9. A fuzzy relation xl = {a, b, c}, Xr(xl) = {{a, b, c}, {a', c'}, {a, c'}, {a', c}} Yr(xl) = {{g,h}, {g',i}, {g,i'}, {g',h'}} Yr(xlzl) = {{g, h}, {g, i'}} It is assumed that: a ~ b ~ a' c \"'\" c' ; 9 ~ g' h ~ h'; i ~i'; zl ~ zl' z2 ~ z2'. Therefore {g',i} ~ {g,i'}, {g', h'} ~ {g, h}, so Yr(xl) ~ Yr(xlzl), and by similar reasoning we must have Yr(xl) ~ Yr(xlz2). We say fuzzy multivalued X ~ Y is satisfied in r2. We now propose the set of fuzzy functional and multivalued dependencies inference rules over a set of atributes U. The first three for fuzzy functional dependencies are repeat here. AI: Reflexivity for fuzzy functional dependencies (FFD) If Y ~ X then X ~ Y. A2: Augmentation for FFD If X ~ Y holds, then XZ ~ Y Z holds. A3: Transitivity for FFD If X ~ Y and Y ~ Z hold, then X ~ Z holds.\n6. 46 HO THUAN, HO CAM HA A4: Complementation for fuzzy multivalued dependencies (FMVD) If X ~ Y holds, then X ~ Z, where Z = R - XY. A5: Augmentation for FMVD If X ~ Y holds, then X Z ~ Y Z holds. A6: Transitivity for FMVD If X ~ Y and Y ~ Z hold then X ~ (Z - Y) holds. Last two axioms that relate fuzzy functional and fuzzy multivalued dependencies are also similar to classical cases. A7: If X ~ Y holds, then X ~ Y. A8: If X ~ Y holds, Z ~ Y, W n Y = 0, and W ~ Z, then X ~ Z holds. Lemma 5.1. The set of axioms (AI-A8) are sound. That is, if the fuzzy dependency (FFD or FMVD) is deduced from a set of FFDs and FMVDs, G, using the axioms, then it is true in any relation in which the dependencies of G are true. Proof. By Lemma 4.1, the axioms AI-A3 is sound. (A4) Complementation for fuzzy multivalued dependencies (FMVD) If X ~ Y holds, then X ~ Z, where Z = R - XY. We shall prove that, if for every X Z-value xz that appears in r we have Y(x) ~ Y(xz) then Z(x) ~ Z(xy) for every XY-value xy that appears in r. Obviously, Z(xy) ~ Z(x). Therefore, we only need to show v Zo(Z (x) ::Jz' E Z (xy) : Zo f'::J z'. (*) Let t, to E r, where t = (x, y, z), to = (xo, YO,zo). Since Zo E Z(x), we have Xo f'::J x, which implies, y E Y(xo). On the other hand Y(xO) ~ Y(xozo), we have also ::Jtl = \u00ab XI,YI,ZI) E r such that YI E Y (xozo) and Y f'::J YI. It means that Xo f'::J Xl, Zo f'::J Zl and Y f'::J YI. By transitivity of equivalence relation (f'::J), we get x f'::J Xl' Consider tuple tl, we found the existing of z' in (*) is pointed (let t' = td, i.e. r satisfies X ~ Z. (A7) If X ~ Y holds, then X ~ Y. We need to show Y(x) ~ Y(xz) Vt = (x, Y, y) E r. (** ) Let Yo E Y (x), clearly Xo f'::J x. Because X ~ Y is valid in r, we have Yo f'::J y. It is easy to see that Y E Y(xz) and Yo f'::J y. The proof is complete. (A8): If X ~ Y holds, Z ~ Y, W n Y = 0, and W ~ Z, then X ~ Z holds. Assume the contrary that we have a fuzzy relation r in which X ~ Y and W ~ Z hold, where Z ~ Y, W n Y = 0 but X ~ Z does not hold. Thus, ::Jtl, t2 E r such that (tdX] f'::J t2[X]) is true but (tdZ] f'::J t2[Z]) is not valid. (* * *) Obviously t2[Y] E Y(tdX]), from h[X] f'::J t2[X], Since X ~ Y holds then ::Jt3 E r : t3[Y] E Y(tdX] tdR - XY]) and t3[Y] f'::J t2[Y], which implies t3[X] f'::J tdX]' (1) t3[R - XY] f'::J tdR - XY], (2) t3[Y] f'::J t2[Y]' (3) From W n Y = 0, combining with (1) and (2), we have t3[W] f'::J tdW]. (4) From Z ~ Y and (3), we have also t3[Z] f'::J t2[Z], Since our contrary assumption (* * *) and transitivity of equivalence relation (f'::J), it can be seen that (t3[Z] f'::J tl[Z]) does not hold in r (5). But (4) and (5) contradicts W ~ Z holds in T. The proof is complete.\n7. AN APPROACH TO EXTENDING THE RELATIONAL DATABASE MODEL 47 Proof of (A5) easy to show from definition of FMVD and properties of equivalence relation (R:j). Techniques of proof for (A6) are similar to those used in [4]. We also suppose that procedure of proof for the completeness of above inference axioms is similar to the classical case. 6. CONCLUSIONS We have suggested the structure for representing uncertain information in the form of relational database. The models, which are given by B. P. Buckles and F. E. Petry [2] and by A. K. Mazumdar [1,6]' are only special cases. Based on the concept of redundancy on a set of tuples, the definitions of fuzzy dependencies (fuzzy functional dependency and fuzzy multivalued dependency) are proposed. It is interesting to note that the set of inference rules, which is similar to classical case [7], is sound and complete as well. In order to continue, we have already begun some studies: research for extending the relational algebra in this model, and extension of this model such that it allows the presence of null values too. REFERENCES [1] Bhattacharjee T. K, Mazumdar A. K., Axiomatisation of fuzzy multivalued dependencies in a fuzzy relational data model, Fuzzy Sets and Systems 96 (1998) 343-352. [2] Buckles B. P and Petry E., A fuzzy representation of data for relational databases, Fuzzy Sets and Systems 1(1980) 213-226. [3] Codd E. F., A relational model of data for large shared data banks, Commun. ACM 13 (6) (1970) 377-387. [4] Ho Thuan, Ho Cam Ha, Huynh Van Nam, Some comments about \"Axiomatisation of fuzzy multivalued dependencies in a fuzzy relational data model\", Journal of Computer Science and Cybernetics 16 (4) (2000) 30-33. [5] Petry E. and Bose P., Fuzzy Databases Principles and Applications, Kluwer Academic Publish- ers, 1996. [6] Raju K. V. and Mazumdar A. K., Functional Dependencies and lossless join decomposition of fuzzy relational database system, ACM Trans, Database System 13 (1988) 129-1966. [7] Ullman J. F., Principles of Database Systems, 2nd Ed, Computer Science Press, Rockvill, MD, 1984. [8] Zadeh L. A., Fuzzy sets, Inform. Control 12 (1965) 338-353. [9] Zadeh L. A., Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1 (1978) 3-28. Received April 10, 2001 Revised July 2, 2001 Ho Thuan - Institute of Information Technology, NCST of Viet Nam Ho Cam Ha - The Hanoi Pedagogical Institute","date":"2021-11-27 02:20:17","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8012638688087463, \"perplexity\": 4262.525789959427}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964358078.2\/warc\/CC-MAIN-20211127013935-20211127043935-00393.warc.gz\"}"} | null | null |
Top products & platforms
IBM Consulting
Design & business strategy
Hybrid multicloud services
Talent management services
IBM Garage
Technology Support Services
What is...
Developer education
Cloud platform support
Centria
Expands its services portfolio to reach out to new industries and sell to new clients
To grow its business and help its parent company Grupo Breca achieve even greater economies of scale, Centria set out to provide its shared services to a broader range of industries. To meet new clients' demands for enhanced support in logistics, inventory and more, Centria worked with IBM® Services to deploy SAP S/4HANA®.
Visit us on Facebook Visit us on Twitter Visit us on YouTube Visit us on YouTube
Learn more Watch video
Centria saw an opportunity to expand its sales to new industries in Grupo Breca, but this would demand better support for inventory and logistics. How could Centria seize this potential for growth?
Joining forces with IBM Services, Centria deployed SAP S/4HANA solutions and harmonized and streamlined key business processes to boost efficiency.
USD200k saved
from leveraging apps and dashboards in SAP Fiori
USD30k cut
in accounting costs
40% reduction
in time required for tasks such as invoice processing
Business challenge story
Centria Servicios Administrativos provides shared services for Grupo Breca, one of Peru's largest conglomerates. Historically, Centria focused on the services sector, but realized that there were tremendous opportunities for expansion in the agriculture, fishing and manufacturing sectors of Grupo Breca, too.
Erika Acosta Cueva, CIO of Centria, explains: "We have made our name supporting service-based organizations in our parent company, Grupo Breca. We recognized that if we could encourage additional Grupo Breca subsidiaries to outsource their IT to us, the subsidiaries could avoid the time and cost of maintaining their own IT landscapes, and we could generate even greater economies of scale for Grupo Breca.
"To seize this growth opportunity, we needed to adapt our business. Grupo Breca's other subsidiaries operate in a broad range of sectors – including mining, fishing and agriculture, which are very product-oriented. To meet their needs, we needed to provide better support for areas such as logistics, inventory, plant maintenance and materials management."
How could Centria extend its existing IT systems and capabilities to help serve the new non-service-sector clients? The team reviewed potential development costs and invited vendors to propose solutions to enable the new initiatives and seize the moment.
" The SAP S/4HANA solution deployed by IBM is helping me transform our business towards standardization, automation and efficiency. "
— Erika Acosta Cueva, CIO, Centria
Transformation story
Centria abandoned piecemeal development and and opted for an integrated strategy, choosing the SAP S/4HANA Enterprise Management solution, a core application covering all mission-critical processes of an enterprise. For help on the journey, Centria enlisted IBM Services.
"We decided to deploy SAP S/4HANA because the solution enabled us to deploy best-practice processes for areas like logistics and inventory out-of-the-box," recalls Erika Acosta Cueva. "To ensure a successful implementation, we wanted a partner with experience in SAP S/4HANA deployments and specifically logistics, and IBM ticked both of those boxes.
"Furthermore, IBM offered local consultants and a real partnership approach, helping us train our in-house IT team so that they could support the SAP S/4HANA solution independently in future. Additionally, IBM showed us how SAP S/4HANA could pave the way for us to offer innovations such as Internet of Things [IoT] technology to our clients in future, demonstrating a real value-add."
SAP S/4HANA Enterprise Management is natively built on the SAP HANA® database, and designed with the SAP Fiori® user experience. Specifically, Centria deployed the SAP S/4HANA Supply Chain, SAP S/4HANA for Customer Management, and SAP S/4HANA Sourcing and Procurement parts of the SAP S/4HANA Enterprise Management solution.
The IBM team helped Centria deploy SAP S/4HANA within an extremely tight timeframe and with minimal disruption to the business. Alongside the solution implementation, IBM helped Centria simplify and standardize key business processes around sales, customers and more to boost efficiency.
"This was my first time working with IBM on a project of this kind, and it went very well," remarks Erika Acosta Cueva. "The IBM project manager worked hard to keep the deployment on track, reacted fast to issues as they came up, and escalated where necessary. It definitely wasn't the kind of slow and bureaucratic process that you might expect from a vendor as large as IBM.
"As part of the implementation, IBM ran several IBM Design Thinking workshops, which proved to be particularly valuable. The Design Thinking approach helps us to focus on how the new solution and processes would affect our business and end-users, and come up with an approach that would work well for them. The workshops also prompted us to consider and address other internal issues that were not part of the project scope, but had a real impact on how well the solutions would work in practice. The findings were valuable and my team was particularly enthusiastic about the approach."
Centria previously worked with a different vendor to deploy SAP S/4HANA Finance, and that deployment included only a handful of SAP Fiori applications, giving end-users restricted scope for completing tasks on mobile devices. The IBM team redesigned the SAP S/4HANA Finance application and introduced around 20 additional SAP Fiori apps, offering greater opportunities for mobile working, and Centria now truly enjoys the benefits of this powerful solution.
Centria's SAP landscape is hosted by IBM Services in an IBM data center. The SAP environment is being migrated to IBM Power System S824L and IBM Power System S822L servers, which are respectively 48 percent and 16 percent faster per core than the current x86 servers. The servers are virtualized using IBM PowerVM® software and run the SUSE Linux Enterprise Server for SAP Applications operating system.
Data is stored on IBM Storwize® V7000 devices virtualized using IBM Spectrum Virtualize™ software. The IBM Storwize V7000 storage features the IBM Easy Tier® function, which automatically moves frequently accessed data to ultra-fast solid-state drives (SSDs) for optimal performance.
Results story
Unlocking huge efficiencies
By harnessing efficient, best-practice ways of working from IBM and SAP S/4HANA, Centria is transforming productivity.
Erika Acosta Cueva remarks: "By streamlining processes and reducing the need for manual data input into SAP, we have cut the time needed for numerous processes across diverse areas of our business by 40 percent on average. Because all data is held in SAP S/4HANA, managers can report on their respective areas more easily and gain deeper insight into operations. Reports that used to take 2 days to generate are now available instantly at the touch of a button, and managers can see live data rather than static reports.
"On top of that, end-users can complete a broader range of tasks – such as logging inventory, tracking turnover, reporting issues involving plant maintenance and generating customer account statements – from their mobile devices. Improvements like that make a real difference to the productivity of our own employees and our clients."
Centria has already achieved massive cost savings.
"Our accounting processes are so much more efficient that we have been able to reassign some staff to other departments, saving around USD 30,000 per year," elaborates Erika Acosta Cueva. "Additionally, before deploying SAP S/4HANA we had been planning to engage suppliers to develop new dashboards and mobile applications for us, at a cost of around USD 200,000. With SAP S/4HANA and SAP Fiori, we gained around 25 mobile applications plus numerous dashboards with no additional investment.
"Also, compression in the SAP HANA database has reduced our data-storage requirements by 32 percent, which in turn decreased the fees we pay for hosting. Furthermore, we have made sure that we assign full SAP licenses only to people who need them. For example, managers who only use SAP Fiori to approve purchase orders can complete that task using a more appropriate license."
The project has turned heads within Grupo Breca, as news of easier reporting and enhanced mobility has travelled fast. Additional subsidiaries have already approached Centria to ask about outsourcing their IT.
The new support for logistics, inventory and more from SAP S/4HANA will enable Centria to bring in business from Grupo Breca companies in other industries, driving growth. Centria can entice prospective clients with exciting innovations. For example, fishing and agriculture companies can install sensors in processing plants and transfer the sensor data to the SAP HANA database for real-time analytics, enabling predictive maintenance and production optimization.
Erika Acosta Cueva concludes: "The SAP S/4HANA solution deployed by IBM is helping transform our business towards standardization, automation and efficiency. With IBM and SAP at my side, I am striving for continuous improvement, and excited to see what the future will bring."
Based in Peru, Centria Servicios Administrativos provides shared services such as IT, finance and controlling to companies in the Grupo Breca conglomerate.
Solution components
GBS AD&I - EA - SAP
IBM Global Business Services
IBM-SAP Alliance
SAP S/4 HANA
Software - PowerVM (not HPC, nor VA Linux)
Storwize V7xxx
To learn more about SAP S/4HANA, visit ibm.com/services/sap/s4hana
Ready to get started? Schedule a consultation with one of our IBM SAP experts: ibm.biz/gbssap4hanana-scheduler
View more client stories or learn more about IBM Services
What is Hybrid Cloud?
What are Containers?
Support - Download fixes, updates & drivers
Partner with us - PartnerWorld
Training - Courses
Security, privacy & trust
Contact IBM
© Copyright IBM Corporation 2018. 1 New Orchard Road, Armonk, New York 10504-1722 United States. Produced in the United States of America, September 2018.
IBM, the IBM logo, IBM Spectrum Virtualize, PowerVM, Storwize, and ibm.com are trademarks of International Business Machines Corp., registered in many jurisdictions worldwide. Other product and service names might be trademarks of IBM or other companies. A current list of IBM trademarks is available on the web at "Copyright and trademark information" at ibm.com/legal/copytrade.shtml.
Not all offerings are available in every country in which IBM operates.
The performance data and client examples cited are presented for illustrative purposes only. Actual performance results may vary depending on specific configurations and operating conditions.
All client examples cited or described are presented as illustrations of the manner in which some clients have used IBM products and the results they may have achieved. Actual environmental costs and performance characteristics will vary depending on individual client configurations and conditions. Contact IBM to see what we can do for you.
The client is responsible for ensuring compliance with laws and regulations applicable to it. IBM does not provide legal advice or represent or warrant that its services or products will ensure that the client is in compliance with any law or regulation.
© 2018 SAP SE. All rights reserved. SAP, R/3, SAP NetWeaver, Duet, PartnerEdge, ByDesign, SAP BusinessObjects Explorer, StreamWork, SAP HANA, and other SAP products and services mentioned herein as well as their respective logos are trademarks or registered trademarks of SAP SE in Germany and other countries. These materials are provided by SAP SE or an SAP affiliate company for informational purposes only, without representation or warranty of any kind, and SAP SE or its affiliated companies shall not be liable for errors or omissions with respect to the materials. This document, or any related presentation, and SAP SE's or its affiliated companies' strategy and possible future developments, products, and/or platform directions and functionality are all subject to change and may be changed by SAP SE or its affiliated companies at any time for any reason without notice. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,616 |
Q: AsyncStorage React Native not working I'm trying to keep the user logged in to my app, so I made the following the user log in.
AsyncStorage.setItem('@MyStorage:Token', res.data.accessToken)
AsyncStorage.setItem('@MyStorage:Flag', true)
And I tried to do so to validate every time I enter the login page
componentWillMount() {
this._validate()
}
_validate = async () => {
try {
const value = await AsyncStorage.getItem('@MyStorage:Flag')
console.log(value)
} catch(e) {
console.log(e)
}
}
But none of the console.log() is returned, what would be the best way to do this?
A: Make sure you actually call setItem() before calling getItem(). In particular, React doesn't support async component lifecycle methods, so you should be very careful about using async/await with React.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 799 |
\section{Introduction}
Recent advances in biological physics have led to the discovery of quantitative relations, or ``laws,'' describing bacterial growth~\cite{Klumpp2008, ScottHwaReview, KlumppPNAS, Pugatch, Alon1, Alon2}, gene expression~\cite{Salman,AmirNatComm}, and cell size control~\cite{AmirPRL,Taheri-Araghi}; see Ref.~\cite{JunReview} for a review and historical perspective. Whether similar relations apply to Eukarya, a domain of life that is evolutionarily distant from Bacteria, remains unclear. Eukarya and Bacteria differ in many ways; with respect to cellular organization, Eukarya contain membrane-bound organelles such as nuclei and mitochondria that Bacteria lack altogether. This spatial partitioning of the eukaryotic cell affects numerous processes involving the transport of essential macromolecules. One such process is the generation of new ribosomes, termed ribosome biogenesis, where ribosomes are the central macromolecular machines of protein synthesis in the cell. In Eukarya, ribosome biogenesis requires that ribosomal subunits be transported from the nucleolus to the nucleoplasm, and eventually to the cytoplasm via nuclear pores, while simultaneously undergoing maturation~\cite{Woolford, Henras, Thomson}. The eukaryotic ribosome is also substantially larger than its bacterial counterpart, having 25 proteins which have no equivalent in bacterial ribosomes~\cite{BenShem}. Furthermore, in contrast to a few non-essential assembly factors in Bacteria, ribosome assembly in yeast, a unicellular eukaryote, requires about 200 accessory proteins which do not even form part of the mature ribosome. If just one accessory protein is missing, ribosome biogenesis cannot proceed~\cite{Karbstein,Dinman}.
In light of these additional complexities, it is not surprising that quantitative relations for eukaryotic growth are still lacking. An indication that it might be possible to generalize certain bacterial growth-laws to lower (unicellular) Eukarya was reported in 2017 by Metzl-Raz et al.~\cite{Barkai}. There the authors demonstrated that ribosomal proteome fractions in budding yeast are proportional to cellular growth rates, as previously observed for Bacteria~\cite{Scott2010,Scott}. Underlying this proportionality is the coupling between cell growth and ribosome biogenesis~\cite{Dai}, i.e. that cell doubling requires a commensurate doubling of ribosomes. The latter leads to an autocatalytic loop and a fundamental bound on cellular growth rates since ribosomal proteins (r-proteins) can only be made by other ribosomes~\cite{Bionum, Dill, REP}.
The important discovery made in Ref.~\cite{Barkai} supports the notion that ribosome biogenesis is growth-limiting in Eukarya just as in Bacteria. Cytoplasmic ribosomes are not only composed of r-protein though; in fact, their main constituent is ribosomal RNA (rRNA). In Bacteria, rRNA is produced by RNA polymerases (RNAPs), which in turn are made by ribosomes. We recently showed that this process leads to another bound on cellular growth rates and to growth-laws which were verified for the bacterium \textit{E. coli}~\cite{KR,Speed-Limit}. But rRNA production in Eukarya diverges from that in Bacteria: Bacteria have just one kind of RNAP in the cell while Eukarya have at least three, two of which -- RNA polymerase I (RNAP I) and RNA polymerase III (RNAP III) -- are involved in the production of rRNA. Moreover, the coordination mechanisms of rRNA and r-protein production in Eukarya are entirely different from Bacteria~\cite{NomuraThoughts}. Yet, despite the greater complexity, here we show that simple growth-laws can still be established for Eukarya.
In this work, we provide a model of ribosome biogenesis in lower Eukarya and study its implications for cell physiology and growth. The analysis yields two growth-laws and two invariants which are the first of their kind for Eukarya. We then corroborate the relations using currently available data for the model organism \textit{S. cerevisiae} (budding yeast), and discuss additional data that will be needed for full verification of all the relations. The growth-laws and invariants offer quantitative predictions and provide a theoretical framework for future studies on \textit{S. cerevisiae} and similar organisms. Our work suggests that the ribosome composition in \textit{S. cerevisiae} is optimized for cell growth as in \textit{E. coli}, but more data are required for verification.
The remainder of this paper is structured as follows. In Section~\ref{II}, we mathematically formulate the kinetics of ribosome production in lower Eukarya. From these equations we obtain upper bounds on the cellular growth rate, which are given in Section~\ref{III}. We show that the bounds are uniquely maximized for a specific ribosome composition in Section~\ref{IV}. Growth rate maximization yields three distinct growth-laws, which are derived in Section~\ref{V}. These include the already known proportionality between r-protein fractions and growth rates, as well as two additional growth-laws for RNAP I and RNAP III which make rRNA in eukaryotic cells. The growth-laws, in turn, yield two invariants. These conserved quantities, which illustrate the coordination of rRNA and r-protein production in the cell, are discussed in Section~\ref{VI}. In Section~\ref{VII}, we provide a physical interpretation of the growth-laws and invariants in terms of proteome fractions. Section~\ref{VIII} offers a case study of the model organism \textit{S. cerevisiae}, showing that predictions from the growth-laws are consistent with currently available data. The analysis offers quantitative predictions for, e.g., the number of ribosomes in the cell, the number of RNAPs I and RNAPs III required for rRNA production, and the coupling between the rates of translation, transcription, and cell growth. Finally, we discuss application of the invariants to determine activities of RNAPs I and III once their proteome fractions are known to better accuracy. Section~\ref{conc} concludes this work with a discussion on future research directions. More detailed derivations, and data for the case study of \textit{S. cerevisiae}, are provided in the Appendices.
\section{Kinetics of ribosome biogenesis}
\label{II}
Ribosomes are critical to cellular growth since they produce all protein in the cell, where protein comprises the largest fraction ($\sim \! 40$\%) of the cell's dry mass~\cite{Bionum} (BNID: 104157). These protein-producing machines are ubiquitous: a rapidly growing yeast cell contains more than 200,000 ribosomes~\cite{Warner, WaldronLacroute75}. Ribosomes, in turn, are composed of ribosomal protein (r-protein) and ribosomal RNA (rRNA), which account for large fractions of the cell's proteome and RNA content. For example, in \textit{S.~cerevisiae}, r-protein and rRNA are estimated to comprise up to a third of the proteome mass~\cite{Barkai} and $\sim \! 80$\% of the total RNA mass~\cite{Warner}, respectively. To better understand the kinetics of ribosome biogenesis, we proceed to
write a set of differential equations describing the average production rates of r-protein and rRNA in the cell.
\begin{figure}[t!]
\begin{centering}
\includegraphics[width=0.5 \textwidth]{autocatalyticloops_cartoon_v2.pdf}
\end{centering}
\vspace{-5mm}
\caption{\textbf{Ribosome biogenesis in lower Eukarya.} Ribosomal protein (r-protein) is synthesized directly by ribosomes, as illustrated by the autocatalytic loop on the right. Meanwhile ribosomal RNA (rRNA) is synthesized by RNA polymerases I and III, symbolized by the top left arrows. In lower Eukarya, RNA polymerase I generates the 35S precursor rRNA which later yields the mature 25S, 18S, and 5.8S rRNAs, while RNA polymerase III generates the 5S rRNA. RNA polymerases, in turn, are made of protein that is synthesized by ribosomes (bottom left arrows). Here we show that these autocatalytic processes give rise to multiple growth-laws and invariants that characterize central aspects of eukaryotic cell growth.}
\label{yeastautocatalytic}
\end{figure}
Ribosomes make r-protein directly (Fig.~\ref{yeastautocatalytic}). The r-protein production rate, measured in amino acids per unit time, can be written as
\begin{equation}
\frac{d(\text{r-protein})}{dt} = k_{\text{ribo}} \, \phi^{\text{r-prot}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \cdot N_{\text{ribo}},
\label{rproteindiffeq}
\end{equation}
where $N_{\text{ribo}}$ is the number of ribosomes in the cell, $f^{\text{active}}_{\text{ribo}}$ is the fraction of ribosomes which are active, $\phi^{\text{r-prot}}_{\text{ribo}}$ is the fraction of active ribosomes making specifically r-protein, and $k_{\text{ribo}}$ is the average peptide elongation rate of an active ribosome. During exponential growth, there is little to no protein degradation~\cite{MiloBook,ProteinDegradation}, and so Eq.~(\ref{rproteindiffeq}) describes the accumulation rate of r-protein in the cell. Note that the fraction of active ribosomes making specifically r-protein, $\phi^{\text{r-prot}}_{\text{ribo}}$, is equivalent to the time fraction an active ribosome spends synthesizing r-protein. These two interpretations are based on either an ensemble or time average: The latter entails tracking the time an active ribosome spends on r-protein synthesis, where time fractions are obtained by averaging over long times, i.e. spanning many cell generations. In the ensemble picture, the fraction of active ribosomes engaged in r-protein synthesis is instead estimated from snapshots of the cell taken at arbitrary times.
\begin{figure*}[t!]
\begin{centering}
\includegraphics[width=0.75\textwidth]{rRNAprocessing_v4.pdf}
\end{centering}
\vspace{-2mm}
\caption{\textbf{Transcription and processing of rRNA.} RNAP I (green) transcribes the 35S pre-rRNA from the ribosomal DNA (rDNA) locus, while the RNAP III (blue) separately transcribes the 5S rRNA (121 nucleotides long). In yeast, the 35S pre-rRNA contains a total of 1504 spacer nucleotides from: ITS1 (361 nt), ITS2 (232 nt), 5'ETS (700 nt), and 3'ETS (211 nt)~\cite{SGD}, where ITS and ETS denote an internally transcribed spacer and an externally transcribed spacer, respectively. These spacer nucleotides are later processed away to yield the mature 35S-derived rRNAs (collectively abbreviated as m35S): 18S (1800 nt), 5.8S (158 nt), and 25S (3396 nt)~\cite{Woolford}.}
\label{rRNAprocessing}
\end{figure*}
To make rRNA, which is the main constituent of cytoplasmic ribosomes, eukaryotic cells use two types of RNAPs: RNAP I and RNAP III (Fig.~\ref{yeastautocatalytic}, Fig.~\ref{rRNAprocessing}). RNAPs themselves are composed solely of protein, and so equations for the accumulation rates of RNAP I- and RNAP III-protein can be written similarly to the above:
\begin{eqnarray}
\frac{d(\text{RPI-protein})}{dt} = k_{\text{ribo}} \, \phi^{\text{RPI}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \cdot N_{\text{ribo}} \label{RNAPIdiffeq} \, , \\
\frac{d(\text{RPIII-protein})}{dt} = k_{\text{ribo}} \, \phi^{\text{RPIII}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \cdot N_{\text{ribo}} \, , \label{RNAPIIIdiffeq}
\end{eqnarray}
where in Eq.~(\ref{RNAPIdiffeq}) we have used the fraction $\phi^{\text{RPI}}_{\text{ribo}}$ of active ribosomes dedicated to the synthesis of RNAP I-protein, and in Eq.~(\ref{RNAPIIIdiffeq}) the fraction $\phi^{\text{RPIII}}_{\text{ribo}}$ of active ribosomes dedicated to RNAP III-protein synthesis.
The production rates of the mature 18S, 25S, and 5.8S rRNAs, which are generated by RNAP I, and of the 5S rRNA generated by RNAP III, can be expressed in nucleotides per unit time as:
\begin{eqnarray}
\frac{d(\text{m35S})}{dt} = k_{\text{RPI}} \, \phi^{\text{m35S}}_{\text{RPI}} \, f^{\text{active}}_{\text{RPI}} \cdot N_{\text{RPI}} \, , \label{35Sdiffeq} \\
\frac{d(\text{5S})}{dt} = k_{\text{RPIII}} \, \phi^{\text{5S}}_{\text{RPIII}} \, f^{\text{active}}_{\text{RPIII}} \cdot N_{\text{RPIII}} \, , \label{5Sdiffeq}
\end{eqnarray}
where m35S on the left-hand side of Eq.~(\ref{35Sdiffeq}) represents the number of nucleotides in all mature 35S-derived rRNAs in the cell, i.e. the 18S, 25S and 5.8S rRNAs, while 5S in Eq.~(\ref{5Sdiffeq}) denotes the number of nucleotides in all 5S rRNAs in the cell (Fig.~\ref{rRNAprocessing}). In addition,
$N_{\text{RPI}}$ and $N_{\text{RPIII}}$ represent the number of RNA polymerases I and III, respectively; the fraction of RNAPs I that are active is given by $f^{\text{active}}_{\text{RPI}}$, and $f^{\text{active}}_{\text{RPIII}}$ is the active fraction of RNAPs III. The quantity $\phi^{\text{m35S}}_{\text{RPI}}$ denotes the fraction of active RNAPs I making 18S, 25S, and 5.8S rRNAs (spacer nucleotides not included), while $\phi^{\text{5S}}_{\text{RPIII}}$ is the fraction of active RNAPs III making 5S rRNA. Finally, $k_{\text{RPI}}$ and $k_{\text{RPIII}}$ are the average rRNA chain elongation (transcription) rates of an active RNAP I and an active RNAP III, respectively.
\section{Upper bounds on cellular growth rate}
\label{III}
The number of ribosomes $N_{\text{ribo}}$ in the cell can be approximated as
\begin{eqnarray}
N_{\text{ribo}} \simeq \frac{\text{r-protein}}{N^{\text{a.a.}}_{\text{ribo}}},
\label{Nriboapprox1}
\end{eqnarray}
where r-protein is measured in units of the number of amino acids per cell, while $N_{\text{ribo}}^{\text{a.a.}}$ is the number of amino acids in the ribosome. Similarly, one can estimate $N_{\text{ribo}}$ as
\begin{eqnarray}
N_{\text{ribo}} \simeq \frac{\text{m35S}}{N^{\text{nucl}}_{\text{m35S}}} \simeq \frac{\text{5S}}{N^{\text{nucl}}_{\text{5S}}} \, , \label{Nriboapprox2}
\end{eqnarray}
where $N^{\text{nucl}}_{\text{m35S}}$ is the combined total number of nucleotides in the 18S, 25S, 5.8S rRNAs, while $N^{\text{nucl}}_{\text{5S}}$ is the number of nucleotides per 5S rRNA. It is important to note that $N^{\text{nucl}}_{\text{m35S}}$ does not include flanking or spacer nucleotides in the 35S-precursor rRNA, as they are cleaved away during rRNA processing (see Fig.~\ref{rRNAprocessing}). Eqs.~(\ref{Nriboapprox1}) and (\ref{Nriboapprox2}) provide overestimates of $N_{\text{ribo}}$ since all r-protein and rRNA in the cell is assumed to be fully assembled into ribosomes. This can be compensated for, however, by the ribosomal activity $f^{\text{active}}_{\text{ribo}}$, which accounts for nascent r-protein and rRNA as inactive.
Similarly, we approximate the number of RNAPs I and III as
\begin{eqnarray}
N_{\text{RPI}} \simeq \frac{\text{RPI-protein}}{N^{\text{a.a.}}_{\text{RPI}}} \, , \label{RNAPIapprox}\\
N_{\text{RPIII}} \simeq \frac{\text{RPIII-protein}}{N^{\text{a.a.}}_{\text{RPIII}}} \, ,
\label{RNAPIIIapprox}
\end{eqnarray}
where the numerators are the number of amino acids in RNAP I-protein and RNAP III-protein in the cell, respectively. Meanwhile the denominators $N^{\text{a.a.}}_{\text{RPI}}$ and $N^{\text{a.a.}}_{\text{RPIII}}$ are the number of amino acids in each RNAP I and each RNAP III, respectively. Again, note that Eq.~(\ref{RNAPIapprox}) and Eq.~(\ref{RNAPIIIapprox}) provide overestimates of $N_{\text{RPI}}$ and $N_{\text{RPIII}}$.
Equations~(\ref{rproteindiffeq})--(\ref{5Sdiffeq}) can be simplified using the approximations of Eqs.~(\ref{Nriboapprox1})--(\ref{RNAPIIIapprox}) to give upper bounds on protein and rRNA production rates in the cell. Substituting Eq.~(\ref{Nriboapprox1}) into Eq.~(\ref{rproteindiffeq}) then yields
\begin{equation}
\frac{d(\text{r-protein})}{dt} = k_{\text{ribo}} \, \phi^{\text{r-prot}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \cdot \frac{\text{r-protein}}{N^{\text{a.a.}}_{\text{ribo}}} \, ,
\end{equation}
whose solution is exponential for balanced growth, in which the parameters $k_{\text{ribo}}$, $\phi^{\text{r-prot}}_{\text{ribo}}$, $f^{\text{active}}_{\text{ribo}}$ are constant by definition. The cellular growth rate $\mu$ is then bounded by
\begin{equation}
\mu \equiv \frac{\ln(2)}{T_d} \leq \frac{k_{\text{ribo}} \, \phi^{\text{r-prot}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}}{N^{\text{a.a.}}_{\text{ribo}}} \, ,
\label{bound1}
\end{equation}
where $T_{d}$ is the cellular doubling time. In the bacterium \textit{E. coli}, it was shown that Eq.~(\ref{bound1}) is not only a bound but in fact an approximate equality~\cite{KR}. The resulting proportionality between the r-protein proteome fraction $\phi^{\text{r-prot}}_{\text{ribo}}$ and the cellular growth rate $\mu$ has been called a ``growth-law of ribosome synthesis''~\cite{JunReview, Scott2010}. In yeast, the same proportionality was established by Kief \& Warner~\cite{KiefWarner} and more comprehensively by Metzl-Raz, et al.~\cite{Barkai}, but the proportionality factor $k_{\text{ribo}}f^{\text{active}}_{\text{ribo}}/N^{\text{a.a.}}_{\text{ribo}}$ in Eq.~(\ref{bound1}) still requires direct experimental verification. Note that the latter need not be constant for $\phi^{\text{r-prot}}_{\text{ribo}} \propto \mu$ to hold. This important point, which is often overlooked, will be discussed further in Section~\ref{VIII}.
Two additional bounds on the cellular growth rate can be derived by making a similar substitution of Eq.~(\ref{Nriboapprox1}) in Eqs.~(\ref{RNAPIdiffeq}) and (\ref{RNAPIIIdiffeq}):
\begin{eqnarray}
\frac{d(\text{RPI-protein})}{dt} = k_{\text{ribo}} \, \phi^{\text{RPI}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \cdot \frac{\text{r-protein}}{N^{\text{a.a.}}_{\text{ribo}}} \, , \label{RNAPIsub} \\
\frac{d(\text{RPIII-protein})}{dt} = k_{\text{ribo}} \, \phi^{\text{RPIII}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \cdot \frac{\text{r-protein}}{N^{\text{a.a.}}_{\text{ribo}}}, \label{RNAPIIIsub}
\end{eqnarray}
\noindent and using the approximations of Eqs.~(\ref{RNAPIapprox})--(\ref{RNAPIIIapprox}) in Eqs.~(\ref{35Sdiffeq})--(\ref{5Sdiffeq}):
\begin{eqnarray}
\frac{d(\text{m35S})}{dt} = k_{\text{RPI}} \, \phi^{\text{m35S}}_{\text{RPI}} \, f^{\text{active}}_{\text{RPI}} \cdot \frac{\text{RPI-protein}}{N^{\text{a.a.}}_{\text{RPI}}} \, , \label{35SdiffeqwRNAPapprox} \\
\frac{d(\text{5S})}{dt} = k_{\text{RPIII}} \, \phi^{\text{5S}}_{\text{RPIII}} \, f^{\text{active}}_{\text{RPIII}} \cdot \frac{\text{RPIII-protein}}{N^{\text{a.a.}}_{\text{RPIII}}}. \label{5SdiffeqwRNAPapprox}
\end{eqnarray}
Taking a time derivative of Eqs.~(\ref{35SdiffeqwRNAPapprox})--(\ref{5SdiffeqwRNAPapprox}) and using Eqs.~(\ref{RNAPIsub})--(\ref{RNAPIIIsub}) for the production rates of RNAP I- and RNAP III-protein, together with the approximations of Eqs.~(\ref{Nriboapprox1})--(\ref{Nriboapprox2}), then yields
\begin{align}
& \frac{d^{2}(\text{m35S})}{dt^{2}} = \frac{k_{\text{RPI}} \, \phi^{\text{m35S}}_{\text{RPI}} \, f^{\text{active}}_{\text{RPI}}}{ N^{\text{a.a.}}_{\text{RPI}}} \cdot \frac{k_{\text{ribo}} \, \phi^{\text{RPI}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}}{N^{\text{nucl}}_{\text{m35S}}} \cdot \text{m35S} \, , \label{35Sorder2diffeq}\\
& \frac{d^{2}(\text{5S})}{dt^{2}} = \frac{k_{\text{RPIII}} \, \phi^{\text{5S}}_{\text{RPIII}} \, f^{\text{active}}_{\text{RPIII}}}{N^{\text{a.a.}}_{\text{RPIII}}} \cdot \frac{k_{\text{ribo}} \, \phi^{\text{RPIII}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}}{N^{\text{nucl}}_{\text{5S}}} \cdot \text{5S}. \label{5Sorder2diffeq}
\end{align}
The exponential solutions of Eqs.~(\ref{35Sorder2diffeq})--(\ref{5Sorder2diffeq}) reveal that the cellular growth rate $\mu$ is bounded by
\begin{equation}
\mu \leq \sqrt{\frac{k_{\text{RPI}} \, \phi^{\text{m35S}}_{\text{RPI}} \, f^{\text{active}}_{\text{RPI}}}{ N^{\text{a.a.}}_{\text{RPI}}} \cdot \frac{k_{\text{ribo}} \, \phi^{\text{RPI}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}}{N^{\text{nucl}}_{\text{m35S}}}} \, ,
\label{bound2}
\end{equation}
and
\begin{equation}
\mu \leq \sqrt{\frac{k_{\text{RPIII}} \, \phi^{\text{5S}}_{\text{RPIII}} \, f^{\text{active}}_{\text{RPIII}}}{N^{\text{a.a.}}_{\text{RPIII}}} \cdot \frac{k_{\text{ribo}} \, \phi^{\text{RPIII}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}}{N^{\text{nucl}}_{\text{5S}}}} \, .
\label{bound3}
\end{equation}
In contrast to bacteria, which have just one type of RNA polymerase and thus one bound on cellular growth rate originating from the production of rRNA~\cite{KR}, lower Eukarya must satisfy two bounds -- one originating from each type of RNA polymerase producing rRNA.
\begin{figure*}[t!]
\begin{centering}
\includegraphics[width=0.75\textwidth]{Fig3_v5.pdf}
\end{centering}
\vspace{-2mm}
\caption{\textbf{Bounds on cellular growth rate from the production of r-protein (orange), 35S-derived rRNA (green), and 5S rRNA (blue). (a)} We plot the three bounds [Eqs.~(\ref{bound1xy}), (\ref{bound2xy}), (\ref{bound3xy})] versus $x_{\text{prot}}$, the mass fraction of the ribosome which is r-protein [Eq.~(\ref{xdef})], and versus $x_{\text{m35S}}$, the mass fraction of the ribosome which is mature 35S-derived rRNA [Eq.~(\ref{ydef})]. Each surface in the $x_{\text{prot}}$-$x_{\text{m35S}}$-$\mu$ space corresponds to one of the three bounds. They are made partially transparent so that their intersections are visible. \textbf{(b)} Plotted is the minimum of all surfaces for every possible $x_{\text{prot}}$ and $x_{\text{m35S}}$. Accessible growth rates lie in the shaded regions below the surfaces. Each shaded region is colored according to its most restricting bound. \textbf{(c)} Side view of the minimal surfaces which intersect to form a cusp, marked by the red point. This point corresponds to the maximal cellular growth rate permitted by the three bounds. \textbf{(d)} The point where all three bounds intersect is clearly seen when viewed from below the bounds. For visual clarity we chose the intersection point to lie further in the interior of the $x_{\text{prot}}$-$x_{\text{m35S}}$ plane; in reality it will lie closer to the diagonal line ($x_{\text{m35S}}=1-x_{\text{prot}}$) since the mass fraction of 5S rRNA, $1-x_{\text{prot}}-x_{\text{m35S}}$, is small. The parameter values used to generate this figure are available in Appendix~\ref{B}.}
\label{surfaces}
\end{figure*}
\section{Graphical representation of bounds}\label{IV}
The derived bounds can be expressed in terms of two variables describing ribosome composition: $x_{\text{prot}}$, the mass fraction of the ribosome which is protein, and $x_{\text{m35S}}$, the mass fraction of the ribosome which is mature rRNA derived from the 35S precursor (18S, 25S, 5.8S rRNAs). Defining the ribosome mass as $M_{\text{ribo}} \simeq N^{\text{a.a.}}_{\text{ribo}} \, m_{\text{a.a.}} + N^{\text{nucl}}_{\text{m35S}} \, m_{\text{nucl}} + N^{\text{nucl}}_{\text{5S}} \, m_{\text{nucl}}$, where $m_{\text{a.a.}}$ and $m_{\text{nucl}}$ are the average masses of an amino acid and nucleotide in the cell, respectively, gives \begin{equation}
x_{\text{prot}} = \frac{N^{\text{a.a.}}_{\text{ribo}} \, m_{\text{a.a.}}}{M_{\text{ribo}}} \, .
\label{xdef}
\end{equation}
The bound of Eq.~(\ref{bound1}) then becomes
\begin{equation}
\mu \leq \frac{m_{\text{a.a.}}}{M_{\text{ribo}}} \cdot \frac{k_{\text{ribo}} \, \phi_{\text{ribo}}^{\text{r-prot}} \, f^{\text{active}}_{\text{ribo}}}{x_{\text{prot}}} \, .
\label{bound1xy}
\end{equation}
Furthermore, the mass fraction of the ribosome which is rRNA, $1-x_{\text{prot}}$, can be partitioned into 35S-derived and 5S rRNA masses. Defining $x_{\text{m35S}}$ as the mass fraction of the former, i.e. the 18S, 25S, and 5.8S rRNAs,
\begin{equation}
x_{\text{m35S}} = \frac{N^{\text{nucl}}_{\text{m35S}} \, m_{\text{nucl}}}{M_{\text{ribo}}},
\label{ydef}
\end{equation}
yields $N^{\text{nucl}}_{\text{m35S}} = \frac{M_{\text{ribo}}}{m_{\text{nucl}}} \cdot x_{\text{m35S}}$ and $N^{\text{nucl}}_{\text{5S}} = \frac{M_{\text{ribo}}}{m_{\text{nucl}}} \cdot (1-x_{\text{prot}}-x_{\text{m35S}})$. Substituting these relations into the remaining two bounds of Eqs.~(\ref{bound2})--(\ref{bound3}) yields
\begin{equation}
\mu \leq \sqrt{\frac{k_{\text{RPI}} \, \phi^{\text{m35S}}_{\text{RPI}} \, f^{\text{active}}_{\text{RPI}}}{ N^{\text{a.a.}}_{\text{RPI}}} \cdot \frac{m_{\text{nucl}}}{M_{\text{ribo}}} \cdot \frac{k_{\text{ribo}} \, \phi^{\text{RPI}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}}{x_{\text{m35S}}}} \, ,
\label{bound2xy}
\end{equation}
\begin{equation}
\mu \leq \sqrt{\frac{k_{\text{RPIII}} \, \phi^{\text{5S}}_{\text{RPIII}} \, f^{\text{active}}_{\text{RPIII}}}{N^{\text{a.a.}}_{\text{RPIII}}} \cdot \frac{m_{\text{nucl}}}{M_{\text{ribo}}} \cdot \frac{k_{\text{ribo}} \, \phi^{\text{RPIII}}_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}}{1-x_{\text{prot}}-x_{\text{m35S}}}} \, .
\label{bound3xy}
\end{equation}
The functional forms of the three bounds are thus $\mu \leq a/x_{\text{prot}}$ [Eq.~(\ref{bound1xy})], $\mu \leq b/\sqrt{x_{\text{m35S}}}$ [Eq.~(\ref{bound2xy})], and $\mu \leq c/\sqrt{1-x_{\text{prot}}-x_{\text{m35S}}}$ [Eq.~(\ref{bound3xy})], where $a$, $b$, and $c$ are positive constants.
A set of bounds is unique to its particular growth condition, as every growth condition specifies different values of the constants $\{a, b, c\}$. For a given growth condition, each bound defines a surface in the three-dimensional $x_{\text{prot}}$-$x_{\text{m35S}}$-$\mu$ space, as illustrated in Fig.~\ref{surfaces}a. The volume which lies under the union of these three surfaces represents cellular growth rates accessible to the organism, as a function of ribosome composition (Fig.~\ref{surfaces}b). The maximal cellular growth rates mutually satisfying two bounds are defined by the line which intersects the two corresponding surfaces. Hence there are three lines defined by the three possible pairs of bounds (Fig.~\ref{surfaces}c), which can be written parametrically in terms of one free variable, e.g. $x_{\text{prot}}$ or $x_{\text{m35S}}$ (Appendix \ref{A}). The point at which the three lines intersect, i.e. the cusp of the union of the three surfaces, is obtained at an optimal ribosome composition that defines the maximum possible cellular growth rate satisfying all three bounds (Fig.~\ref{surfaces}c). This point, where all three surfaces meet, is clearly seen when viewed from below (Fig.~\ref{surfaces}d).
A set of bounds from ribosome biogenesis, similar to those derived above, was first obtained for bacteria~\cite{KR}. There, it was shown that the $1:2$ protein to RNA mass ratio in the \textit{E. coli} ribosome is optimal in that it offers the maximal growth rate permitted by the bounds in a variety of growth conditions. A similar principle may also apply to Eukarya, but direct verification of this hypothesis is currently not possible due to missing data. Verification will require simultaneous measurements of the growth rate and all parameters in Eqs.~(\ref{bound1xy}), (\ref{bound2xy}), and (\ref{bound3xy}), in various growth conditions. However, even for a well-studied model organism like \textit{S. cerevisiae}, such a dataset is currently unavailable.
The situation described above calls for comprehensive measurements of biologically relevant kinetic and physiological parameters in the yeast \textit{S. cerevisiae} and in other Eukarya, similar to those done for \textit{E. coli}~\cite{BremerDennis}. While collecting such data is expected to be challenging and time-consuming, it will significantly advance our understanding of yeast, and more generally, of Eukarya. In the case of \textit{E. coli}, a comprehensive dataset was key in recognizing that the bacterium achieves the maximal growth rate permitted by ribosome biogenesis. This finding led to a previously unrecognized growth-law and an invariant of bacterial growth~\cite{KR}. In lieu of complete datasets for Eukarya like \textit{S. cerevisiae}, we posit that their bounds can also be considered as approximate equalities, just as in Bacteria. It yields a number of insights: In the following sections, we derive growth-laws and invariants for Eukarya, showing that the resulting predictions are in good agreement with currently available data. These results self-consistently support the postulate of growth rate maximization, and shed new light on the coordination of transcription and translation kinetics as required by ribosome biogenesis. It also allows one to deduce numerical values of unknown kinetic and physiological parameters in the yeast \textit{S. cerevisiae}.
\section{Growth-laws from growth rate maximization}
\label{V}
In analogy to the bacterial case, we interpret the upper bounds of Eq.~(\ref{bound1}) and Eqs.~(\ref{bound2})--(\ref{bound3}) as approximate equalities. Eq.~(\ref{bound1}) then simplifies to
\begin{equation}
\boxed{ \tau_{\text{r-prot}} \cdot \mu \simeq f^{\text{active}}_{\text{ribo}} \, \phi^{\text{r-prot}}_{\text{ribo}}} \, ,
\label{growthlaw1}
\end{equation}
where on the left-hand side we have defined $\tau_{\text{r-prot}} = N^{\text{a.a.}}_{\text{ribo}} / k_{\text{ribo}} $ as the average time it takes a ribosome to synthesize a full set of r-proteins.
Two other relations, or ``growth-laws,'' result from the three bounds found earlier, assuming that cells achieve the optimal growth rate. For example, squaring Eqs.~(\ref{bound1}) and (\ref{bound2}) and setting their right-hand sides equal, while keeping one power of $\mu$ from Eq.~(\ref{bound1}), yields
\begin{equation}
\boxed{\tau_{\text{m35S}} \cdot \mu \simeq \frac{(\phi^{\text{m35S}}_{\text{RPI}} \, f^{\text{active}}_{\text{RPI}} \phi^{\text{RPI}}_{\text{ribo}} ) \, / N^{\text{a.a.}}_{\text{RPI}} }{\phi^{\text{r-prot}}_{\text{ribo}} / N^{\text{a.a.}}_{\text{ribo}}}} \, ,
\label{growthlaw2}
\end{equation}
where we have defined $\tau_{\text{m35S}} = N^{\text{nucl}}_{\text{m35S}} / k_{\text{RPI}}$ as the average time it takes an RNAP I to synthesize a set of 18S, 25S, 5.8S rRNAs. Similarly, defining $\tau_{\text{5S}} = N^{\text{nucl}}_{\text{5S}} / k_{\text{RPIII}} $ as the average time for an RNAP III to synthesize a 5S rRNA, from Eqs.~(\ref{bound1}) and (\ref{bound3}) we obtain
\begin{equation}
\boxed{\tau_{\text{5S}} \cdot \mu \simeq \frac{ (\phi^{\text{5S}}_{\text{RPIII}} \, f^{\text{active}}_{\text{RPIII}} \, \phi^{\text{RPIII}}_{\text{ribo}}) / N^{\text{a.a.}}_{\text{RPIII}} }{\phi^{\text{r-prot}}_{\text{ribo}} / N^{\text{a.a.}}_{\text{ribo}}}} \, .
\label{growthlaw3}
\end{equation}
A simple physical interpretation of the growth-laws in Eqs.~(\ref{growthlaw2}) and (\ref{growthlaw3}) will be discussed in a subsequent section.
\section{Invariants of cellular growth}
\label{VI}
To eliminate the explicit dependence on growth rate in the relations derived above, we divide the first growth-law [Eq.~(\ref{growthlaw1})] by the second [Eq.~(\ref{growthlaw2})], and multiply the numerator and denominator of the left-hand side by $m_{\text{nucl}} \, m_{\text{a.a.}}$. Recognizing that $ m_{\text{a.a.}} N^{\text{a.a.}}_{\text{ribo}} = x_{\text{prot}} \, M_{\text{ribo}}$ and $m_{\text{nucl}} N^{\text{nucl}}_{\text{m35S}} = x_{\text{m35S}} \, M_{\text{ribo}}$, we obtain:
\begin{equation}
\boxed{\frac{x_{\text{prot}}}{x_{\text{m35S}}} \simeq \frac{m_{\text{a.a.}}}{m_{\text{nucl}}} \cdot \frac{N^{\text{a.a.}}_{\text{RPI}}}{N^{\text{a.a.}}_{\text{ribo}}} \cdot \frac{k_{\text{ribo}} }{k_{\text{RPI}}} \cdot \frac{\phi^{\text{r-prot}}_{\text{ribo}} f^{\text{active}}_{\text{ribo}} \phi^{\text{r-prot}}_{\text{ribo}}}{\phi^{\text{m35S}}_{\text{RPI}} \, f^{\text{active}}_{\text{RPI}} \, \phi^{\text{RPI}}_{\text{ribo}}} } \, .
\label{inv1}
\end{equation}
On non-evolutionary timescales, the ribosome composition is fixed and hence the ratio between the r-protein and 35S-derived rRNA mass fractions on the left-hand side of Eq.~(\ref{inv1}) is constant. The translation and transcription parameters on the right-hand side must therefore be coordinated so as to satisfy this constraint. That is, the numerical values of these parameters may vary between growth conditions, but in such a way that the right-hand side of the equation remains constant and equal to the left. The right-hand side of Eq.~(\ref{inv1}) can thus be viewed as non-trivial invariant of eukaryotic growth, i.e. it is predicted to remain constant irrespective of growth conditions.
Similarly, dividing Eqs.~(\ref{growthlaw2}) by (\ref{growthlaw3}) and multiplying numerator and denominator by $m_{\text{nucl}}$, immediately reveals an invariant quantity via the mass ratio between 35S-derived rRNA and 5S rRNA:
\begin{equation}
\boxed{\frac{x_{\text{m35S}}}{1-x_{\text{prot}}-x_{\text{m35S}}} \simeq \frac{N^{\text{a.a.}}_{\text{RPIII}}}{N^{\text{a.a.}}_{\text{RPI}}} \cdot \frac{k_{\text{RPI}}}{k_{\text{RPIII}}} \cdot \frac{\phi^{\text{m35S}}_{\text{RPI}} \, f^{\text{active}}_{\text{RPI}} \, \phi^{\text{RPI}}_{\text{ribo}}}{\phi^{\text{5S}}_{\text{RPIII}} \, f^{\text{active}}_{\text{RPIII}} \, \phi^{\text{RPIII}}_{\text{ribo}} } } \, .
\label{inv2}
\end{equation}
There are many ways of expressing the two independent invariants. For example, an equivalent to Eq.~(\ref{inv1}) is obtained upon division of Eq.~(\ref{growthlaw1}) by Eq.~(\ref{growthlaw3}) to yield $x_{\text{prot}}/(1-x_{\text{prot}}-x_{\text{m35S}})$, i.e. the ratio between the r-protein and the 5S rRNA mass fractions (Appendix~\ref{C}). Physical interpretations of the invariants are discussed in the following section.
\section{Interpretation of growth-laws and invariants using proteome fractions}
\label{VII}
In the case that the parameters $\phi^{\text{r-prot}}_{\text{ribo}}$, $\phi^{\text{RPI}}_{\text{ribo}}$, and $\phi^{\text{RPIII}}_{\text{ribo}}$ cannot be measured directly, they can be approximated by proteome fractions. In the absence of active and differential degradation among proteins, the fraction $\phi^{\chi}_{\text{ribo}}$ of active ribosomes making a protein of type $\chi$ is equal to the proteome fraction of $\chi$, i.e. ($\chi$-protein)/(total protein), since all protein in the cell is synthesized by ribosomes at an average rate $k_{\text{ribo}}$. In \textit{E. coli} this approximation holds well because active protein degradation is negligible~\cite{MiloBook}. In Eukarya, active degradation may be more significant in, e.g., stressful conditions and hence the proteome fraction approximation should be used only when suitable.
A recent study on turnover rates of 3,160 proteins in exponentially growing \textit{S. cerevisiae} revealed a median protein half-life of 2.18 hr, which matches the corresponding cellular doubling time (2.0 $\pm$ 0.1 hr)~\cite{ProteinDegradation}. Differential protein degradation was also measured. Specifically, the median half-life of ribosomal proteins (1.7 hr) was found to be $\sim\!20$\% lower than the overall protein half-life; however, the authors of the study note that this difference may be an artifact of the measurement method. Moreover, while some proteins in yeast seem to be actively degraded even in exponential growth, nearly all proteins exhibit half-lives close to the cellular doubling time. It was thus concluded that active degradation of protein in exponential growth is small, and that the replacement rate of the proteome is dominated by growth and division. Similar protein turnover trends were observed in human cells~\cite{Boisvert,Gawron}. Thus it appears that in exponential growth, the quantities $\phi^{\text{r-prot}}_{\text{ribo}}$, $\phi^{\text{RPI}}_{\text{ribo}}$, and $\phi^{\text{RPIII}}_{\text{ribo}}$ can be approximated by their respective proteome fractions.
The growth-laws of Eqs.~(\ref{growthlaw1}), (\ref{growthlaw2}), and (\ref{growthlaw3}) become more transparent with the proteome fraction approximations. In the first growth-law [Eq.~(\ref{growthlaw1})]: $\tau_{\text{r-prot}} \cdot \mu = f^{\text{active}}_{\text{ribo}} \, \phi^{\text{r-prot}}_{\text{ribo}}$, the quantity $\phi^{\text{r-prot}}_{\text{ribo}}$ can be interpreted as the proteome fraction of r-protein in the cell. The right-hand side can then be interpreted as the active r-protein proteome fraction. Alternatively, since $f^{\text{active}}_{\text{ribo}}$ is the fraction of ribosomes that are active, of which a fraction $\phi^{\text{r-prot}}_{\text{ribo}}$ is synthesizing r-protein, their product $f^{\text{active}}_{\text{ribo}} \, \phi^{\text{r-prot}}_{\text{ribo}}$ is the fraction of all ribosomes in the cell that are active and synthesizing r-protein. Thus the first growth-law in Eq.~(\ref{growthlaw1}) becomes:
\begin{equation}
\tau_{\text{r-prot}} \cdot \mu \simeq \text{fraction of ribosomes making r-protein} \, .
\label{growthlaw1interpretation}
\end{equation}
In the case of the second growth-law [Eq.~(\ref{growthlaw2})], the product $\phi^{\text{m35S}}_{\text{RPI}} \, f^{\text{active}}_{\text{RPI}} \phi^{\text{RPI}}_{\text{ribo}}$ in the numerator can be interpreted as the proteome fraction of RNAP I-protein actively synthesizing 18S, 25S, and 5.8S rRNAs. In the denominator, $\phi^{\text{r-prot}}_{\text{ribo}}$ is the r-protein proteome fraction. Multiplying the right-hand side of Eq.~(\ref{growthlaw2}) by the quantity (total protein)/(total protein) then reveals it to be a ratio between the number of RNAPs I making mature rRNA and the number of ribosomes in the cell:
\begin{equation}
\tau_{\text{m35S}} \cdot \mu \simeq \frac{\text{\# of RNAPs I making m35S (18S/25S/5.8S)}}{\text{\# of ribosomes}} \, .
\label{growthlaw2interpretation}
\end{equation}
Note that Eq.~(\ref{growthlaw2}) can also be interpreted for the number of active RNAPs I, all of which are dedicated to the synthesis of the 35S precursor rRNA (flanking and spacer nucleotides included, see Fig. \ref{rRNAprocessing}). Because $N^{\text{nucl}}_{\text{35S}}/N^{\text{nucl}}_{\text{m35S}}=\phi^{\text{35S}}_{\text{RPI}} / \phi^{\text{m35S}}_{\text{RPI}}$, where $N^{\text{nucl}}_{\text{35S}}$ is the number of nucleotides in the 35S pre-rRNA and $\phi^{\text{35S}}_{\text{RPI}}$ denotes the fraction of active RNAPs I (all making the 35S pre-rRNA), we obtain
\begin{equation}
\tau_{\text{35S}} \cdot \mu \simeq \frac{\text{\# of active RNAPs I}}{\text{\# of ribosomes}} \, ,
\label{growthlaw2interpretation2}
\end{equation}
where $\tau_{\text{35S}}=N^{\text{nucl}}_{\text{35S}}/k_{\text{RPI}}$. An analogous interpretation can be made for the third growth-law [Eq.~(\ref{growthlaw3})], yielding
\begin{equation}
\tau_{\text{5S}} \cdot \mu \simeq \frac{\text{\# of RNAPs III making 5S}}{\text{\# of ribosomes}} \, .
\label{growthlaw3interpretation}
\end{equation}
The invariants of Eqs.~(\ref{inv1}) and (\ref{inv2}) can also be interpreted using proteome fractions. The first
[Eq.~(\ref{inv1})] simplifies to (Appendix~\ref{D})
\begin{equation}
\frac{x_{\text{prot}}}{x_{\text{m35S}}}\simeq \frac{m_{\text{a.a.}}}{m_{\text{nucl}}} \cdot \frac{k_{\text{ribo}} }{k_{\text{RPI}}} \cdot \frac{\text{\# of ribosomes making r-protein}}{\text{\# of RNAPs I making 18S/25S/5.8S}} \, .
\label{inv1int}
\end{equation}
Meanwhile the second invariant contains a similar ratio:
\begin{equation}
\frac{x_{\text{m35S}}}{1-x_{\text{prot}}-x_{\text{m35S}}} \simeq \frac{k_{\text{RPI}}}{k_{\text{RPIII}}} \cdot \frac{\text{\# of RNAPs I making 18S/25S/5.8S}}{\text{\# of RNAPs III making 5S}} \, ,
\label{inv2int}
\end{equation}
which demonstrates that RNAPs I and RNAPs III are coordinated for the stoichiometric production of rRNA. Similar to the case of \textit{E. coli}~\cite{KR}, we expect the quantities on the right-hand sides of Eqs.~(\ref{inv1int})--(\ref{inv2int}) to be invariant for an exponentially growing eukaryote, regardless of external conditions. The numerical values of these invariants are set by the left-hand sides of the equations, and may thus differ from organism to organism in accordance with the endogenous ribosome composition.
\section{\textit{S. cerevisiae} as a case study}
\label{VIII}
To demonstrate the predictive potential of the relations derived above, we apply them to the model organism \textit{S. cerevisiae} using currently available data. There has not yet been a systematic study of an eukaryote in a specific growth condition which includes all relevant parameters, as was done for the bacterium \textit{E. coli}~\cite{BremerDennis}. However, we collected typical parameter ranges from various sources to serve as benchmark values (Appendix~\ref{E}) and were able to recover a number of results. For example, below we deduce the dependence of ``ribosomal efficiency'' ($k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}$) on growth rate, the number of RNAPs I per RNAP III required for rRNA production, and the number of ribosomes in the cell. These results encourage future experiments to verify the remaining predictions. We also outline methods to infer the activities of RNAP I and RNAP III once more data become available.
\begin{figure*}[t!]
\begin{centering}
\includegraphics[width=0.75\textwidth]{rprot_growthlaw_v3.pdf}
\vspace{-2mm}
\end{centering}
\caption{\textbf{Growth-law for ribosomal proteome fractions [Eq.~(\ref{growthlaw1})] and Michaelis-Menten behavior of $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}$, in the bacterium \textit{E. coli} (upper panels) and in the eukaryote \textit{S. cerevisiae} (bottom panels)}. In panel (a), we plot \textit{E. coli} r-protein data from Bremer \& Dennis~\cite{BremerDennis} (circles) and provide a linear fit (solid line): $\phi^{\text{r-prot}}_{\text{ribo}} = 0.093 \mu + 0.031$. The Michaelis-Menten behavior of $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}$ can be extracted from the linear fit via Eq.~(\ref{MMtoymodel}) to give: $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \text{ (a.a./sec)} \simeq 22 \mu /(0.33 + \mu)$, where $\mu$ is given in hr$^{-1}$. This Michaelis-Menten prediction is denoted by the solid line in panel (b), which is in close agreement with experimental values (circles). The same analysis can be applied to \textit{S. cerevisiae}. In panel (c), we plot data (orange circles) and a linear fit for r-protein fractions vs. growth rate as provided by Metzl-Raz, et al.~\cite{Barkai}. We extract the Michaelis-Menten form $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \text{ (a.a./sec)} \simeq 6.9 \mu /(0.16 + \mu)$ from the linear fit via Eq.~(\ref{MMtoymodel}), as shown in panel (d) by the solid line. Furthermore, in panel (d) we infer values of $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}$ for each data point in panel (c) using the growth-law in Eq.~(\ref{growthlaw1}). These predictions appear to be in agreement with measurements by Waldron \& Lacroute~\cite{WaldronLacroute75} (orange triangles) despite the different \textit{S. cerevisiae} strain.}
\label{rprotgrowthlaw}
\end{figure*}
\subsection{Growth-law for ribosomal protein}
We first consider the proportionality between $\phi^{\text{r-prot}}_{\text{ribo}}$ and growth rate, where we adopt the common interpretation of $\phi^{\text{r-prot}}_{\text{ribo}}$ as the r-protein proteome fraction in the cell [Eq.~(\ref{growthlaw1})]. The same growth-law was shown to hold in the bacterium \textit{E. coli} (Fig.~\ref{rprotgrowthlaw}a). Plotting $\phi^{\text{r-prot}}_{\text{ribo}}$ vs. $\mu$ as per convention~\cite{Barkai,KlumppPNAS} yields a proportionality factor $N^{\text{a.a.}}_{\text{ribo}}/(k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}})$. In principle, both translation rate $k_{\text{ribo}}$ and ribosomal activity $f^{\text{active}}_{\text{ribo}}$ can vary with growth rate. For example, in \textit{E. coli} $f^{\text{active}}_{\text{ribo}}$ remains constant at 85\% across growth rates, while $k_{\text{ribo}}$ exhibits a Michaelis-Menten dependence characteristic of enzymes, saturating at $\sim\!22$ a.a./sec in rapid growth~\cite{BremerDennis, KlumppPNAS, KR}. The product $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}$, which appears in the proportionality constant $N^{\text{a.a.}}_{\text{ribo}}/(k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}})$, then also exhibits a Michaelis-Menten dependence (Fig.~\ref{rprotgrowthlaw}b, circles). We conjecture that the product of translation rate and ribosome activity also has a Michaelis-Menten form in yeast:
\begin{equation}
k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} = \frac{k^{\text{max}}_{\text{eff}} \mu }{\mu_{\text{HM}}+\mu},
\label{MMform}
\end{equation}
where $k^{\text{max}}_{\text{eff}}$ is the saturation value, and $\mu_{\text{HM}}$ is the growth rate at half its maximum, $k^{\text{max}}_{\text{eff}}/2$. The Michaelis-Menten dependence manifests itself in the growth-law plots via a non-zero vertical intercept. To see this, we insert Eq.~(\ref{MMform}) into the growth-law [Eq.~(\ref{growthlaw1})]:
\begin{align}
\phi^{\text{r-prot}}_{\text{ribo}} & \simeq \frac{N^{\text{a.a.}}_{\text{ribo}}}{k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}} \, \mu \simeq N^{\text{a.a.}}_{\text{ribo}} \left( \frac{\mu_{\text{HM}}+\mu}{k^{\text{max}}_{\text{eff}} \mu } \right) \mu \nonumber \\ & \simeq \underbrace{\frac{N^{\text{a.a.}}_{\text{ribo}}}{k^{\text{max}}_{\text{eff}}}}_{\text{slope}} \, \mu + \underbrace{\frac{N^{\text{a.a.}}_{\text{ribo}} \, \mu_{\text{HM}}}{k^{\text{max}}_{\text{eff}}}}_{\text{intercept}}
\label{MMtoymodel}
\end{align}
Hence the linear dependence on growth rate is preserved as in the case of a constant-valued $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}$, but a non-zero intercept is introduced. Indeed, a non-zero intercept has been observed in yeast experiments and was interpreted as an excess ribosomal proteome fraction in preparation for increased translation demands when growth conditions change~\cite{Barkai, Waldron77, Koch71}. In light of Eq.~(\ref{MMtoymodel}), the origin of this non-zero intercept might be traced to a Michaelis-Menten behavior of the ribosomal activity and translation rate product.
The constants $k^{\text{max}}_{\text{eff}}$ and $\mu_{\text{HM}}$ of the Michaelis-Menten form in Eq.~(\ref{MMform}) can be extracted from a linear fit of $\phi_{\text{ribo}}^{\text{r-prot}}$ vs. $\mu$, via Eq.~(\ref{MMtoymodel}). As an example, we apply it to \textit{E. coli} data~\cite{BremerDennis} shown in Fig.~\ref{rprotgrowthlaw}a. We first obtain a linear fit to the data, $\phi_{\text{ribo}}^{\text{r-prot}} \simeq 0.093 \mu + 0.031$, and deduce a Michaelis-Menten behavior of $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \simeq 22 \mu / (0.33+\mu)$, where we recall that the number of amino acids in the $\textit{E. coli}$ ribosome is 7536~\cite{Bionum}. As shown in Fig.~\ref{rprotgrowthlaw}b, the fit is in good agreement with data~\cite{BremerDennis}.
\begin{figure*}[htb]
\begin{centering}
\includegraphics[width=0.75\textwidth]{deducing_kribo_v2.pdf}
\vspace{-2mm}
\end{centering}
\caption{\textbf{Inferring the dependence of peptide elongation rate $k_{\text{ribo}}$ on growth rate in yeast.} In panel (a) we plot polysomal profiling data (orange squares) and the fit $f^{\text{active}}_{\text{ribo}} \simeq \mu / (0.16 + \mu)$ from Fig.~3B of Metzl-Raz, et al.~\cite{Barkai}. The Michaelis-Menten constant of the $f^{\text{active}}_{\text{ribo}}$ fit is the same as that inferred previously for ribosomal efficiency: $k_{\text{ribo}} f^{\text{active}}_{\text{ribo}} \simeq 6.9 \mu / (0.16 + \mu)$. This implies that the peptide elongation rate $k_{\text{ribo}}$ is approximately constant at 6.9 a.a./sec. In panel (b) we plot this predicted translation rate (solid line), and compare to values inferred using Eq.~(\ref{growthlaw1}) and r-protein proteome data (Fig.~\ref{rprotgrowthlaw}) from Metzl-Raz, et al.~\cite{Barkai}.}
\label{inferkribo}
\end{figure*}
We follow the same procedure for \textit{S. cerevisiae} using the data and linear fit reported in Fig.~2A of Ref.~\cite{Barkai}: $\phi_{\text{ribo}}^{\text{r-prot}} \simeq 0.35\mu / \ln(2) + 0.08$ (Fig.~\ref{rprotgrowthlaw}c). We extracted the following Michaelis-Menten behavior of the effective translation rate in a.a./sec (Fig.~\ref{rprotgrowthlaw}d): $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \simeq 6.9 \mu /(0.16 + \mu)$, where we used $N^{\text{a.a.}}_{\text{ribo}}=12467$~\cite{SGD} (obtained from a compiled list of ribosomal proteins, see supplemental Excel file). It implies that the saturation value of $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}$ is $\sim \! 7$ a.a./sec, which is in good agreement with data reported in the literature. Specifically, cytoplasmic ribosomes in yeast were reported to have average translation rates of $k_{\text{ribo}} \sim 2.8$ to 10.0 a.a./sec~\cite{BoehlkeFriesen,Bonven79,WaldronLacroute75, Piques}. A higher rate of 10.5 a.a./sec was also reported~\cite{Waldron77} under the assumption that translation rate is independent of growth rate, while ribosomal activity varies from 50\%--84\%. Meanwhile, Bonven \& Gull{\o}v~\cite{Bonven79} reported an active ribosome fraction $f^{\text{active}}_{\text{ribo}}$ of 36\% to 59\%. An independent study by Metzl-Raz et al.~\cite{Barkai} estimated the active fraction of ribosomes using polysomal profiling, finding it to range from $\sim\!40$\% to 75\% (Fig.~3 of Ref.~\cite{Barkai}). The maximum values reported for $k_{\text{ribo}} \sim \! 10.0$ a.a./sec and $f^{\text{active}}_{\text{ribo}} \sim \! 75\%$ thus yields a product $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \sim \! 7.5$ a.a./sec, which is in close agreement with the saturation value of $\sim \! 7$ a.a./sec obtained above. Furthermore, values of the ``ribosomal efficiency'' $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}$ measured by Waldron
\& Lacroute~\cite{WaldronLacroute75}, albeit for a different
\textit{S. cerevisiae} strain, appear to follow the same Michaelis-Menten trend (triangular markers in Fig.~\ref{rprotgrowthlaw}d).
\subsection{Inferring the dependence of translation rate on growth rate in yeast}
The product $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}}$ of ribosomal activity and translation rate appears to exhibit a Michaelis-Menten dependence on growth rate. However, their separate behaviors, i.e. $k_{\text{ribo}}$ vs. $\mu$ and $f^{\text{active}}_{\text{ribo}}$ vs. $\mu$, are less clear. Does ribosomal activity in yeast remain constant while translation rate depends on growth rate in a Michaelis-Menten fashion, as in \textit{E. coli}? Indeed, there are conflicting reports in the literature on \textit{S. cerevisiae}: Waldron et al.~\cite{Waldron77} reported constant translation rates but varying ribosomal activity, while Bonven \& Gulløv~\cite{Bonven79} found that both translation rates and ribosomal activity vary with growth rates. Meanwhile Boehlke \& Friesen~\cite{BoehlkeFriesen} also found $k_{\text{ribo}}$ to vary with growth rate, but assumed a ribosomal activity of 90\%. More recently, Metzl-Raz et al.~\cite{Barkai} used polysomal profiling to estimate the active fraction $f^{\text{active}}_{\text{ribo}}$ of ribosomes (Fig.~\ref{inferkribo}a), where monosomes were assumed to be inactive. They found the Michaelis-Menten behavior $f^{\text{active}}_{\text{ribo}} \simeq \mu/(0.16+\mu)$. Note that the Michaelis-Menten constant, 0.16, is the same as that of the product $k_{\text{ribo}} \, f^{\text{active}}_{\text{ribo}} \simeq 6.9 \mu/(0.16+\mu)$ extracted in Fig.~\ref{rprotgrowthlaw}. It follows that $k_{\text{ribo}} \approx 6.9$ a.a./sec (Fig.~\ref{inferkribo}b). Thus translation rate appears to remain approximately constant across growth rates, as reported by Waldron, et al.~\cite{Waldron77}.
\subsection{Growth-law for RNA polymerases I}
A similar analysis can be done for the growth-law involving RNAP I-protein [Eqs.~(\ref{growthlaw2interpretation}), (\ref{growthlaw2interpretation2})]. However, current data for yeast are insufficient to determine how RNAP I transcription rate and activity depend on growth rate. In \textit{E. coli}, the behaviors of transcription rate and RNAP activity are reversed compared to their translation counterparts: It is RNAP activity which varies with growth rate and saturates at 31\%, while the rRNA transcription rate stays constant at 85 nt/sec across growth conditions (Fig.~\ref{RNAPgrowthlaws}a)~\cite{BremerDennis}. In analogy to \textit{E. coli}, we plot the growth-law of Eq.~(\ref{growthlaw2interpretation}) for the case of a constant transcription rate, thereby embedding all variability in RNAP I activity. (Should $k_{\text{RPI}}$ vary in a Michaelis-Menten fashion with growth rate, a non-zero intercept will appear as in the case of r-protein.) Experiments by French, et al.~\cite{FrenchRNAPIrates} on \textit{S. cerevisiae} grown in a YPD medium at 30$^{\circ}$C -- the same temperature as in Metzl-Raz, et al.~\cite{Barkai} experiments -- indicate RNAP I transcription rates of $k_{\text{RPI}} \sim 54$ to 60 nt/sec for a doubling time of 100 min. Ko{\v s} \& Tollervey report slightly lower transcription rates of 40 nt/sec at 30$^{\circ}$C~\cite{Kos}. However, Ko{\v s} \& Tollervey used synthetic growth media which have significantly longer doubling times of $\sim \! 140$ min as compared to $\sim \! 90$ min for YPD growth media~\cite{Sherman}. This may indicate that there is indeed some dependence of transcription rates on growth rate, but given the absence of more extensive data, we assume the simplistic picture of a constant transcription rate and present the full range of reported rates via the confidence bounds in Fig.~\ref{RNAPgrowthlaws}b. Note that we have used $N^{\text{nucl}}_{\text{m35S}} = 5354$~\cite{Woolford,Melnikov} (Appendix~\ref{E}), which appears in $\tau_{\text{m35S}}$ on the left-hand side of Eq.~(\ref{growthlaw2interpretation}). We also provide an alternate form of the growth-law [Eq.~(\ref{growthlaw2interpretation2})] for the number of active RNAPs I (Fig.~\ref{RNAPgrowthlaws}c), where the number of nucleotides in each 35S pre-rRNA (including spacer nucleotides) is $N^{\text{nucl}}_{\text{35S}} = 6858$~\cite{SGD} (Appendix~\ref{E}).
\begin{figure*}[htb]
\begin{centering}
\includegraphics[width=0.8\textwidth]{Fig6_v4.pdf}
\vspace{-2mm}
\end{centering}
\caption{\textbf{Predictive growth-laws for the number of RNA polymerases making rRNA relative to the number of ribosomes, assuming constant transcription rates.} In panel (a) we plot the ratio of the number of RNA polymerases making rRNA to the number of ribosomes in the bacterium \textit{E. coli}. Transcription rates were observed to stay constant at $\sim \! 85$ nt/sec across growth conditions~\cite{BremerDennis}. The slope of the solid line, which is a bacterial growth-law equivalent to Eqs.~(\ref{growthlaw2interpretation})--(\ref{growthlaw3interpretation}), is the time required for one RNA polymerase to make a full set of rRNA. The growth-law (solid line) is in excellent agreement with data (circles). In panels (b)--(d), we plot these growth-laws for yeast [Eqs.~(\ref{growthlaw2interpretation})--(\ref{growthlaw3interpretation})]. The slope in panel (b) is given by the time for an RNAP I to transcribe a full set of mature 35S-derived rRNAs, i.e. the 18S, 25S, and 5.8S rRNAs [Eq.~(\ref{growthlaw2interpretation})]. In panel (c) the slope is the time required for an RNAP I to transcribe a 35S pre-rRNA, including spacer nucleotides, and thus we obtain the ratio between the number of active RNAPs I and ribosomes [Eq.~(\ref{growthlaw2interpretation2})]. Plotting the last growth-law [Eq.~(\ref{growthlaw3interpretation})] in panel (d), the slope is the time it takes an RNAP III to transcribe a 5S rRNA. Transcription rates were assumed to remain constant with respect to growth rate, in analogy to \textit{E. coli}. Reported values at 30$^{\circ}$C range between $k_{\text{RPI}} \sim 40 - 60$ nt/sec~\cite{Kos, FrenchRNAPIrates} and $k_{\text{RPIII}} \sim 58-76$ nt/sec~\cite{FrenchRNAPIII}; the confidence bounds correspond to the maximum and minimum values.}
\label{RNAPgrowthlaws}
\end{figure*}
\subsection{Growth-law for RNA polymerases III}
The remaining growth-law [Eq.~(\ref{growthlaw3interpretation})] for the ratio between the number of RNAPs III making 5S rRNA and the number of ribosomes, vs. growth rate, is plotted in Fig.~\ref{RNAPgrowthlaws}d. The proportionality factor is $\tau_{\text{5S}} = N^{\text{nucl}}_{\text{5S}}/k_{\text{RPIII}}$, where $N^{\text{nucl}}_{\text{5S}} = 121$~\cite{Woolford, SGD, Melnikov}. As before, we assume a constant-valued transcription rate, spanning the range $k_{\text{RPIII}} \! \sim \! 58-76$ nt/sec reported by French, et al.~\cite{FrenchRNAPIII} for yeast grown at 30$^{\circ}$C using YPD medium.
\subsection{How many RNAPs I per RNAP III are required for rRNA production?}
Upon dividing the second growth-law by the third, we obtain the the number of RNAPs I making 18S/25S/5.8S per RNAP III making 5S rRNA. Or, if using the alternate version of the growth-law in Eq.~(\ref{growthlaw2interpretation2}), we obtain the number of active RNAPs I per RNAP III making 5S. To estimate their numerical values, we use the nominal values of transcription rates $k_{\text{RPI}} \approx 60$ nt/sec and $k_{\text{RPIII}} \approx 61$ nt/sec reported by French, et al.~\cite{FrenchRNAPIrates, FrenchRNAPIII}. The characteristic timescales are then $\tau_{\text{m35S}} \approx 89$ sec and $\tau_{\text{5S}} \approx 2.0$ sec. An exponentially growing yeast cell in YPD medium at 30$^{\circ}$C is therefore predicted to have approximately $\tau_{\text{m35S}}/\tau_{\text{5S}} \approx 45$ RNAPs I making 18S/25S/5.8S per RNAP III synthesizing 5S rRNA. Equivalently, if including 35S spacer nucleotides, it takes an RNAP I about $\tau_{\text{35S}} \approx 114$ sec to transcribe a full 35S pre-rRNA (6858 nts). Hence, we find there are $\tau_{\text{35S}}/\tau_{\text{5S}} \approx 57$ active RNAPs I per RNAP III making 5S rRNA. These numbers can be compared to measurements by French, et al.~\cite{FrenchRNAPIrates, FrenchRNAPIII} in wild-type yeast cells: The total number of engaged RNAPs I per cell ranged from $\sim \! 3980$ to 4850, with an average of $\sim \! 72$ engaged RNAPs III per cell. For every RNAP III engaged in 5S synthesis, there are then $\sim \! 55$ to 67 engaged RNAPs I. This is in close agreement with our theoretical estimate of $\sim \! 57$ active RNAPs I per RNAP III making 5S.
\subsection{How many ribosomes are in the cell?}
The number of ribosomes per cell can also be inferred from the RNAP growth-laws. For example, consider Eq.~(\ref{growthlaw2interpretation2}) combined with the numbers given above, i.e. $\sim \! 3980$ to 4850 engaged RNAPs I per cell, and a 35S transcription timescale of $\tau_{\text{35S}} \approx 114$ sec. Assuming doubling times of $\approx \! 100$ min for yeast in YPD media at $30^{\circ}$C~\cite{Warner, WaldronLacroute75}, we find the number of ribosomes per cell to lie in the range 301,400 to 367,300. While this range may seem high compared to the 200,000 estimate provided by one source~\cite{Warner}, it agrees well with measurements of $\sim \! 348,000$ ribosomes/cell by Waldron \& Lacroute~\cite{WaldronLacroute75}. Note that such estimates decrease for faster growth rates (assuming the same number of RNAPs), e.g. for doubling times of 90 min instead of 100 min we find a range of $\sim \! 271,300$ to 330,600 ribosomes/cell.
A similar estimate can be obtained via the RNAP III growth-law [Eq.~(\ref{growthlaw3interpretation})]. Recall the 5S transcription timescale $\tau_{\text{5S}} \approx 2.0$ sec and the estimate of $\sim \! 72$ engaged RNAPs III per cell. For a doubling time of $\sim \! 100$ minutes, we then obtain an estimate of $\sim \! 314,200$ ribosomes/cell, which is consistent with the range predicted by the RNAP I growth-law. Conversely, one could obtain estimates for the number of RNAPs I and III making rRNA in the cell, based on measurements of the number of ribosomes per cell.
\subsection{Future outlook: Using the invariants to deduce activities of RNA polymerases I and III from their proteome fractions}
\begin{figure*}[htb]
\begin{centering}
\includegraphics[width=\textwidth]{activeRPfractions_v3.pdf}
\vspace{-5mm}
\end{centering}
\caption{\textbf{Predicted proteome fractions of active RNAPs I and RNAPs III in yeast.} Panel (a) displays the predicted proteome fraction of active RNAPs I, $f^{\text{active}}_{\text{RPI}} \phi^{\text{RPI}}_{\text{ribo}}$, vs. growth rate according to Eq.~(\ref{growthlaw2}) and the ribosomal proteome fraction fit from Ref.~\cite{Barkai}: $\phi^{\text{r-prot}}_{\text{ribo}}
\simeq (0.35/\ln 2) \mu + 0.08$. We assume here that the RNAP III transcription rate is constant; the confidence bounds correspond to its reported range of $k_{\text{RPI}} \sim 40-60$ nt/sec. Similarly, in panel (b) we plot the predicted proteome fraction of active RNAPs III, $f^{\text{active}}_{\text{RPIII}} \phi^{\text{RPIII}}_{\text{ribo}}$, vs. growth rate using Eq.~(\ref{growthlaw3}) and the same fit for the ribosomal proteome fraction. We assume a constant RNAP III transcription rate in the range $k_{\text{RPIII}} \sim 58-76$ nt/sec, and $\phi^{\text{5S}}_{\text{RPIII}} \approx 0.11-0.14$, where lower values in the latter correspond to lower growth rates since there are then more tRNAs per ribosome~\cite{WaldronLacroute75}. RNAP I activity ($f^{\text{active}}_{\text{RPI}}$) and RNAP III activity ($f^{\text{active}}_{\text{RPIII}}$) can be deduced once the RNAP I and RNAP III proteome fractions are known. Under the noted assumptions, the active RNAP I and active RNAP III proteome fractions feature a quadratic dependence on the growth rate $\mu$, but their ratio is constant at $\approx 8$ as shown in panel (c).}
\label{activeRPfractions}
\end{figure*}
Large-scale proteomics studies allow for the estimation of various proteome fractions in the cell. While there is still large variability in current state-of-the-art proteomics studies~\cite{UnificationProt}, in principle such data can be compared to our predicted values for proteome fractions of ribosomes, and of RNAPs I and III making rRNA. We outline a method below to extract RNAP I and III activities which, to our knowledge, have not yet been reported. This method can be used in the near future as more accurate proteomics measurements become available.
The numerical values of the invariants are given by the true ribosome composition, as per the left-hand sides of Eqs.~(\ref{inv1}) and (\ref{inv2}). Their values are determined by the protein and rRNA masses of the \textit{S. cerevisiae} ribosome: Each ribosome is composed of 1.40 MDa protein (supplementary Excel sheet) and 1.79 MDa rRNA ~\cite{SGD}. The rRNA mass was obtained from nucleotide sequences of 18S (587.0 kDa), 25S (1109.7 kDa), 5.8S (51.4 kDa), and 5S (39.4 kDa) mature rRNAs~\cite{SGD}. This yields a total ribosome mass of 3.2 MDa, such that $x_{\text{prot}} \approx 0.439$ and $x_{\text{m35S}} \approx 0.548$. The numerical value of the first invariant [Eq.~(\ref{inv1})] is then $x_{\text{prot}}/x_{\text{m35S}} \approx 0.80$, while that of the second [Eq.~(\ref{inv2})] is $x_{\text{m35S}}/(1-x_{\text{prot}}-x_{\text{m35S}}) \approx 44.388$.
Upon examining the right-hand side of the first invariant in Eq.~(\ref{inv1}), all but the rightmost ratio is known. The values described earlier for RNAP I transcription rate $k_{\text{RPI}}$ and peptide elongation rate $k_{\text{ribo}}$ can be used in Eq.~(\ref{inv1}). The number of amino acids in the RNAP I is $N^{\text{a.a.}}_{\text{RPI}}=5236$, while the ribosome has $N^{\text{a.a.}}_{\text{ribo}}=12467$ amino acids (Appendix~\ref{E}, supplementary Excel file)~\cite{SGD}. We estimate the average amino acid and nucleotide masses as $m_{\text{a.a.}} \approx 112$ Da and $m_{\text{nucl}} \approx 326$ Da, based on the composition of the ribosome and three RNA polymerases. While these values require fine tuning to reflect all amino acids and nucleotides in the cell, they are already in good agreement with the average \textit{E. coli} amino acid mass (109 Da) and nucleotide mass (324.3 Da)~\cite{Bionum}.
Returning to the right-hand side of Eq.~(\ref{inv1}), we can also deduce the fraction $\phi^{\text{m35S}}_{\text{RPI}}$ of active RNAPs I which synthesize mature rRNAs as opposed to 35S spacer nucleotides (Fig.~\ref{rRNAprocessing}). Accounting for spacer nucleotides in pre-rRNA was shown to be critical in \textit{E. coli}~\cite{KR}. In yeast, the 35S pre-rRNA contains a total of 1504 spacer nucleotides from: ITS1 (361 nts), ITS2 (232 nts), 5'ETS (700 nts), and 3'ETS (211 nts)~\cite{SGD}, where ITS and ETS denote an internally transcribed spacer and an externally transcribed spacer, respectively. Including these spacer nucleotides yields a total of 6858 nucleotides in each 35S pre-rRNA. We therefore estimate the fraction of active RNAPs I dedicated to the transcription of mature rRNAs as $\phi^{\text{m35S}}_{\text{RPI}} \simeq 5354/6858 \simeq 78\%$.
Remaining on the right-hand of Eq.~(\ref{inv1}) are the proteome fractions $\phi^{\text{r-prot}}_{\text{ribo}}$ and $\phi^{\text{RPI}}_{\text{ribo}}$, ribosomal activity $f^{\text{active}}_{\text{ribo}}$, and RNAP I activity $f^{\text{active}}_{\text{RPI}}$. As discussed earlier, the ribosomal activity can be estimated using the Michaelis-Menten dependence on growth rate shown in Fig.~\ref{inferkribo}. It follows that RNAP I activity can be deduced once the ribosomal and RNAP I proteome fractions are known.
RNAP III activity can be determined from the second invariant [Eq.~(\ref{inv2})] in a similar fashion. On the right-hand side, we have the number of amino acids $N^{\text{a.a.}}_{\text{RPI}} = 5236$ and $N^{\text{a.a.}}_{\text{RPIII}} = 6151$ in RNAP I and III, respectively~\cite{SGD}. Ranges of the RNAP I and III transcription rates $k_{\text{RPI}}$ and $k_{\text{RPIII}}$, mentioned in a previous section, are provided by French et al.~\cite{FrenchRNAPIrates,FrenchRNAPIII}. The quantity $\phi^{\text{m35S}}_{\text{RPI}} \approx 78\%$ is also known. Thus, aside from RNAP I and III activities and proteome fractions, remaining is the fraction $\phi^{\text{5S}}_{\text{RPIII}}$ of active RNAPs III which synthesize 5S rRNA. This quantity can be estimated using measurements for the number of tRNAs per ribosome in the cell~\cite{WaldronLacroute75}. RNAPs III synthesizes the 5S rRNA, nuclear tRNAs, and a few other small nuclear RNAs whose contribution we henceforth neglect~\cite{SGD}. Waldron \& Lacroute found that there are about 9.5 to 12.2 tRNAs per ribosome in the \textit{S. cerevisiae} cell, depending on growth rate. The average length of a tRNA is 80 nucleotides (supplementary Excel file)~\cite{SGD}. Thus, for each 5S rRNA (121 nt long), an active RNAP III synthesizes 760 to 976 tRNA nucleotides. We therefore estimate that $\phi^{\text{5S}}_{\text{RPIII}} \approx 11\%$ to 14\% of active RNAPs III synthesize 5S rRNA.
Assuming that RNAP I activity was deduced from the first invariant [Eq.~(\ref{inv1})] as described above, only RNAP I and RNAP III proteome fractions are needed to determine RNAP III activity. Alternatively, if RNAP I activity is not known, the RNAP III activity can still be extracted using ribosomal activity and the ribosomal proteome fraction: RNAP I activity is altogether eliminated from the second invariant [Eq.~(\ref{inv2})] upon multiplication with the first [Eq.~(\ref{inv1})].
Lastly, in Fig.~\ref{activeRPfractions} we illustrate the predicted proteome fraction of active RNAPs I ($f^{\text{active}}_{\text{RPI}} \phi^{\text{RPI}}_{\text{ribo}}$) and of active RNAPs III ($f^{\text{active}}_{\text{RPIII}} \phi^{\text{RPIII}}_{\text{ribo}}$) using the growth-laws [Eqs.~(\ref{growthlaw2}), (\ref{growthlaw3})]. There we assume a ribosomal proteome fraction as given by the fit in Ref.~\cite{Barkai}: $\phi^{\text{r-prot}}_{\text{ribo}}
\simeq (0.35/\ln 2) \mu + 0.08$. We also assume constant RNAP I and RNAP III transcription rates which lie in the ranges $k_{\text{RPI}} \sim 40-60$ nt/sec and $k_{\text{RPIII}} \sim 58-76$ nt/sec. Once the RNAP I and RNAP III proteome fractions are known, RNAP I and RNAP III activities can be readily extracted.
\section{Concluding remarks}\label{conc}
In this work, we presented a kinetic analysis of ribosome biogenesis for lower Eukarya in balanced exponential growth. Three growth-laws and two invariants, akin to those found for Bacteria earlier this year~\cite{KR}, were derived. The first growth-law establishes a proportionality between the cellular growth rate and the proteome mass fraction of r-protein. This proportionality has already been observed in yeast~\cite{KiefWarner, Barkai}, allowing for the inference of a Michaelis-Menten behavior of the ``ribosomal efficiency,'' i.e. the product of ribosomal activity and peptide elongation rate. The inferred dependence on growth rate was then shown to be in good agreement with an independent set of measurements, despite the use of a different yeast strain~\cite{WaldronLacroute75}. The second and third growth-laws, which yield the number of RNAPs I and III making rRNA per ribosome, also appear to be in good agreement with measurements thus far~\cite{FrenchRNAPIrates, FrenchRNAPIII}. These results suggest that Bacteria and lower Eukarya obey similar growth-laws despite differences in cellular organization and complexity.
Because a comprehensive eukaryotic dataset is lacking in the literature, several predictions from our analysis still require verification. Noteworthy in that regard are the timescales \{$\tau_{\text{r-prot}},\tau_{\text{m35S}},\tau_{\text{5S}}$\} appearing in the growth-laws [Eqs.~(\ref{growthlaw1interpretation}), (\ref{growthlaw2interpretation}), (\ref{growthlaw3interpretation})], which couple translation and transcription rates to cell physiology via the ribosome composition. Their values are consistent with available data for a limited set of growth conditions. However, concurrent measurements of translation and transcription rates \textit{in vivo} are necessary to fully corroborate the growth-laws in light of the microscopic interpretation of the timescales involved.
The predicted invariant quantities of eukaryotic growth, given by Eqs.~(\ref{inv1}) and (\ref{inv2}), also await experimental verification. Together with the growth-laws, these invariants could eventually be used as a proxy for direct measurements of various kinetic and physiological parameters in eukaryotic cells. For example, they can be used to infer values of RNAP activity, which have not yet been measured. A method to deduce such parameters was outlined in the previous section, where we applied the invariants to \textit{S. cerevisiae}.
Since the kinetic analysis presented here relies only on the assumptions of balanced exponential growth and growth rate maximization, the relations we have derived are likely to hold for species other than budding yeast. This would indicate that the ribosome composition in such organisms is tuned to maximize cellular growth rates, as was already verified for \textit{E. coli} \cite{KR} but remains to be confirmed for \textit{S. cerevisiae} and other microorganisms. Furthermore, because there is some variation in cytoplasmic ribosome composition amongst Eukarya, the relations derived herein might help advance our understanding of ribosome heterogeneity and its consequences~\cite{Moll}. Specifically, the invariants imply that ribosome composition [left-hand sides of Eqs.~(\ref{inv1}), (\ref{inv2})] is directly coupled to cell physiology [right-hand sides of Eqs.~(\ref{inv1}), (\ref{inv2})]. Yet, how the latter changes to accommodate for different ribosome compositions, i.e. via changes in proteome fractions, translation, or transcription kinetics, remains an open question.
Finally, it would be interesting to see whether similar growth-laws and invariants hold for higher, more evolved Eukarya, as these share many features of ribosome biogenesis with lower Eukarya and the eukaryotic core proteome appears to be quite stable across species~\cite{EukaryaProteomeStable}. Particularly interesting in this regard are cancer cells which exhibit rapid cell proliferation like Bacteria and yeast~\cite{Dai, Thomson}. Hyperactivated ribosome production is a known signature of rapidly proliferating cancer cells~\cite{Dai,Pelletier}. During tumorigenesis, excessive rRNA transcription leads to enlarged nucleoli, which are the primary sites of ribosome biogenesis in the eukaryotic cell~\cite{White}. Consequently, nucleolar size in cancer tissues is sometimes used as an indicator of the severity of the disease~\cite{CancerNucleoli}. A more quantitative understanding of ribosome biogenesis would advance cancer research and our understanding of tumorigenesis. To this end, the analysis presented herein may aid in the search for cancer cell growth-laws.
\subsection*{Acknowledgments}
The authors thank Eyal Metzl-Raz and Naama Barkai for their help with polysomal profiling and proteomics data. S.K. thanks Elizabeth R. Chen for helpful advice on the figures. S.K. was supported by the Zuckerman STEM postdoctoral fellowship. S.R. acknowledges support from the Azrieli Foundation, from the Raymond and Beverly Sackler Center for Computational Molecular and Materials Science at Tel Aviv University, and from the Israel Science Foundation (Grant No. 394/19).
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,392 |
namespace XpdfNet
{
using System;
using System.Collections.Generic;
using System.IO;
using System.Text;
public class DirectoryServiceWindows : DirectoryServiceBase
{
private const string PDFToText = "pdftotext.exe";
public override string Filename
{
get
{
string filename = Path.Combine(this.WorkingDirectory, PDFToText);
return filename;
}
}
public override string GetArguments(XpdfParameter parameter)
{
var arguments = this.JoinXpdfParameters(parameter);
return arguments;
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,891 |
\section{List of scales}
\label{app:Scales}
\subsection{List of energy and time scales}
\begin{itemize}
\item elastic scattering time $\tau_{\rm el}$.
\item coherence time $ 1/\Delta$
\item Tunneling time $\mathcal T$
\item 2+1 D stiffness $J$ at zero temperature. Clean case: $J \sim E_F$. Dirty case: $J = \Delta E_F \tau_{\rm el}$.
\end{itemize}
\subsection{List of length scales}
\begin{itemize}
\item Fermi wave length $\lambda_F$
\item UV length scale $\lambda_0$. Clean case: $\lambda_0 =\lambda_F$. Dirty case: $\lambda_0 = \lambda_F/\sqrt{\Delta \tau_{\rm el}}$
\item Thomas Fermi wave length $\lambda_{\rm TF}$
\item Coherence length $\xi$. Clean case: $\xi = v_F/\Delta$, dirty case: $\xi = v_F \sqrt{\Delta/\tau_{\rm el}}$.
\item Pearl length $\lambda_M= \lambda_{\rm TF} c^2/v_0^2$.
\end{itemize}
\section{Vortex interaction parameters and screening}
\label{sec:model}
For the convenience of the reader, this section summarizes basic properties of vortex interactions in the finite strip.
\subsection{Long-wavelength action}
We consider the following effective long-wavelength action of the superconducting plate, see Fig.~\ref{fig:Setup}
\begin{equation}
S = \int_{(x, y, \tau)} \left [ \frac{J}{\pi} \left (\frac{2e}{c} \v A - \nabla \phi \right )^2 + \frac{Z}{\pi} \left (2 e A_0 + \partial_\tau \phi\right )^2 \right ], \label{eq:O2action}
\end{equation}
where $\int_{(x, y, \tau)} = \int_{-L/2}^{L/2} dx \int_{-W/2}^{W/2} dy \int_{-\infty}^{\infty} d\tau$, supplemented with the Maxwell action of electromagnetic fields $(A_0,\vec A)$ living in (3+1) dimensional space-time.
As the phase field $\phi$ may contain singularities it is important to keep in mind that $\vec{\nabla} \phi$ is in general \textit{not} a gradient field. The notation used in Eq.~\eqref{eq:O2action} is suggestive and mathematically correct only away from the singularities.
The parameters $J,Z$ of this action define a characteristic length scale $\lambda_0 = 1/\sqrt{J Z}$ and speed $v_0 = \sqrt{J/Z}$.\cite{AbrahamsTsuneto1966,Stoof1993} In addition, they define length scales associated to the screening of electric charge $\lambda_{\rm TF} = 1/[16 {e^2} Z] \sim \lambda_0 v_0/[\alpha_{\rm QED} c]$ (``Thomas-Fermi length'') and current $\lambda_M = c^2/[16 e^2 J] = \lambda_{\rm TF} {c^2}/{v_0^2} \sim \lambda_0 c/[\alpha_{\rm QED} v_0]$ (``Pearl-London length''), where $1/\alpha_{\rm QED} \approx 137$ if the sample is suspended in vacuum.
In our calculations, we use $v_0 \ll c$ and additionally assume the following realistic hierarchy of length scales $ L \gg \lbrace W, \lambda_M \rbrace \gg \xi \gg \lbrace \lambda_{\rm TF}, \lambda_0 \rbrace $. Note that, in typical experimental samples, the Pearl-London length, which is about four to five orders of magnitude larger than $\lambda_0 \gtrsim 1 nm$, can be smaller, larger or comparable to the system's width.
Since we are considering a charged superconductor, the smooth part of the Goldstone mode $\phi$ can be reabsorbed in a redefinition of the electromagnetic fields $(A_0,\v A)$ (``Anderson-Higgs-mechanism''). However, singular configurations of $\phi$, such as vortices, and an externally applied current bias can not be ``eaten'' by a gauge transformation of the vector potential. Differentiation of the action \eqref{eq:O2action} with respect to the gauge potentials $(A_0,\v A)$ implies the 2D charge and current densities, $\rho$ and $\v j_{\rm tot} = \v j + j_0 \hat e_x$, respectively, where
\begin{subequations}
\begin{eqnarray}
\rho &=& - 4 e \frac{Z}{\pi} \left (\partial_\tau \psi + 2 e A_0\right ), \\
\v j &=& \frac{4 e}{c} \frac{J}{\pi} \left (\nabla \psi - \frac{2 e}{c} \v A\right ), \label{eq:currentdensity}
\end{eqnarray}
and
\begin{equation}
j_0 \equiv \frac{I}{W c} = const.
\end{equation}
\end{subequations}
is the externally injected, fixed background current density. Here, we have separated the phase into two contributions
\begin{equation}
\phi = \psi +\phi_I
\end{equation}
where the time independent field $\phi_I$ enters $j_0$ and $\psi$ represents the fluctuating part of the phase field. The finite geometry implies the boundary conditions
\begin{equation}
\left .j_x \right \vert_{x= \pm L/2} = 0, \;\left .j_y \right \vert_{y= \pm W/2} = 0. \label{eq:boundarycond}
\end{equation}
We will be interested in the limit of linear response in $I$.
\subsection{Vortex configurations.}
\label{sec:VoltageGeneration}
As mentioned in the introduction, the finite voltage in superconductors relies on quantum phase slips and tunneling of vortex excitations. Here, we provide further details leading to the technical definition of the problem.
Generally, in a 2D system characterized by coordinates $(x_1,x_2)$, a vortex of winding $n_w$ at $(x_{1,0},x_{2,0})$ is defined by the singular field configuration
\begin{align}
\psi_{n_w,x_{1,0},x_{2,0}}(x_1,x_2) &= n_w \arctan\left [\frac{x_2 - x_{2,0}}{x_1 - x_{1,0}}\right ] \notag \\
&+ \pi \theta(x_{1,0} - x_1).\label{eq:generalVortexDef}
\end{align}
This mapping represents the principal branch of the phase field. In our convention, the branch cut is chosen on the line $x_1 = x_{1,0}$, $x_2 < x_{2,0}$. In the limit $\lambda_M \gg W$ vortex field lines in a charged superconductor are the same as in a neutral superfluid. A vortex field complying with the no out flux boundary conditions~\eqref{eq:boundarycond}, can be constructed by an infinite series of mirror vortices and has the form,\cite{OvchinnikovVarlamov2015} (see Sec.~\ref{app:VortexPotScreening})
\begin{eqnarray}
\psi^{\rm (M)}_{n_w,x_0,y_0}(x,y) &=& n_w \Big \lbrace \arctan\left [\frac{\tan\left (\frac{\pi}{2W} (y -y_0)\right )}{\tanh \left (\frac{\pi}{2W}(x-x_0)\right )}\right ] \notag \\
&&- \arctan\left [\frac{\tan\left (\frac{\pi}{2W} (y + y_0- W)\right )}{\tanh \left (\frac{\pi}{2W}(x-x_0\right )}\right ]\notag \\
&&- \pi \theta(y+y_0) \text{sign}(x-x_0)\Big \rbrace. \label{eq:MirrorVortex}
\end{eqnarray}
This configuration is shown in Fig.~\ref{fig:UnbindingCartoon}.
\subsection{Vortex interactions}
\label{app:VortexIA}
The definining property
\begin{equation}
\nabla \times (\nabla \psi^{\rm (M)}_{n_w,x_0,y_0}(x,y)) = 2\pi n_w \delta(\v x - \v x_0),
\end{equation}
readily leads to the single vortex potential presented in the main tex
, i.e. a logarithmic attraction
\begin{equation}
V(\v x) \simeq 2 J \ln(\vert \v x \vert/\xi)
\end{equation}
for a vortex -antivortex pair which is at distance $\v x$.
The trigonometric function in the potential of a single vortex in a finite strip
can be derived from Eq.~\eqref{eq:MirrorVortex} or as follows: Consider a sequence of vortices and anti-vortices in an infinite plane at positions
\begin{equation}
y_+^{(i)} = i d - y, \quad
y_-^{(i)} = (i-1) d + y, \quad y \in (0,d/2), i \in \mathbb Z.
\end{equation}
For $d = W/2$ and $y= y_0 + d/4$ this sequence corresponds to the sequence of mirror charges of a single vortex in a strip of width $W$ and at position $y_0$.
The total potential energy is
\begin{equation}
V = 2J \sum_{i >j} \ln\left[\frac{y_+^{(i)} - y_-^{(j + 1)}}{y_-^{(i)}-y_-^{(j)}} \frac{y_-^{(i)} - y_+^{(j)}}{y_+^{(i)}-y_+^{(j)}}\right].
\end{equation}
This obviously diverges linearly with the number of dipoles. The energy per dipole is
\begin{eqnarray} \label{eq:VperDipole}
V_{\text{per dipole}} &=& 2J \sum_{n > 1} \ln \left [\frac{(n - 1/2)^2 + (2 y/d -1/2)^2}{n^2} \right] \notag \\
&=& 2 J \ln \left [\sin\left (\frac{2\pi y}{d} \right) \right] + J \times \text{const.}.
\end{eqnarray}
The constant term is $y$ and $d$ independent and thus physically irrelevant, we therefore do not discuss possible regularization schemes of this logarithmically divergent term. Clearly, this reproduces the potential for a single vortex in a finite strip as given in the main text,
\begin{align} \label{eq:SingleVortexPot}
V(y_0) &= 2J \ln \left [\frac{\cos(\pi y_0/W)}{\xi/W}\right ]
\end{align}
We also use Eq.~\eqref{eq:SingleVortexPot} for the calculation of multivortex tunneling actions.
\section{Screening of vortices via London electromagnetism}
\label{app:Screening}
We here briefly summarize the effect of screening of vortices and phase slips and determine that none of these effects is important in the parameter regime of interest.
We largely follow \cite{DuanLeggett1992, Duan1993} and omit retardation effects in view of the small parameter $v_0/c$.
Since the action of electromagnetic fields is Gaussian, integration of electromagnetic fields is equivalent to the saddle point treatment dictated by the Maxwell equations (we use Lorenz gauge),
\begin{subequations}
\begin{eqnarray}
\lbrace - \partial_{c \tau}^2 - \nabla_{3D}^2 \rbrace A_0 &=& 4 \pi \rho W\tilde \delta(y) \delta(z), \\
\lbrace - \partial_{c \tau}^2 - \nabla_{3D}^2 \rbrace \v A &=& 4 \pi \v j W \tilde \delta(y) \delta(z). \label{eq:MaxwellEquations:Elfield}
\end{eqnarray}
\label{eq:MaxwellEquations}
\end{subequations}
We introduced the notation $\tilde \delta(y) = \theta(y+W/2)\theta(W/2-y)/W$, where $\theta(x)$ is the Heaviside function. Since the background current $j_0$ is kept fixed, it should not be further screened and does not enter these Maxwell's equations. Integration of electromagnetic fields leads to the effective action $S= S_0 + S_I$ of the matter field\cite{DuanLeggett1992,Duan1993}
\begin{subequations}
\begin{eqnarray}
S_0 &=& \int_{(x,y,\tau) }\Big[ \frac{J}{\pi} \nabla \psi \left (\nabla \psi-\frac{2e}{c} \v A \right ) \notag \\
&& + \frac{Z}{\pi}\partial_\tau \psi \left (\partial_\tau \psi+2 e A_0 \right ) \Big ], \label{eq:O2action:afterintegration} \\
S_I &=& 2 \int_{(x,y,\tau) } \frac{c j_0}{2e} \left (\partial_x \psi - \frac{2e}{c} A_x\right ).\label{eq:O2action:SI}
\end{eqnarray}
\end{subequations}
The electromagnetic fields entering Eq.~\eqref{eq:O2action:afterintegration} are solutions to Eq.~\eqref{eq:MaxwellEquations} for a given field configuration $\psi$. The regular part of $\psi$ can be removed by partial integration combined with the continuity equation (gauge invariance).
\subsection{Screening of the phase-slip}
\label{sec:ScreeningPhaseslip}
We consider a phase slip in the phase field $\psi$ at space-time $ (x_0, \tau_0)$.
The gradient field is ($\tilde \tau = v_0 \tau$)
\begin{equation}
\nabla \psi(\underline x)= \left (\begin{array}{c}
\partial_x \\
\partial_{\tilde \tau}
\end{array} \right ) \psi = \frac{1}{x^2 + \tilde \tau^2}\left (\begin{array}{c}
- \tilde \tau \\
x
\end{array} \right )
\end{equation}
with $\underline x^T = (x, \tilde \tau)$.
In Fourier space we find
\begin{equation}
(\nabla \psi) (\v q) = - \frac{2\pi i}{\v q ^2} \left (\begin{array}{c}
- q_{\tilde \tau} \\
q_x
\end{array} \right )
\end{equation}
where $\v q = (q_x, q_{\tilde \tau})$.
We 4D Fourier transform Eq.~\eqref{eq:MaxwellEquations} using $\tilde \delta(y) = \delta(y)$ and introduce $\tilde{\underline{A}}_{1D} (\v q)= \underline A (q_x, y = 0, z = 0, q_{\tilde \tau})$, use the integral
\begin{equation}
\int \frac{dq_y dq_z}{(2\pi)^2} \frac{1}{q_x^2 + q_y^2 + q_z^2} = \frac{ \ln \vert \frac{1}{q_x r_x}\vert}{2\pi}
\end{equation}
with $r_x \sim \xi$ the extension of the asymmetric vortex core in $x-$direction to obtain
\begin{subequations}
\begin{eqnarray}
\left ( \frac{2\pi}{ \ln \vert \frac{1}{q_x r_x}\vert} + 2 \pi \gamma_E \right ) \tilde A_{0,1D} &=&- \frac{\pi \gamma_E v_0}{e} \partial_{\tilde \tau} \psi (\v q) \\
\left ( \frac{2\pi}{ \ln \vert \frac{1}{q_x r_x}\vert} + 2 \pi \gamma_M \right ) \tilde A_{x,1D} &=& \frac{\pi \gamma_M c}{e} \partial_x \psi (\v q).
\end{eqnarray}
\label{eq:London}
\end{subequations}
Here, $\gamma_{M,E} = W/\lambda_{M,E}$. This leads to
\begin{eqnarray}
[\partial_x \psi - \frac{2e}{c} A_x](\v q) &=& \frac{\gamma_M^{-1}}{\gamma_M^{-1} + \ln \vert \frac{1}{q_x r_x} \vert} \partial_x \psi(\v q)\\
\frac{1}{v_0} [\partial_\tau \psi + {2e} A_0](\v q) &=& \frac{\gamma_E^{-1}}{\gamma_E^{-1} + \ln \vert \frac{1}{q_x r_x} \vert} \partial_{\tilde{\tau}} \psi(\v q).
\end{eqnarray}
We observe that screening is important for $ -\ln \vert{q_x r_x} \vert > \gamma_{M,E}^{-1}$ and thus only for large systems $L > \xi e^{\gamma_M^{-1}}$.
Anticipating, that the saddle point configuration of the dipole occurs at $x_+ = x_-$ we obtain
\begin{eqnarray}
S_{\rm IA} &=& \frac{2 \tilde J W}{\pi} \int dq_x dq_{\tilde \tau} \Big \lbrace \frac{q_{\tilde \tau}^2}{\v q^4} \frac{\gamma_M^{-1}}{\gamma_M^{-1} + \ln \vert \frac{1}{q_x r_x} \vert} \notag \\
&& + \frac{q_{x}^2}{\v q^4} \frac{\gamma_E^{-1}}{\gamma_E^{-1} + \ln \vert \frac{1}{q_x r_x} \vert} \Big\rbrace \left [1- \cos(q_{\tilde \tau} \Delta \tilde \tau)\right ] \notag \\
&=& \int_0^1 du \Big \lbrace \frac{1}{u}\frac{2 \tilde J W \gamma_M^{-1}}{\gamma_M^{-1} - \ln (u)} \left [1- e^{-\frac{\vert \Delta \tilde\tau \vert}{r_x} u} \left (1-\frac{\vert \Delta \tilde\tau \vert}{r_x} u \right ) \right ] \notag\\
&&+ \frac{1}{u}\frac{2 \tilde J W \gamma_E^{-1}}{\gamma_E^{-1} - \ln (u)} \left [1- e^{-\frac{\vert \Delta \tilde\tau \vert}{r_x} u} \left (1+\frac{\vert \Delta \tilde\tau \vert}{r_x} u \right ) \right ] \notag \\
&\simeq& 2 \tilde J W\Big \lbrace \gamma_M^{-1} \ln \left [1+ \gamma_M \ln\left (\frac{\vert \Delta \tilde\tau \vert}{r_x}\right )\right ] \notag \\
&&+ \gamma_E^{-1} \ln \left [1+ \gamma_E \ln\left (\frac{\vert \Delta \tilde\tau \vert}{r_x}\right )\right ] \Big \rbrace.
\end{eqnarray}
The symbol $\simeq$ means equality in the limit ${\vert \Delta \tilde\tau \vert}/{r_x} \rightarrow \infty$. We repeat that magnetic screening should only be kept provided $\gamma_M^{-1}= \lambda_M/W < \ln[L/\xi]$.
So long as $\gamma_M \ln(\delta \tau v_0/\xi) \ll 1$, i.e. $\delta \tau \Delta \ll e^{\lambda_M/W}$ can be omitted, while electric screening effects can always be omitted. This concludes the derivation underlying our statement of the main text: Magnetic screening effects of quantum phase slips are negligible in the parameter regime of $W/\xi$, and lead to the double logarithm quoted in the main text.
\subsection{Screening of a vortex}
\label{app:VortexPotScreening}
We first discuss the screening of a static vortex configuration in the bulk of the system Eq.~\eqref{eq:MaxwellEquations} become
\begin{equation}
[- \nabla^2_{3D} + 2 \lambda_M^{-1} \delta(z)] \v A(\v x) = \frac{c \lambda_M^{-1}}{e} \nabla \psi(\v x) \delta(z).
\end{equation}
Fourier transformation and the definition of $\v A_{2D} (\v q) = \v A (\v q,0)$ leads to
\begin{equation}
2 [\vert \v q \vert + \lambda_M^{-1}] \v A_{2D}(\v q) = \frac{c \lambda_M^{-1}}{e} \nabla \psi(\v q)
\end{equation}
and thus to
\begin{equation}
[\nabla \psi - \frac{2e}{c} \v A](\v q) = \frac{\vert \v q\vert }{\vert \v q\vert + \lambda_M^{-1}} \nabla \psi (\v q).
\end{equation}
In the case of a vortex, $\nabla_\mu \psi (\v q) = \epsilon_{\mu \nu} 2 \pi i q_\nu/\v q^2$, we can write after inverse Fourier transformation
\begin{subequations}
\begin{equation}
[\partial_\mu \psi - \frac{2e}{c} A_\mu](\v x) = - \epsilon_{\mu \nu} \partial_\nu F(r/\lambda_M)
\end{equation}
with
\begin{eqnarray}
F(a) &=& - \frac{\pi}{2} \left (\mathbf H_0(a) - Y_0(a)\right ) \notag \\
&\simeq & - \ln(1+ 1/a) + \frac{\gamma_{\rm EM}- \ln(2)}{1 + a^2}.
\end{eqnarray}
\end{subequations}
Here, $\gamma_{\rm EM}$ is the Euler-Mascheroni constant, $\mathbf H_0$ the Struve function of order zero, $Y_0$ the zeroth Bessel function of the second kind and the symbol $\simeq$ means asymptotic equality for both $a \gg 1$ and $a \ll 1$. Since only the derivative of $F$ enters into the action, we omit the second term, which has vanishing derivative in both limits.
It is also possible to calculate the resummation of image charges of a vortex at $(0,y_0)$ such that $\v j$ satisfies the boundary conditions. We define $F^{(M)}(x,y)$ via
\begin{widetext}
\begin{eqnarray}
[\partial_y \psi - \frac{2e}{c} A_y] &=& \partial_x F^{(M)}(x,y) \notag \\
&=& \sum_k \Big [\frac{x}{x^2+(y-y_0 + 2 kW)^2} \frac{\lambda_M}{\lambda_M + \sqrt{ x^2+(y-y_0 + 2 kW)^2}} \notag \\
&& - \frac{x}{x^2+(y+y_0 + W - 2 kW)^2} \frac{\lambda_M}{\lambda_M + \sqrt{x^2+(y+y_0 + W - 2 kW)^2} } \Big ] \notag \\
&=& \int_{-\infty}^\infty du g(\sqrt{u^2 + \bar x^2}) \frac{\bar x}{\sqrt{u^2 +\bar x^2}} \left [ \delta(u) - \frac{\bar \lambda/\pi}{\bar \lambda^2 + u^2} \right ] \notag \\
&=& - \frac{2}{\pi} \int_0^\infty du \partial_u \left (\frac{\bar x}{\sqrt{u^2 +\bar x^2}} g(\sqrt{u^2 +\bar x^2}) \right ) \text{arccot} (u/\bar \lambda).
\end{eqnarray}
\end{widetext}
Here, the summation has been evaluated by a contour integral. We introduced the notation $\bar x = x/\pi W, \bar y = y/\pi W, \bar \lambda = \lambda_M/\pi W$ and
\begin{eqnarray}
g(\bar x) &=& \frac{\sinh(\bar x) \pi/2W }{\cosh(\bar x) - \cos(\bar y - \bar y_0)} \notag \\
&&- \frac{\sinh(\bar x) \pi/2W }{\cosh(\bar x) + \cos(\bar y + \bar y_0)} .
\end{eqnarray}
Note that $g(\bar x) \vert_{y_0 = \pm W/2} = 0 $, and thus $j_y \vert_{y_0 = \pm W/2} = 0$, in accordance with the boundary conditions.
We define
\begin{eqnarray}
G(\bar x) &=& \frac{1}{2} \Big ( \ln \left [\cosh(\bar x) - \cos(\bar y - \bar y_0) \right ] \notag \\
&& - \ln \left [\cosh(\bar x) + \cos(\bar y + \bar y_0) \right ] \Big )
\end{eqnarray}
to obtain
\begin{equation}
F^{(M)} = - \frac{2}{\pi} \int_0^\infty du \partial_u G(\sqrt{u^2 + \bar x^2}) \text{arccot}(u/\bar \lambda).
\end{equation}
In the screeningless limit $\lambda_M/W \rightarrow \infty$ this can be regarded as the derivation of Eq.~\eqref{eq:MirrorVortex}.
\section{Vortex tunneling}
\label{app:VortexTunneling}
In this section we present details on vortex tunneling.
\subsection{Single vortex kink}
We first consider the kink solution, $y_{\rm kink}(\tau)$, for a single vortex tunneling across the system, $y_{\rm kink}(-\mathcal T/2) = -W/2+\xi$ and $y_{\rm kink}(\mathcal T/2) = W/2-\xi$, which solves the equation of motion
\begin{equation}
- m \ddot y + V'(y) = 0,
\end{equation}
where $V(y)$ given by Eq.~\eqref{eq:SingleVortexPot}.
The tunneling action can be calculated using energy conservation
\begin{eqnarray}
S_{\rm pot} &=& \int_{-W/2+\xi}^{W/2-\xi} dy \sqrt{2m V(y)} \notag \\
&=& \frac{4W\sqrt{mJ}}{\pi} \left.
\underbrace{\int_{0}^{\pi/2- \bar \xi} d\bar y \sqrt{\alpha/2 + \ln(\cos(\bar y)/\bar{\xi})}}_{I_\alpha(\bar \xi)} \right \vert_{\alpha = 0}
\end{eqnarray}
Here, $\bar \xi = \pi \xi/W$. It is obvious that $I_0(\bar \xi = \pi/2) = 0$, i.e. $f(\pi/2)=0$ as quoted in the main text.
The tunneling time in the inner part of a wide strip ($W \gg \xi$) can be calculated as
\begin{eqnarray}
\mathcal T &=& \int_{-W/2+\xi}^{W/2-\xi} dy \left .\sqrt{\frac{m}{4 J\left (\frac{\alpha}{2} + \ln \left [\frac{\cos(\bar y)}{\bar \xi}\right ]\right )}} \right \vert_{\alpha = 0}\notag \\
&=& \left .\frac{W}{\pi v} \int_0^{\frac{\pi}{2} - \bar \xi}d \bar y \frac{1}{\sqrt{\frac{\alpha}{2} + \ln \left [\frac{\cos(\bar y)}{\bar \xi}\right ]}} \right \vert_{\alpha = 0}\notag \\
&=& \frac{W}{\pi v} 4\left . \frac{d}{d \alpha} I_\alpha (\bar \xi)\right \vert_{\alpha = 0}.
\end{eqnarray}
Note that there is an additional contribution of order $1/\Delta$ which corresponds to the time to nucleate a vortex and thus is the lower bound for $\mathcal T$ entering $S_{\rm cond} = J \mathcal T$ int he main text. This concludes the derivation of the results presented around Eq.~\eqref{eq:Bounce2D} of the main text.
Using energy conservation one may also evaluate the asympototic trajectory near the turning points, e.g. $y = \mp W/2 \pm \xi \pm \delta y$, where $0<\delta y \ll \xi$ and
\begin{equation}
\delta \dot y = 2v\sqrt{\ln( 1+\delta y/\xi )} \simeq 2v \sqrt{{\delta y }/{\xi}},
\end{equation}
which is solved by
\begin{equation}
\delta y(\tau) = v^2 (\tau- \tau_{i,f})^2/\xi, \label{eq:ApproxSol}
\end{equation}
where $\tau_{i,f}$ is the initial or final time.
\subsubsection{Asymptotic evaluation of auxiliary integral}
We here present the asymptotic evaluation of the auxiliary integral $I_\alpha$. Note that the sum $I_0(\bar \xi) + I'_0(\bar \xi)$ is plotted in Fig.~\ref{fig:MultiVortex} c) of the main text.
\begin{subequations}
\begin{eqnarray}
I_\alpha (x) &=& \int_x^1 du (- \partial_u \arccos(u)) \sqrt{\frac{\alpha}{2} + \ln(u/x)} \notag \\
&=& \sqrt{\frac{\alpha}{2}} \arccos(x) + \int_x^1 du \frac{\arccos(u) }{2u \sqrt{\frac{\alpha}{2} + \ln(u/x)}} \notag\\
&=& \sqrt{\frac{\alpha}{2}} \left (\arccos (x)- \left (\frac{\pi}{2} - x\right ) \right ) \notag \\
&+& \left (\frac{\pi}{2}-1\right ) \sqrt{\frac{\alpha}{2} - \ln{x}} + I_{1,\alpha} (x)+ I_{2,\alpha} (x),
\end{eqnarray}
where
\begin{eqnarray}
I_{1,\alpha}(x) &=& \int_x^1 du \sqrt{\frac{\alpha}{2} +\ln[u/x]} \notag \\
&=& \frac{\sqrt{\pi } e^{-\frac{\alpha}{2} } x}{2} \left[\text{erfi}\left(\sqrt{\frac{\alpha}{2} }\right)-\text{erfi}\left(\sqrt{\frac{\alpha}{2} -\ln (x)}\right)\right] \notag \\
&& + \sqrt{\frac{\alpha}{2} -\ln (x)}-x\sqrt{\frac{\alpha}{2} } \\
I_{2,\alpha}(x) &=& \int_x^1 du\frac{\arccos(u) - \left (\frac{\pi}{2}-u\right )}{2u \sqrt{\frac{\alpha}{2} + \ln(u/x)}} \notag \\
&\simeq& \frac{2 - \pi \ln(2)}{4 \sqrt{\frac{\alpha}{2} - \ln(x)}}.
\end{eqnarray}
\label{eq:InearlyExact}
\end{subequations}
Here, we twice integrated by parts in order to reduce $I_\alpha (x)$ to a simpler integral, $I_{1,\alpha}(x)$, and an integral which is small and determined by $u \sim 1$, $I_{2,\alpha}(x)$, which we evaluated approximately in the limit $x \ll 1$. Here $\text{erfi}$ is the imaginary error function. Expanding the result up to next to leading order in $1/\sqrt{\frac{\alpha}{2} - \ln(x)}$, we obtain
\begin{equation}
I_\alpha(x) \simeq \frac{\pi}{2}\left [\sqrt{\frac{\alpha}{2} - \ln(x)} - \frac{1}{2} \frac{\ln(2)}{\sqrt{\frac{\alpha}{2} - \ln(x)}} \right ]. \label{eq:IAsymp}
\end{equation}
\subsection{Bounce solution and variational action}
\label{app:Bounce}
We now consider edge unbinding for the potential, Eq.~\eqref{eq:SingleVortexPot} supplemented with a tilt, $V_I = -\beta y$, where $\beta =\Phi_0 I/W$ at small $\beta$.
As an Ansatz, we consider two kinks located at positions $\pm \delta \tau/2$
\begin{equation}
y_{\rm bounce} = y_{\rm kink}(\tau + \delta \tau/2) - y_{\rm kink}(\tau - \delta \tau/2) - (W/2 -\xi).
\end{equation}
For $\delta \tau > \mathcal T$, the two kink solutions do not overlap and the action is
\begin{equation}
S_{\rm bounce}(\delta \tau) = 2 S_{\rm kink}^{a)} - \beta (W - 2\xi) \delta \tau.
\end{equation}
However, if $0< (\mathcal T -\delta \tau)/2 \equiv \tau_f \ll \mathcal T$ the overlap leads to non-linear interaction between the kinks.
Specifically, the $\beta = 0$ part of the potential contribution to the action is
\begin{align}
S_{\beta = 0}
&\simeq 2\int_{-\infty}^0 d \tau\Big \lbrace \frac{m\dot y_{\rm kink} (\tau + \frac{\delta \tau}{2})^2}{2} + V(y_{\rm kink} (\tau + \frac{\delta \tau}{2})) \notag \\
& + \delta y_{\rm kink} (\tau) [m \ddot y_{\rm kink} (\tau + \frac{\delta \tau}{2}) - V'(y_{\rm kink} (\tau + \frac{\delta \tau}{2}))] \notag \\
& - \partial_\tau[m \delta y_{\rm kink} (\tau) \dot y_{\rm kink}(\tau + \frac{\delta \tau}{2})] + m \delta \dot y_{\rm kink} (\tau)^2/2\Big \rbrace.
\end{align}
Here, we used the $\tau \rightarrow - \tau$ symmetry of the Ansatz and we have expanded the action in small $\delta y_{\rm kink}(\tau) = y_{\rm kink}(\tau - \delta \tau/2) + (W/2 - \xi)$. The second line vanishes, because $y_{\rm kink}$ solves the equation of motions. This leads to
\begin{align}
S_{\beta = 0} &= 2 S_{\rm pot} - 2 \int_{0}^{\tau_f} d \tau m\dot y_{\rm kink} (\tau + \frac{\delta \tau}{2})^2 \notag \\
& - 2 m \delta y_{\rm kink} (0) \dot y_{\rm kink} (\delta \tau/2)\notag \\
&+ \int_{- \tau_f}^0 d\tau m \dot y_{\rm kink}( \tau - \frac{\delta \tau}{2})^2 \notag \\
&= 2 S_{\rm kink}^{\rm a)} - \frac{16 m v^4}{3 \xi^2}\tau_f^3.
\end{align}
Here, we have used the approximate solution Eq.~\eqref{eq:ApproxSol} near the turning point. In total this leads to a $\delta \tau$ dependent bounce action
\begin{eqnarray}
S_{\rm bounce}(\delta \tau) &\simeq & 2 S_{\rm kink}^{a)} - \beta (W - 2\xi) \mathcal T \notag \\
&+& \beta (W - 2\xi) (\mathcal T - \delta \tau) \notag \\
&-& E_{\rm cond} (\mathcal T - \delta \tau) \notag\\
&-& \frac{2m v^4}{3 \xi^2} (\mathcal T - \delta \tau)^3
\end{eqnarray}
Here, the second last line is the correction to the condensation energy paid at during the time of the bounce $\mathcal T + \delta \tau$, which is shorter than the time of two kinks.
This concludes the derivation of Eq.~\eqref{eq:Bounce2D} of the main text.
\section{Multivortex configurations}
\label{app:MultivortexAction}
In this section we present details on the co-tunneling events of multiple vortices.
\begin{figure}
\includegraphics[scale=.7]{ProcessAIntegrationsNoCone.pdf}
\caption{Graphical representation of the variational \textit{Ansatz} \eqref{eq:AnsatzMultivortex} for the action in case a) and $n = 3$. Each arrow contributes $s(d)$, Eq.~\eqref{eq:AnsatzSd}, to the total action, where $d$ is the distance in real space between the points of nucleation and annihilation of the vortices. The major approximation is that the motion along the arrows is linear with constant speed $v(d)$. All space time positions of nucleation except $Y_{n+1} = -W/2$ are variational parameters on which also the space time positions of annihilation depend.}
\label{fig:ProcessAIntegrations}
\end{figure}
\subsection{Variational \textit{Ansatz} and solution}
We consider processes which involve $n$ dipoles in the bulk of the system. We estimate the contribution of these processes by means of the following variational \textit{Ansatz} for the action, see also Fig.~\ref{fig:ProcessAIntegrations}. For the edge unbinding, i.e. processes of type Fig.~\ref{fig:MultiVortex} a) we write
\begin{subequations}
\begin{equation}
S_{a)} = \sum_{i = 1}^{n} S_{\rm kink}(\vert \v X_i - \v X_{i,i+1}\vert) + \sum_{i = 0}^{n} S_{\rm kink}(\vert \v X_{i,i+1}- \v X_{i +1} \vert),\label{eq:AnsatzMultivortexa}
\end{equation}
and for the case of Fig.~\ref{fig:MultiVortex} b)
\begin{equation}
S_{b)} = \sum_{i = 1}^{n} S_{\rm kink}(\vert \v X_i - \v X_{i,i+1}\vert) + \sum_{i = 0}^{n-1} S_{\rm kink}(\vert \v X_{i,i+1}- \v X_{i +1}\vert),\label{eq:AnsatzMultivortexb}
\end{equation}
and we remind the reader that
\begin{equation}
S_{\rm kink}(d) = S_{\rm pot}(d) + S_{\rm cond}(d)\label{eq:AnsatzSd}
\end{equation}
with
\begin{align}
S_{\rm pot}(d) &= 2 m v\, d \sqrt{ - \ln \left ( \frac{2 \xi}{d}\right )}, \\
S_{\rm cond}(d) &= m v\, d /\sqrt{ - \ln \left ( \frac{2 \xi}{d}\right )},
\end{align}
for $d \gg \xi$, (the general expression is presented in Fig.~\ref{fig:MultiVortex} c).
\label{eq:AnsatzMultivortex}
\end{subequations}
Following the graphical representation of Fig~\ref{fig:MultiVortex} and Fig.~\ref{fig:ProcessAIntegrations}, we label initial positions $\v X_i = (X_i,Y_i)$ and initial times $\tau_i$ with indices $i$ ordered from top to bottom, i.e. $Y_i >Y_{i+1}$. The positions $\v X_{i,i+1} = (X_{i,i+1},Y_{i,i+1})$ and times $\tau_{i,i+1}$ represent the points in space time, at which recombined vortex pairs annihilate. The tunneling event is dominated by contributions which fulfill $Y_{i,i+1} > Y_{i+1,i+2}$. Furthermore, for case a) we define $\v X_{n+1}= (X_{n+1},-W/2)$ and for case b) $\v X_{n,n+1} = (X_{n,n+1},-W/2)$. In both cases a) and b) $\v X_{0,1}= (X_{0,1},W/2)$.
Of course, processes with vortices and antivortices interchanged or processes of the type a) with a net vortex transfer from top to bottom are also present. Their contribution equals the contribution of one of the processes discussed here and are thus not discussed separately.
The calculation involves two assumptions. The first is the approximation of linear motion with constant velocity $v(d)$ in an interval of distance $d$ (e.g. $d = \vert \v X_1 - \v X_{1,2} \vert$). In fact, writing $\mathcal T = d/v(d)$ leads to $v(d)$ which is nearly consistent with the maximal vortex speed as imposed by energy conservation (up to a factor of 2). The second approximation is that each space time position $(\v X_{i,i+1}, \tau_{i,i+1})$ depends only on the two starting points of adjacent vortices, i.e. on $(\v X_{i}, \tau_{i})$ and $(\v X_{i+1}, \tau_{i+1})$. This second approximation has no influence on the saddle point action, but it does affect the fluctuation determinant. The parameter regime of validity of these approximations shall be discussed below.
\subsubsection{Saddle-point configurations}
We vary the Ansatz~\eqref{eq:AnsatzMultivortex} with respect to the starting times and positions of the vortices. It is convenient to use a lighter notation $S_{\rm kink}(d) = s(d)$. This yields (here $\mu,\nu = x, y$)
\begin{eqnarray}
d_{\v X_{k,\mu}} S_{a),b)} &=& \Big \lbrace s'(\vert \v X_{k-1,k} - \v X_{k} \vert ) \reallywidehat{(\v X_{k-1,k} - \v X_{k} )}_\nu \notag \\
&-& s'(\vert \v X_{k-1} - \v X_{k-1,k} \vert ) \reallywidehat{( \v X_{k-1} - \v X_{k-1,k})}_\nu \Big \rbrace \notag \\
&\times& \partial_{\v X_{k,\mu}} (\v X_{k-1,k})_\nu \notag \\
&+&\Big \lbrace s'(\vert \v X_{k,k+1} - \v X_{k+1} \vert ) \reallywidehat{(\v X_{k,k+1} - \v X_{k+1} )}_\nu \notag \\
&-& s'(\vert \v X_{k} - \v X_{k,k+1} \vert ) \reallywidehat{( \v X_{k} - \v X_{k,k+1})}_\nu \Big \rbrace \notag \\
&\times& \partial_{\v X_{k,\mu}} (\v X_{k,k+1})_\nu \notag \\
&-& s'(\vert \v X_{k-1,k} - \v X_{k} \vert ) \reallywidehat{(\v X_{k-1,k} - \v X_{k} )}_\mu \notag \\
&+& s'(\vert \v X_{k} - \v X_{k,k+1} \vert ) \reallywidehat{( \v X_{k} - \v X_{k,k+1})}_\mu,
\end{eqnarray}
and
\begin{eqnarray}
d_{\tau_{k}} S_{a),b)} &=& \Big \lbrace s'(\vert \v X_{k-1,k} - \v X_{k} \vert ) \reallywidehat{(\v X_{k-1,k} - \v X_{k} )}_\nu \notag \\
&-& s'(\vert \v X_{k-1} - \v X_{k-1,k} \vert ) \reallywidehat{( \v X_{k-1} - \v X_{k-1,k})}_\nu \Big \rbrace \notag \\
&\times& \partial_{\tau_{k}} (\v X_{k-1,k})_\nu \notag \\
&+&\Big \lbrace s'(\vert \v X_{k,k+1} - \v X_{k+1} \vert ) \reallywidehat{(\v X_{k,k+1} - \v X_{k+1} )}_\nu \notag \\
&-& s'(\vert \v X_{k} - \v X_{k,k+1} \vert ) \reallywidehat{( \v X_{k} - \v X_{k,k+1})}_\nu \Big \rbrace \notag \\
&\times& \partial_{\tau_{k}} (\v X_{k,k+1})_\nu.
\end{eqnarray}
Recall that in case a) [case b)] $Y_{01} = W/2$ and $Y_{n+1} = -W/2$ [$Y_{01} = W/2$ and $Y_{n,n+1} = -W/2$] are fixed and thus not variational parameters. By consequence, $\partial_{\v X_1} Y_{01} \equiv 0$ in both cases, and additionally in case b) $\partial_{\v X_n} Y_{n,n+1} \equiv 0$ while in case a) the terms proportional to $\partial_{Y_{n+1}} \v X_{n,n+1}$ should be omitted.
Clearly, a solution of these equations is given by $\reallywidehat{(\v X_{k-1,k} - \v X_{k} )}=\reallywidehat{( \v X_{k-1} - \v X_{k-1,k})} \quad \forall k$, $X_i = X_j \quad \forall i,j$, and equal distances in $y$-direction $Y_{i-1,i}-Y_i = Y_i - Y_{i,i+1} =d_N \quad \forall i$. In case a) $d_N = W/(2n +1)$, and in case b) $d_N = W/(2n)$. By consequence of the linear motion all starting times are the same, $\tau_i = \tau_j \quad \forall i,j$. This is the physical solution we perturb about.
\subsubsection{Determination of space time positions of vortex annihilation}
For the derivation of the fluctuation determinant, it will be necessary to determine the dependence $\v X_{i,i+1} (\v X_i, \tau_i ; \v X_{i+1}, \tau_{i+1})$. Here we present this dependence perturbing weakly about the saddle-point solution.
The \textit{Ansatz} of linear motion implies for the motion of vortices on downward oriented arrows of Fig.~\ref{fig:ProcessAIntegrations}
\begin{subequations}
\begin{equation}
\v x(\tau) = \v X_k - v(\vert \v X_k - \v X_{k,k+1} \vert) \reallywidehat{\v X_k - \v X_{k,k+1}} (\tau - \tau_k)
\end{equation}
while the motion on upwards oriented arrows is
\begin{equation}
\v x(\tau) = \v X_{k+1} + v(\vert \v X_{k,k+1} - \v X_{k+1} \vert) \reallywidehat{\v X_{k,k+1} - \v X_{k+1}} (\tau - \tau_{k+1})
\end{equation}
\end{subequations}
We determine the moment of annihilation $\tau_{k,k+1}$ by equating the two expressions. This leads to
\begin{equation}
\tau_{k,k+1} = \frac{\Delta X_k + v(\Delta X_k ) \tau_k + \Delta X_{k+1} v(\Delta X_{k+1}) \tau_{k+1}}{v(\Delta X_{k}) + v(\Delta X_{k+1}) },
\end{equation}
where $\Delta X_{k} = \vert \v X_k - \v X_{k,k+1} \vert $ and $\Delta X_{k+1} = \vert \v X_{k,k+1} - \v X_{k+1} \vert$. Inserting this solution into the \textit{Ansatz} for $\v x(\tau)$ in the quasi classical equations of motion yields
\begin{eqnarray}
\v X_{k,k+1} &=& \reallywidehat{\v X_k - \v X_{k + 1}} \frac{v(\Delta X_{k}) v(\Delta X_{k+1})}{v(\Delta X_{k}) + v(\Delta X_{k+1}) } (\tau_k - \tau_{k +1}) \notag \\
&+& \frac{ v(\Delta X_{k+1} ) \v X_k + v(\Delta X_{k}) \v X_{k+1}}{v(\Delta X_{k}) + v(\Delta X_{k+1}) }.
\end{eqnarray}
\subsubsection{Fluctuation determinant (Gaussian approximation)}
We here present the calculation of the fluctuation determinant. Thus, space time fluctuations of initial positions are treated at Gaussian level.
For the calculation of the fluctuation determinant, we need the derivative of $\v X_{k,k+1}$ with respect to $\v X_{k}$,$\v X_{k+1}$,$\tau_{k}$ and $\tau_{k+1}$ at the saddle point (SP). We thus obtain in the bulk of the system
\begin{subequations}
\begin{eqnarray}
\partial_{\v X_{k,\nu}} (\v X_{k,k+1})_\mu \vert_{SP} &=& \frac{\delta_{\mu \nu}}{2} \notag \\
&=& \partial_{\v X_{k,\nu}} (\v X_{k,k+1})_\mu \vert_{SP} , \\
\partial_{\tau_k} (\v X_{k,k+1})_\mu \vert_{SP}&=& \underbrace{\frac{v(d_N)/2}{1 - \frac{v'(d_N) d_N}{2v(d_N)} }}_{=: \tilde v_n/2}\delta_{\mu, y} \notag \\
&=& -\partial_{\tau_{k+1}} (\v X_{k,k+1})_\mu \vert_{SP} .
\end{eqnarray}
At the upper boundary we obtain
\begin{eqnarray}
\partial_{\v X_1,\nu}(\v X_{0,1})_\mu \vert_{SP} &=& \delta_{\mu,\nu} \delta_{\mu,x}, \\
\partial_{\tau_1}(\v X_{0,1})_\mu \vert_{SP} &=& 0.
\end{eqnarray}
an analogous result for the $\partial_{\v X_n,\nu}(\v X_{n,n+1})_\mu \vert_{SP}, \partial_{\tau_n}(\v X_{n,n+1})_\mu \vert_{SP}$ in the case b). For case a), we remind the reader that $Y_{n+1}$ is not a variational parameter.
\end{subequations}
By means of the previous expressions one can determine the correction to the action determining Gaussian fluctuations around the saddle point solution. Direct calculation of second derivatives of the action Eq.~\eqref{eq:AnsatzMultivortex} show that fluctuations in $x$, $y$ and $\tau$ directions do not mix. We obtain
\begin{subequations}
\begin{eqnarray}
\delta S_{a)} &=& \frac{1}{2} \Bigg \lbrace \frac{s'(d_N)}{d_N} \Big [\frac{1}{2} (\delta X_1)^2 - \delta X_1 \delta X_2 + \delta X_2^2 \notag \\
&& - \delta X_2 \delta X_3 + \dots + \delta X_n^2 - \delta X_n \delta X_{n + 1} + \frac{1}{2} \delta X_{n+1}^2 \Big ] \notag \\
&& + s''(d_N) \tilde v_n^2 \Big [\frac{1}{2} (\delta \tau_1)^2 - \delta \tau_1 \delta \tau_2 + \delta \tau_2^2 \notag \\
&& - \delta \tau_2 \delta \tau_3 + \dots + \delta \tau_n^2 - \delta \tau_n \delta \tau_{n + 1} + \frac{1}{2} \delta \tau_{n+1}^2 \Big ] \notag \\
&& + s''(d_N) \Big [\frac{3}{2} (\delta Y_1)^2 - \delta Y_1 \delta Y_2 + \delta Y_2^2 \notag \\
&& - \delta Y_2 \delta Y_3 + \dots - \delta Y_{n-1} \delta Y_{n}+ \delta Y_n^2 \Big ] \Bigg \rbrace
\end{eqnarray}
and
\begin{eqnarray}
\delta S_{b)} &=& \frac{1}{2} \Bigg \lbrace \frac{s'(d_N)}{d_N} \Big [\frac{1}{2} (\delta X_1)^2 - \delta X_1 \delta X_2 + \delta X_2^2 \notag \\
&& - \delta X_2 \delta X_3 + \dots + \delta X_{n-1}^2 - \delta X_{n-1} \delta X_{n} + \frac{1}{2} \delta X_{n}^2 \Big ] \notag \\
&& + s''(d_N) \tilde v_n^2 \Big [\frac{1}{2} (\delta \tau_1)^2 - \delta \tau_1 \delta \tau_2 + \delta \tau_2^2 \notag \\
&& - \delta \tau_2 \delta \tau_3 + \dots + \delta \tau_{n-1}^2 - \delta \tau_{n-1} \delta \tau_{n} + \frac{1}{2} \delta \tau_{n}^2 \Big ] \notag \\
&& + s''(d_N) \Big [\frac{3}{2} (\delta Y_1)^2 - \delta Y_1 \delta Y_2 + \delta Y_2^2 \notag \\
&& - \delta Y_2 \delta Y_3 + \dots - \delta Y_{n-1} \delta Y_{n}+ \frac{3}{2}\delta Y_n^2 \Big ] \Bigg \rbrace .
\end{eqnarray}
\label{eq:app:FluctAction}
\end{subequations}
Note that in both cases a) and b) there are two zero modes. They become apparent when we shift the integration variables $\delta X_i \rightarrow \delta X_{i} + \delta {X_{i+1}} \quad \forall i = 1,2,\dots$ (the same for $\tau_i$s), correspond to the center of mass coordinate and are a consequence of translation invariance in $x$- and $\tau$- direction, respectively. Following the standard procedure, zero mode integrals have to be performed exactly and to be kept out of the fluctuation determinant.
The fluctuation determinant is incorporated (up to a constant) into the entropic contribution to the action $\delta S_H$ which in case a) is
\begin{subequations}
\begin{eqnarray}
\delta S_{H, a)} &=& - \ln \Bigg \lbrace \prod_{i = 1}^n \int_{-\infty}^\infty \frac{dY_i}{2\xi} \frac{dX_i}{2\xi} \frac{d \tau_i}{2\xi/v_0} e^{-\delta S_{a)}}\Bigg \rbrace \notag \\
& \simeq & n \ln \left [s''(d_N) (2\xi)^2\right ] + n \ln \left [\tilde v_n/v_0\right ] \notag \\
&&+ \frac{n}{2} \ln \left [(2\xi)^2 s'(d_N)/d_N\right ]
\end{eqnarray}
while in case b) it is
\begin{eqnarray}
\delta S_{H, b)} &=& - \ln \Bigg \lbrace \prod_{i = 1}^n \int_{-\infty}^\infty \frac{dY_i}{2\xi} \prod_{i = 1}^{n-1} \int_{-\infty}^\infty \frac{dX_i}{2\xi} \frac{d \tau_i}{2\xi/v_0} e^{-\delta S_{b)}}\Bigg \rbrace \notag \\
& \simeq & (n- \frac{1}{2}) \ln \left [s''(d_N) (2\xi)^2\right ] + (n-1) \ln \left [\tilde v_n/v_0\right ] \notag \\
&& + \frac{n-1}{2} \ln \left [(2\xi)^2 s'(d_N)/d_N\right ].
\end{eqnarray}
\end{subequations}
In the concluding section of the main text, we present a simplified estimate, which matches the large $n$ limit of the calculations above, i.e.
\begin{equation}
\delta S_H \sim n \ln [s''(d_N)(2 \xi)^2] = n \ln\left [\frac{\partial^2}{\partial(d_N/2\xi)^2} s(d_N) \right ]
\end{equation}
We can use that $s(d_N)$ is actually a function of $(d_N/2\xi)$, so that modulo unimportant factors of order unity
\begin{equation}
\delta S_H \sim n \ln [s''(d_N)(2 \xi)^2] \sim n \ln\left [s(d_N) \right ],
\end{equation}
where $d_N \sim 2\xi$ at the optimum.
\section{Effect of mesoscopic fluctuations on vortex tunneling}
\label{App:Disorder}
In this section, we estimate the effect of randomness in the superconducting stiffness $J$
(corresponding to the disorder-induced mesoscopic fluctuations of the gap)
on the resistance generated vortex tunneling events.
The effect of gap fluctuations can be modeled by a random stiffness
$$J(\v x) = J [1 + \rho(\v x) ]$$
with
$$\langle \rho(\v x) \rho(\v x') \rangle = \rho^2 \xi^2 \delta(\v x - \v x'),$$
where $ \rho \sim 1/[E_F\tau_{\rm el}(E_F\tau_{\rm el}-\mathcal C)]$ and $\mathcal C \sim 1$
is small for moderate disorder.~\cite{SkvortsovFeigelman2005}
The tunneling action for a single-vortex tunneling in the presence of such randomness is approximately given by Taylor expansion
\begin{equation}
S = S_{\rm kink} + \int_{-W/2+\xi}^{W/2-\xi}dy \sqrt{2m V(y)} \rho(\v x)/2,
\end{equation}
and thus the ``local resistance'' is given by
\begin{equation}
R(x) = R_0 \exp\left [- \int_{-W/2+\xi}^{W/2-\xi} dy \sqrt{2m V(y)} \rho(\v x) \right],
\end{equation}
where $R_0$ is the result without fluctuations.
Then, it readily follows that $R(x)$ is white-noise, log-normal distributed,
\begin{align}
\langle \ln R(x) \rangle &= \ln R_0, \\
\langle \ln R(x)\ln R(x') \rangle& = 2m \rho^2
\xi^2 \delta(x - x') \int_{-W/2+\xi}^{W/2-\xi} dy\, V(y) .
\end{align}
The total resistance is given by the integral of $R(x)$ over $x$, i.e., by the average local resistance. Both typical and average resistance behave as ${\ln~R\propto-W}$.
In multi-vortex tunneling events, the tunneling distances $d_i$ depend on the disorder configuration and are generically no longer equal $d_i \neq d$. At the same time, at the level of the approximations involved here, one may estimate the effect of pinning by $d_i = d$
\begin{equation}
R(x) = R_0 \exp\left [- \frac{W}{d}\int_{-d/2+\xi}^{d/2-\xi} dy \sqrt{2m V(y)} \rho(\v x) \right],
\end{equation}
leading to
\begin{align}
\langle \ln R(x) \rangle &= \ln R_0, \\
\langle \ln R(x)\ln R(x') \rangle &=
\frac{2m \rho^2W^2 \xi^2}{d^2} \delta(x - x') \int_{-\frac{d}{2}+\xi}^{\frac{d}{2}-\xi} dy\, V(y),
\end{align}
where $d =\mathcal O(\xi)$ for the optimum number of vortices involved in the tunneling event.
We thus find that, both in the single-vortex and multi-vortex tunneling processes, a local resistance $R(x)$ is weakly (for large normal-state conductances) random and log-normal distributed. The exponential (with $W$) scaling of the total resistance of the strip is not affected by fluctuations in this regime.
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,115 |
{"url":"https:\/\/hal.inria.fr\/inria-00455303\/en\/","text":"# Long non-crossing configurations in the plane\n\n* Corresponding author\nAbstract : We revisit several maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computational Geometry, 1993). Given a set of $n$ points in the plane in general position (no three points collinear), compute a longest non-crossing configuration composed of straight line segments that is: (a) a matching (b) a Hamiltonian path (c) a spanning tree. Here we obtain new results for (b) and (c), as well as for the Hamiltonian cycle problem: (i) For the longest non-crossing Hamiltonian path problem, we give an approximation algorithm with ratio $\\frac{2}{\\pi+1} \\approx 0.4829$. The previous best ratio, due to Alon et al., was $1\/\\pi \\approx 0.3183$. Moreover, the ratio of our algorithm is close to $2\/\\pi$ on a relatively broad class of instances: for point sets whose perimeter (or diameter) is much shorter than the maximum length matching. The algorithm runs in $O(n^{7\/3}\\log{n})$ time. (ii) For the longest non-crossing spanning tree problem, we give an approximation algorithm with ratio 0.502 which runs in $O(n \\log{n})$ time. The previous ratio, 1\/2, due to Alon et al., was achieved by a quadratic time algorithm. Along the way, we first re-derive the result of Alon et al. with a faster $O(n \\log{n})$-time algorithm and a very simple analysis. (iii) For the longest non-crossing Hamiltonian cycle problem, we give an approximation algorithm whose ratio is close to $2\/\\pi$ on a relatively broad class of instances: for point sets with the product $\\bf{<}$diameter$\\times$ convex hull size $\\bf{>}$ much smaller than the maximum length matching. The algorithm runs in $O(n^{7\/3}\\log{n})$ time. No previous approximation results were known for this problem.\nKeywords :\nDocument type :\nConference papers\nJean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.311-322, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science\n\nCited literature [14 references]\n\nhttps:\/\/hal.inria.fr\/inria-00455303\nContributor : Publications Loria <>\nSubmitted on : Wednesday, February 10, 2010 - 9:49:50 AM\nLast modification on : Wednesday, February 10, 2010 - 9:50:33 AM\nDocument(s) archiv\u00e9(s) le : Friday, June 18, 2010 - 7:50:26 PM\n\n### File\n\ndumitrescu2.pdf\nFiles produced by the author(s)\n\n### Identifiers\n\n\u2022 HAL Id : inria-00455303, version 1\n\n### Citation\n\nAdrian Dumitrescu, Csaba D. T\u00f3th. Long non-crossing configurations in the plane. Jean-Yves Marion and Thomas Schwentick. 27th International Symposium on Theoretical Aspects of Computer Science - STACS 2010, Mar 2010, Nancy, France. pp.311-322, 2010, Proceedings of the 27th Annual Symposium on the Theoretical Aspects of Computer Science. \u3008inria-00455303\u3009\n\nRecord views","date":"2018-03-22 21:10:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6636310815811157, \"perplexity\": 938.6388784091147}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-13\/segments\/1521257648003.58\/warc\/CC-MAIN-20180322205902-20180322225902-00208.warc.gz\"}"} | null | null |
package com.ppweather.app.util;
public interface HttpCallbackListener {
void onFinish(String response);
void onError(Exception e);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,731 |
namespace SVI {
SVIStaticModelNode::SVIStaticModelNode(SVIGLSurface *surface) :
SVIModelNode(surface) {
}
void SVIStaticModelNode::render(BeginModeType beginType) {
update();
SVIProgramParams renderParams;
SVIProgramHandler *pHandler = NULL;
SVIProgram *pProgram = NULL;
renderParams.addElement(EM_3DMODEL);
pProgram = mSVIGLSurface->getProgramManager()->getProgram(&renderParams);
if (pProgram == NULL || !pProgram->getActivated()) return;
pHandler = pProgram->getHandler();
pProgram->use();
SVIVector4 color = SVIVector4(1.0f, 1.0f, 1.0f, 1.0);
SVIMatrix viewMat = mCamera->getViewMatrix();
SVIMatrix projectionMat = mCamera->getProjMatrix();
viewMat = (*mGlobalTransform) * viewMat;
pHandler->setUniform(HD_U_PROJ, projectionMat);
pHandler->setUniform(HD_U_VIEW, viewMat);
pHandler->setUniform(HD_U_COLOR, color);
SVIVector3 lightPosition = SVIVector3(0.25f,0.25f,10.0f);
SVIVector4 lightAmbient = SVIVector4(0.6f,0.6f,0.6f,1.0f);
SVIVector4 lightDiffuse = SVIVector4(0.68f,0.66f,0.63f,1.0f);
SVIVector4 lightSpecular = SVIVector4(0.3f,0.28f,0.275f,1.0f);
SVIMatrix normalMatrix = *mGlobalTransform;
normalMatrix.invert();
normalMatrix.transpose();
SVIFloat lightShininess = 50.0f;
pHandler->setUniform(HD_U_NORMAL,normalMatrix);
pHandler->setUniform(HD_U_LIGHT_OFFSET,lightPosition);
pHandler->setUniform(HD_U_AMBIENT,lightAmbient);
pHandler->setUniform(HD_U_DIFFUSE,lightDiffuse);
pHandler->setUniform(HD_U_SPECULAR,lightSpecular);
pHandler->setUniform(HD_U_SHININESS,lightShininess);
glEnable(GL_DEPTH_TEST);
glDepthFunc(GL_LESS);
glEnable(GL_CULL_FACE);
glCullFace(GL_BACK);
if(!mMeshList.empty())
for(int i = 0; i < (int)mMeshList.size(); ++i) {
mMeshList[i]->mProgramHandler = pHandler;
mMeshList[i]->render(beginType);
}
if(!mChildList.empty())
for(int i = 0; i < (int)mChildList.size(); ++i) {
mChildList[i]->setCamera(mCamera);
mChildList[i]->render(beginType);
}
}
void SVIStaticModelNode::update() {
if(mParent != NULL) {
// globalTM = localTM * parentTM
*mGlobalTransform = *mLocalTransform * *(mParent->getGlobalTransform());
}
else {
*mGlobalTransform = *mLocalTransform;
}
}
SVISceneNode* SVIStaticModelNode::deepCopy(SVIBool withSubSlide) {
SVIStaticModelNode *copyNode = new SVIStaticModelNode(mSVIGLSurface);
copyNode->mParent = mParent;
//SceneNodeList mChildList;
copyNode->mId = mId;
*(copyNode->mLocalTransform) = *mLocalTransform;
*(copyNode->mGlobalTransform) = *mGlobalTransform;
// increase refer count
copyNode->mMeshList = mMeshList;
if(withSubSlide) {
copyChildNodeList(copyNode);
}
return copyNode;
}
} // end namespace SVI | {
"redpajama_set_name": "RedPajamaGithub"
} | 333 |
Lucius is an average teenager dreaming of a career as a professional gamer. He is one of the lucky few selected to participate in Codename: Freedom, a new game that promises to push Virtual Reality to the ultimate level.
Unbeknownst to him, the Game Developers were commissioned to design Freedom for the sole purpose of creating super soldiers in preparation for the coming war.
With the pain dampeners turned off and an army of monsters waiting for him, will Lucius find a reason to push his body to the limit, or quit, giving up on his dream forever? | {
"redpajama_set_name": "RedPajamaC4"
} | 1,631 |
<?php
namespace EntWeChat\Suite;
use EntWeChat\Server\Guard as ServerGuard;
use EntWeChat\Support\Collection;
use EntWeChat\Support\Log;
use Symfony\Component\HttpFoundation\Response;
class Guard extends ServerGuard
{
const EVENT_CREATE_AUTH = 'create_auth';
const EVENT_CANCEL_AUTH = 'cancel_auth';
const EVENT_CHANGE_AUTH = 'change_auth';
const EVENT_SUITE_TICKET = 'suite_ticket';
/**
* Event handlers.
*
* @var \EntWeChat\Support\Collection
*/
protected $handlers;
/**
* Get handlers.
*
* @return \EntWeChat\Support\Collection
*/
public function getHandlers()
{
return $this->handlers;
}
/**
* Set handlers.
*
* @param array $handlers
*/
public function setHandlers(array $handlers)
{
$this->handlers = new Collection($handlers);
return $this;
}
/**
* {@inheritdoc}
*/
public function serve()
{
$message = $this->getMessage();
// Handle Messages.
if (isset($message['MsgType'])) {
return parent::serve();
}
Log::debug('Suite Request received:', [
'Method' => $this->request->getMethod(),
'URI' => $this->request->getRequestUri(),
'Query' => $this->request->getQueryString(),
'Protocal' => $this->request->server->get('SERVER_PROTOCOL'),
'Content' => $this->request->getContent(),
]);
// If sees the `auth_code` query parameter in the url, that is,
// authorization is successful and it calls back, meanwhile, an
// `authorized` event, which also includes the auth code, is sent
// from WeChat, and that event will be handled.
if ($this->request->get('auth_code')) {
return new Response(self::SUCCESS_EMPTY_RESPONSE);
}
$this->handleEventMessage($message);
return new Response(self::SUCCESS_EMPTY_RESPONSE);
}
/**
* Handle event message.
*
* @param array $message
*/
protected function handleEventMessage(array $message)
{
Log::debug('Suite Event Message detail:', $message);
$message = new Collection($message);
$infoType = $message->get('InfoType');
if ($handler = $this->getHandler($infoType)) {
$handler->handle($message);
} else {
Log::notice("No existing handler for '{$infoType}'.");
}
if ($customHandler = $this->getMessageHandler()) {
$customHandler($message);
}
}
/**
* Get handler.
*
* @param string $type
*
* @return \EntWeChat\Suite\EventHandlers\EventHandler|null
*/
public function getHandler($type)
{
return $this->handlers->get($type);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,043 |
package driver
import (
"errors"
"golang.org/x/exp/shiny/driver/internal/errscreen"
"golang.org/x/exp/shiny/screen"
)
func main(f func(screen.Screen)) {
f(errscreen.Stub(errors.New("no driver for accessing a screen")))
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,337 |
\section{\bf Introduction}
For each non-negative integer $k$, the
$q-$integer $[k]_q$ and the $q-$factorial $[k]_q!$ are respectively
defined by $$ [k]_q=\left\{\begin{array}{ll} (1-q^k)\big / (1-q),\
\ &q\neq 1\\k,&q=1\end{array},\right.$$ and $$
[k]_q!=\left\{\begin{array}{ll} [k]_q\, [k-1]_q\cdots [1]_q,\ \ &k\ge
1\\1,&k=0\end{array}.\right.\ $$ For the integers $n,\ k $
satisfying $ n\ge k\ge 0$, the $q-$binomial coefficients are
defined by
$$\left[\begin{array}{c}n\\k\end{array}\right]_q=\frac{[n]_q!}{[k]_q![n-k]_q!}\
$$
(see e.g. \cite{TE}).
We consider the $q$-exponential function in the following form:
\begin{eqnarray*}
\lim_{n\rightarrow \infty}\frac{1}{(1-x)_q^n} &=& \lim_{n\rightarrow \infty}\sum_{k=0}^\infty \left[ {\begin{array}{*{20}{c}}
{n+k-1} \\
k \\
\end{array}} \right]_q x^k \\
&=& \lim_{n\rightarrow \infty}\sum_{k=0}^\infty \frac{(1-q^{n+k-1})....(1-q^n)}{(1-q)(1-q^2)...(1-q^k)}x^k\\
&=& \sum_{k=0}^\infty \frac{x^k}{(1-q)(1-q^2)...(1-q^k)}=e_q(x).
\end{eqnarray*}
Another form of $q$-exponential function is given as follows:
\begin{eqnarray*}
\lim_{n\rightarrow \infty}(1+x)_q^n=\sum_{k=0}^\infty \frac{q^{k(k-1)/2}x^k}{(1-q)(1-q^2)...(1-q^k)}=E_q(x).
\end{eqnarray*}
It is easily observed that $e_q(x)E_q(-x)=e_q(-x)E_q(x)=1$.\\
Based on the $q$-integers Phillips \cite{Phillips} introduced the $q$ analogue of the well known Bernstein polynomials. For $f\in C[0,1]$ and $0<q<1$, the $q$-Bernstein polynomials are defined as
\begin{equation}\label{1}
{\mathcal{B}_{n,q}}\left( {f,x} \right) = \sum\limits_{k = 0}^n {b_{k,n}^q(x)} f\left( \frac{[k]_q}{[n]_q} \right),
\end{equation}
where the $q$-Bernstein basis function is given by
$$b_{k,n}^q(x) = \left[ {\begin{array}{*{20}{c}}
{n} \\
k \\
\end{array}} \right]_q x^k (1 - x)_q^{n - k}, x\in [0,1]$$
and $\left(a-b\right)_{q}^{n}=\prod\limits_{s=0}^{n-1}(a-q^{s}b),\quad a,b\in\mathbb{R}.$
Also Trif \cite{Trif} proposed the $q$ analogue of well known Meyer-K\"{o}nig-Zeller operators. For $f\in C[0,1]$ and $0<q<1$, the $q$-Meyer-K\"{o}nig-Zeller operators are defined as
\begin{equation}\label{1}
{\mathcal{M}_{n,q}}\left( {f,x} \right) = \sum\limits_{k = 0}^\infty m_{k,n}^q(x) f\left( \frac{[k]_q}{[n]_q} \right),
\end{equation}
where the $q$-MKZ basis function is given by
$$m_{k,n}^q(x) = \left[ {\begin{array}{*{20}{c}}
{n+k+1} \\
k \\
\end{array}} \right]_q x^k (1 - x)_q^{n}, x\in [0,1].$$
For $f\in C[0,\infty)$ and $0<q<1$, the $q$-Beta operators are defined as
\begin{equation}\label{1}
{\mathcal{V}_{n}}\left( {f,x} \right) = \frac{1}{[n]_q}\sum\limits_{k = 0}^\infty v_{k,n}^q(x) f\left( \frac{[k]_q}{q^{k-1}[n]_q} \right),
\end{equation}
where the $q$-Beta basis function is given by $$v_{k,n}^q(x) = \frac{q^{k(k-1)/2}}{B_q(k+1,n)}\frac{x^k}{(1+x)_q^{n+k+1}}, x\in [0,\infty )$$
and $B_q(m,n) $ is $q$-Beta function.\\
In the present paper we establish the generating functions for $q$-Bernstein, $q$-Meyer-K\"{o}nig-Zeller and $q$-Beta basis functions.
\section{\bf Generating Function for $q$-Bernstein basis}
\begin{thm}\label{thm:1}
$b_{k,n}^q(x) $ is the coefficient of $\frac{t^n}{[n]_q!}$ in the expansion of
$$\frac{x^kt^k}{[k]_q!}e_q((1-q)(1-x)_qt).$$
\end{thm}
\begin{proof}
First consider
\begin{eqnarray*}
\frac{x^kt^k}{[k]_q!}e_q((1-q)(1-x)_qt)&=&\frac{x^kt^k}{[k]_q!}\sum_{n=0}^\infty \frac{(1-x)_q^nt^n}{[n]_q!}\\
&=&\frac{1}{[k]_q!}\sum_{n=0}^\infty \frac{x^k(1-x)_q^nt^{n+k}}{[n]_q!}\\
&=&\sum_{n=0}^\infty \frac{[n+1]_q[n+2]_q.....[n+k]_qx^k(1-x)_q^nt^{n+k}}{[n+k]_q![k]_q!}\\
&=&\sum_{n=0}^\infty \left[\begin {array}{c}
n+k \\
k
\end{array}
\right]_q\frac{x^k(1-x)_q^nt^{n+k}}{[n+k]_q!}\\
&=&\sum_{n=k}^\infty \left[\begin {array}{c}
n \\
k
\end{array}
\right]_q \frac{x^k(1-x)_q^{n-k}t^n}{[n]_q!}=\sum_{n=0}^\infty b_{k,n}^q(x)\frac{t^n}{[n]_q!}.
\end{eqnarray*}
This completes the proof of generating function for $b_{k,n}^q(x).$
\end{proof}
\section{\bf Generating Function for $q$-MKZ basis}
\begin{thm}\label{thm:1} $m_{k,n}^q(x) $ is the coefficient of $t^k$ in the expansion of $\frac{(1-x)_q^n}{(1-xt)_q^{n+2}}.$
\end{thm}
\begin{proof}
It is easily seen that
\begin{eqnarray*}
\frac{(1-x)_q^n}{(1-xt)_q^{n+2}}= \sum_{k=0}^\infty \left[\begin {array}{c}
n+k+1 \\
k
\end{array}
\right]_q(1-x)_q^n x^kt^k= \sum_{k=0}^\infty m_{k,n}^q(x) t^k .
\end{eqnarray*}
This completes the proof.
\end{proof}
\section{\bf Generating Function for $q$-Beta basis}
\begin{thm} It is observed by us that $v_{k,n}^q(x)$ is the coefficient of
$\frac{t^k}{[n+k]_q!}$ in the expansion of $\frac{1}{(1+x)_q^{n+1}}E_q\left(\frac{(1-q)xt}{(1+q^{n+1}x)_q}\right).$
\end{thm}
\begin{proof}
First using the definition of $q$-exponential $E_q(x),$ we have
\begin{align*}
\frac{1}{(1+x)_q^{n+1}}E_q\left(\frac{(1-q)xt}{(1+q^{n+1}x)_q}\right)&=\frac{1}{(1+x)_q^{n+1}}\sum_{k=0}^\infty q^{k(k-1)/2}\frac{x^k}{(1+q^{n+1}x)_q^k}\frac{t^k}{[k]_q!}\\
&=\sum_{k=0}^\infty q^{k(k-1)/2}\frac{x^k}{(1+x)_q^{n+k+1}}\frac{t^k}{[k]_q!}\\
&=\sum_{k=0}^\infty q^{k(k-1)/2}\frac{x^kt^k}{(1+x)_q^{n+k+1}}\frac{[k+1]_q[k+2]_q...[n+k]_q}{[n+k]_q!}\\
&=\sum_{k=0}^\infty q^{k(k-1)/2}\frac{x^k}{(1+x)_q^{n+k+1}}{\left[ {\begin{array}{*{20}{c}}
{n + k } \\
n \\
\end{array}} \right]_q}\frac{[n]_q t^k}{[n+k]_q!}\\
&=\sum_{k=0}^\infty \frac{1}{B_q(k+1,n)} q^{k(k-1)/2}\frac{x^k}{(1+x)_q^{n+k+1}}\frac{ t^k}{[n+k]_q!}\\
&=\sum_{k=0}^\infty v_{k,n}^q(x)\frac{ t^k}{[n+k]_q!}.
\end{align*}
This completes the proof of generating function.\\
\end{proof}
{\bf Acknowledgement:} The present work was done when the first author visited Division of General Education-Mathematics, Kwangwoon University, Seoul, S. Korea during June 2010.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,448 |
#import "BioKIDSAppDelegate_iPhone.h"
@implementation BioKIDSAppDelegate_iPhone
- (void)dealloc
{
[super dealloc];
}
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 106 |
Brickyard Lucid Systems
Mi'kmaq creator of software system finalist for national award
Photo: Nelson Cloud / Cando
Donald Hanson is hoping First Nation communities across Canada start utilizing Lucid, the band management software system he created. For his efforts his company was a finalist in 2017 for Cando's Indigenous Private Sector Business award.
By Sam Laskaris
Cando Writer
A band management software system that he created is earning an Indigenous man some cross-country praise.
Donald Hanson, who is Mi'kmaq and a member of the Membertou First Nation on Cape Breton Island, is the creator of Lucid.
The software system was designed to support First Nation communities and organizations across the country. Its aim is to increase their transparency and accountability, thus enhancing their over-all effectiveness.
"It's transparent and easy to follow," Hanson said of the software system, adding that is why the name of the product is aptly called Lucid. "That's the whole idea of the system."
Partly because he created Lucid, Hanson was the finalist this year for Cando's Indigenous Private Sector Business award.
Green Leaf Enterprises, a business located in the tiny Nova Scotia community of Wilmot, ended up winning the award in this category.
The winner and finalist were selected at the Cando Conference, which wrapped up on Oct. 25, in Fredericton, N.B.
Cando, the national organization that promotes Indigenous economic development, also honored winners and finalists in individual economic development officer and community of the year categories.
The Lucid system provides four key features that will assist users. They are budgeting, human resources, document management and community reporting.
Since launching Lucid in April of this year, Hanson has convinced communities or groups from six provinces - Nova Scotia, New Brunswick, Ontario, Saskatchewan, British Columbia and Quebec – as well as the Northwest Territories to sign up for his pilot project. He will offer the software for free for a three-month period in the hopes users will purchase the service afterwards.
"There is a lot of people looking to get this type of service," he said. "There is a need and I want to fill it."
Hanson had previously worked for more than a decade in federal civil service. His desire to create a system such as Lucid stemmed from the fact he often witnessed the impact created from a lack of a proper management framework.
"Communities I worked with in the past had the best intentions," he said. "But I've seen the need for something like (Lucid) and I understand it."
Hanson was also thrilled to be singled out for his venture by Cando.
"It was a real honor and a privilege just being nominated which sounds a bit cliché but true nonetheless," he said. "It is very re-affirming to know that my peers see the value of the Lucid system enough to nominate me for this prestigious award from a nationally recognized organization such as Cando."
And he was not the least bit upset he was named the finalist instead of being chosen the winner in his category.
"Coming second is still a great accomplishment considering it was in all of Canada," he said. "Besides, when you consider the duration and milestones that the winner achieved I am proud to come in second."
Hanson was also pleased he was able to showcase his project in front of a national audience.
"This gave me a unique opportunity to present my business to the key stakeholders in all regions and help increase the awareness of my product," he said.
And the response he received was quite positive.
"I have been overwhelmed with the amount of positive feedback from the conference attendees with many of them saying how needed this type of system is for our communities and how many of them identify the potential synergies which can be developed as a national tool," he said. "Many of the EDOs see my vision and how Lucid provides the basis for increased capacity for economic growth." | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,077 |
The growing consciousness on environmental sustainability has made several companies to join the campaign on green living which is the aim of green advertising. It is on this premise that this study undertakes an assessment of green advertising on clean environment in south-south Nigeria. Using the survey and content analysis methods of research, the researcher sampled 291 respondents randomly selected from three south-south states (i.e. Edo, Delta and Rivers States) and also content analyzed green advertising messages on some selected disposable products. The findings reveal among other things that individuals are conscious of having clean environment with or without green advertising messages on products or through the media. In view of this, the researcher recommends among other things that there is need for audience research to ascertain the best approach to creating impact oriented green advertising.
The ways in which the environment and issues relating explicitly to the environment are represented in the media have been continuously evolving ever since the environmental movement came into being. The environment has been the focus of some of the most memorable media spectacles of the last 25 years (Cox, 2008: 32). In 1987 a document prepared by the World Commission on Environment and Development defined sustainable development as "meeting the needs of the present without compromising the ability of future generations to meet their own need." This became known as the Brundtland Report and was another step towards widespread thinking on sustainability in everyday activity (Banerjee, Gulus & Lyer, 1995).
Arising from the Brundtland Report and Environmental Movements across the globe, environmental issues became an increasingly public concern during the last decades. Issues of global warming and climate change have come to the forefront, thus raising interest even in corporate advertising. World leaders are increasingly worried about the environment in which we live. Leaders of the world have had various meetings and summits on climate change, global warming and other related global environmental issues. This is important because man completely depends on his environment for survival and sustenance. The massive disastrous activities of man to the environment and its immense importance have raised environmental issues to the top of international agenda.
Today, as the world is concerned about sustainable environment, climate change or global warming, the need to preserve, protect and promote the environment has become paramount to us and our survival. The numerous environmental problems being experienced in the world today such as the Asian Tsunami, hurricanes, floods, volcanic eruptions, earthquakes, pollutions, solid wastes and other numerous environmental problems occasioned by man are issues of great concern to nations of the world. The environment is indeed degraded in many ways. One of such ways by which the environment has been degraded and defaced is the indiscriminate disposal or dumping of solid wastes like Can drinks, bottles, food packs and many others on our streets and roads.
The role of mass media in contemporary society has been a topic of inquiry, which has created as many questions as it has answered. The attitude of an individual towards environmental issues in Nigeria can be traced to how effective the media have played its role in sensitizing and moulding opinions towards sustainable environment, which is what green advertising seeks to achieve. An environmental friendly media will adopt all available strategies towards achieving favourable attitudinal change on environmental issues.
As an advertising strategy that has the characteristics of being able to promote a green lifestyle and at times, enhance a corporate image of social responsibility, green advertising promotes good living through a clean and healthy environment.
Many individuals as well as organisations are yet to change their attitudes or behaviours and organisational policies in favour of sustainable development and clean environment. Many consumers manufacturing firms in Nigeria are yet to contribute towards clean environment.
However, global companies like Coca-Cola, Toyota, IBM, and manufacturer of fruit drinks like 5 Alive (Coca-Cola Nig.), Chivita (Chi Nig.), and others now focus on green advertising and sustainability of the environment. Organisations are now taking interest in green advertising and environmental management through their products and services. Environmental issues also have strategic implications for organisations. Consumer concerns about the environment have been on the increase in recent years. The deteriorating environment that has developed in recent decades had made marketing researchers to find a new line of research that has been given various labels, such as ecological marketing (Chamorro, Rubio and Miranda, 2009:233). It is the analysis of how marketing activities impact on the environment and how the environmental variable can be incorporated into the various decisions of corporate marketing. With the increasing number of "green" customers, businesses attempt to understand and respond to external pressures to improve their environmental performance (Chen, 2008:271).
The environment is central to every human activity and as such, would be used in coordinating the resources for a "synergistic approach to management of the environment" (Nwabueze, 2007:45). There have been many approaches towards clean environment. One of such approaches is the adoption and application of advertising into environmental management or studies. Advertising is exciting, dynamic and pervasive in nature.
The Advertising Practitioners Council of Nigeria (APCON) defines advertising as the non-personal communication of information, usually paid for and usually persuasive in nature about products or ideas by identified sponsors through various media (APCON, cited in Benson-Eluma, 2004:3). This implies that advertising is a persuasive communication that tries to persuade the target audience to respond positively to the goods or service. As part of its functions, advertising is to educate and inform. Nwabueze (2007:86) believes that advertising can be used as part of its functions to educate and inform the public on environmental management or clean environment. This can be done in advertisements and in the packaging of products and services. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,128 |
\section{Introduction}\label{sec:Introduction}
The aim of this paper is to compute some Hodge theoretic invariants of certain classical differential systems in one variable. These are the so-called irregular Hodge numbers, which have been introduced recently by Sabbah \cite{Sa15}.
They are called irregular
because they are attached to differential systems which may have irregular singular points, a feature that is excluded for classical variations
of Hodge structures as well as for the more general Hodge modules. The very definition of these numbers rely on the theory of mixed twistor $\mathcal D$-modules of T.~Mochizuki (\hspace{-.5pt}\cite{Mo13}). Twistor $\mathcal D$-modules generalise Hodge modules, in the sense that the underlying $\mathcal D$-module of a twistor $\mathcal D$-module
can have irregular singularities. In particular, one can define a version of the Fourier-Laplace transformation functor within the category of mixed twistor $\mathcal D$-modules, which is impossible for mixed Hodge modules.
The drawback of this generalization is that one cannot directly assign a filtration to a twistor $\mathcal D$-module, and hence
it is not easy to attach numerical invariants like Hodge numbers to it. In the above mentioned paper \cite{Sa15}, Sabbah constructs
an intermediate category between mixed Hodge modules and mixed twistor $\mathcal D$-modules (called irregular mixed Hodge modules) which is on the one hand sufficiently large to be stable under
all relevant operations that are defined for twistor $\mathcal D$-modules (in particular, the Fourier-Laplace transformation), but which allows one to define a filtration,
called irregular Hodge filtration, for each of its objects. The construction is related to the earlier papers \cite{Yu, SaEsYu, Sa14}, where for certain
projective morphisms $f:X\rightarrow \mathds P^1$, a (rationally indexed) filtration was introduced on the twisted de Rham complex
$(\Omega^\bullet(*D), d+df\wedge)$, where $D\subset X$ is a certain normal crossing boundary divisor such that $f_{|X\backslash D}$ yields a regular function.
Instead of considering meromorphic differential forms, one can also use the subcomplex of so-called $f$-adapted logarithmic forms (also
called Kontsevich complex, see \cite{KKP2})
$\Omega^\bullet_f$, which consists of
forms such that the exterior product with $df$ is still logarithmic along $D$.
From an $E_1$-degeneration property of the corresponding spectral sequence proved in \cite{SaEsYu}, one obtains a filtration on the twisted de Rham cohomology, called irregular Hodge filtration
of the regular function $f: X\backslash D \rightarrow \AA^1$. We refer to \cite{SaEsYu} for more details.
Notice also that the paper \cite{KKP2} gives three definitions of so-called Landau-Ginzburg Hodge numbers associated to a family $f:X\rightarrow \mathds P^1$,
one of them being $\dim H^p(\Omega^q_f)$. Conjecturally these three definitions coincide, but this seems to require some more assumptions (see \cite{Shamoto} and \cite{Sa18} for some partial results). Although these Hodge numbers have only integer indices, they are closely related to the dimensions of the graded parts of the filtration
from \cite{SaEsYu}. Ultimately, according to \cite{KKP2} and following predictions from homological mirror symmetry, one hopes for a correspondence between the Hodge numbers of some, say, projective varieties entering in the A-model and the irregular Hodge numbers of its (Landau-Ginzburg) B-model.
For the moment, there are quite a few examples where the irregular Hodge filtration can actually be computed.
A central result of \cite{Sa15} states that rigid irreducible $\mathcal D$-modules on the projective line
underlie objects of the category of irregular mixed Hodge modules, and consequently admit a unique irregular Hodge filtration, provided that their formal local monodromies are unitary.
Rigid $\mathcal D$-modules are particularly interesting since they can be algorithmically constructed from simple objects by an algorithm due to Arinkin and Katz (cf. \cite{Arin}).
Among the most studied and best understood examples of such rigid $\mathcal D$-modules are the classical hypergeometric $\mathcal D$-modules. In the regular case (which corresponds to classical variations of complex Hodge structures), Fedorov has given in \cite{Fe} a closed formula for the Hodge numbers (without computing the Hodge filtration itself however) conjectured by Corti and Golyshev in \cite{CorGol} using the work \cite{DettSa} of Dettweiler and Sabbah.
In the present paper, we consider the case of purely irregular hypergeometric modules. Our principal result, Theorem \ref{thm:HodgeData}, completely determines the irregular Hodge filtration and gives a very simple formula for the irregular Hodge numbers, which is in some sense
similar to the shape of Fedorov's formula. The main ingredients are a reduction process (as explained in \cite{BMW}) to obtain classical hypergeometric $\mathcal D$-modules from
some higher dimensional ones, the so-called GKZ-systems, techniques from \cite{Reich2} and \cite{ReiSe,ReiSe2} (going back to \cite{Sa8}) to understand
Hodge module structures on these GKZ-systems as well as a quite explicit solution to the so-called Birkhoff problem that is
inspired by calculations in toric mirror symmetry (see again \cite{ReiSe} as well as \cite{DS2} and also \cite{dGMS}).
Since the first version of this paper was written, Hodge invariants for hypergeometric systems have been considered
in some other articles. First, the formula for the Hodge numbers of purely irregular systems has also been obtained by Sabbah and Yu in the final version of
\cite{Sa15} by different means. Another approach to Fedorov's formula for the case of regular systems (giving more precise information
on the various Hodge invariants) has been given by N.~Martin (see \cite{Mar18}).
Moreover, we have considered the case of hypergeometric operators of type $(n,1)$ (see Definition
\ref{def:ClassicHyp} below)
in a common paper with Th.~Reichelt (\hspace{-.5pt}\cite{SevCastReich}) using the computation of Hodge filtrations on GKZ-systems
from \cite{ReiSe3}. Finally, Sabbah and Yu have recently given a complete formula for the irregular Hodge numbers
for all confluent hypergeometric systems in \cite{SaYu18}. However, for the moment the irregular Hodge filtration itself
is not determined in the general case.
Let us recall some notation that will be adopted throughout the paper. For a smooth complex algebraic variety $X$, we write $\mathcal D_X$ for the sheaf of algebraic differential operators on $X$. If $X$ is affine, we sometimes switch freely between sheaves of $\mathcal D_X$-modules and modules
of global sections. We will denote the abelian categories of holonomic resp. regular holonomic $\mathcal D_X$-modules by $\operatorname{Mod}_\text{h}(\mathcal D_X)$ resp. $\operatorname{Mod}_\text{rh}(\mathcal D_X)$, and analogously with the respective bounded derived categories.
For a morphism $f:X\rightarrow Y$, we denote the direct resp. inverse image functors for $\mathcal D$-modules as usual by $f_+$ resp. $f^+$ (see
\cite{Hotta} for a thorough discussion of these and related functors).
We put $\mathds G_m:=\text{Spec\,} \mathds C[t,t^{-1}]$; if we want to fix a coordinate on this one-dimensional torus, we also write ${\mathds G}_{m,t}$.
We denote by $\cR^{\operatorname{int}}_{\AA_z^1\times X}$ the
sheaf of Rees rings on $X$ (with integrable structure), that is, the subsheaf of non-commutative algebras of $\mathcal D_{\AA^1_z\times X}$ generated by $zp^*\Theta_X$ and $z^2\partial_z$, where $p:\AA^1_z\times X \rightarrow X$ is the projection. If
$(x_1,\ldots,x_n)$ are local coordinates on $X$, then $\cR^{\operatorname{int}}_{\AA_z^1\times X}$ is locally given by
$\mathcal O_{\AA^1_z\times X}\langle z^2\partial_z, z\partial_{x_1},\ldots,z\partial_{x_n}\rangle$.
Occasionally, we will also need the sheaf $\mathcal{R}_{\AA^1_z\times X}$, which is generated
by $zp^*\Theta_X$ only, i.e., locally given by
$\mathcal O_{\AA^1_z\times X}\langle z\partial_{x_1},\ldots,z\partial_{x_n}\rangle$.
We let $\operatorname{MHM}(X)$ be the abelian category of algebraic mixed Hodge modules (see \cite{SaitoMHM}) on $X$. We consider moreover the category $\operatorname{MHM}(X,\mathds C)$ of \emph{complex} mixed Hodge modules (see, e.g., \cite[Definition 3.2.1]{DettSa}).
As an example, if $X$ is the algebraic torus $\mathds G_m^d$ with coordinates $y_1,\ldots,y_d$, then
for any $\alpha=(\alpha_1,\ldots,\alpha_d)\in \mathds R^d$, the free $\mathcal O_{\mathds G_m^d}$-module of rank $1$
$$
\mathcal O_{\mathds G_m^d}^\alpha := \mathcal D_{\mathds G_m^d}/(y_k\partial_{y_k}+\alpha_k+1)_{k=1,\ldots,d}
$$
(see also Definition \ref{def:Oalpha} below) underlies an object in $\operatorname{MHM}(\mathds G_m^d,\mathds C)$.
On the other hand, $\operatorname{MTM}(X)$ denotes the abelian category of algebraic mixed twistor $\mathcal D$-modules on $X$ (see \cite{Mo13}).
The category $\operatorname{MTM}^{\text{int}}(X)$ consists of those mixed twistor $\mathcal D$-modules where the underlying $\mathcal{R}_{\AA^1_z\times X}$-modules
have an integrable structure, i.e., where they are modules over $\cR^{\operatorname{int}}_{\AA_z^1\times X}$.
The category $\text{IrrMHM}(X)$, as defined in \cite[Def. 2.52]{Sa15}, is a certain subcategory of $\operatorname{MTM}^{\text{int}}(X)$
(actually of a variant, called ${_\iota\!}\operatorname{MTM}^{\text{int}}(X)$, which is shown to be equivalent to $\operatorname{MTM}^{\text{int}}(X)$ in [ibid., \S~1])
consisting of objects $\widehat\mathcal M$ that satisfy certain properties. The first of them is that the object ${^\theta}\widehat\mathcal M$ obtained from $\widehat\mathcal M$ by substituting $z\theta$ for $z$ is still an object of ${_\iota\!}\operatorname{MTM}^{\text{int}}({}^\theta\! X)$, where ${}^\theta\! X=\mathds{G}_{m,\theta}\times X$. That is a remarkable assumption, having its origin in \cite{HS1}, but we have to impose a further property, namely that such rescaled objects must have a certain tame behaviour when $\theta$ goes to infinity (or at the origin of $\tau=1/\theta$, in other words), related to regularity along $\{\tau=0\}\times\AA_z^1\times X$. This two conditions are, essentially, what we ask for a mixed twistor $\mathcal D$-module on $X$ to be a mixed twistor-rescaled $\mathcal D$-module on $X$ (\hspace{-.5pt}\cite[Def. 2.50]{Sa15}). The last condition is a $z$-grading property appearing after identifying $\tau$ with $z$ (cf. [ibid., Def. 2.26]). For more details, see [ibid., \S~2].
Although the construction of this category may seem rather involved, its main feature is that the $\mathcal D_X$-module $\mathcal M$ associated to an object $\widehat{\mathcal M}$ in $\operatorname{IrrMHM}(X)$ carries a good filtration $F_\bullet^{\text{irr}} \mathcal M$, indexed by $\mathds R$, called the irregular Hodge filtration, which in turn behaves well with respect to several functorial operations. Notice however that this filtration, contrarily to the case of mixed Hodge modules, is not part of the definition of an object of $\operatorname{IrrMHM}(X)$. Very roughly, it can be thought of as defined by the intersection of the canonical $V$-filtration
along $\tau=0$ (or rather the filtration induced on the restricted object when $\tau=z$) with the $z$-adic filtration on $\widehat\mathcal M$. In particular, the jumping indices of the irregular Hodge filtration are of the form
$\{\alpha+k\,|\,k\in \mathds Z\}$ for a certain finite set of real numbers $\alpha$.
\textbf{Acknowledgements.} We would like to thank Takuro Mochizuki, Thomas Reichelt and Claude Sabbah for their interest in our work and for many stimulating discussions. We are grateful to the anonymous referee for the many valuable comments and remarks. We thank the Max Planck Institute for Mathematics in the Sciences, where a significant part of the work presented here has been carried out.
\section{Hypergeometric modules and dimensional reductions}\label{sec:GKZHorn}
\label{sec:reduction}
In this section we will introduce two different kinds of hypergeometric $\mathcal D$-modules: classical and GKZ. We will dedicate more time to classical ones, since they form one of the main objects of study of the paper, and will end by showing the relation between both types, which will be useful for us in the future. We state one of our main results (Theorem \ref{thm:HypIrrMHM}), which is proven in the next section.
\begin{defi}\label{def:ClassicHyp}
Let $(n,m)\neq(0,0)$ be a pair of nonnegative integers, and let $\alpha_1,\ldots,\alpha_n$ and $\beta_1,\ldots,\beta_m$ be elements of $\mathds C$. The (classical) hypergeometric $\mathcal D$-module of type $(n,m)$ associated with the $\alpha_i$ and the $\beta_j$ is defined as the quotient of $\mathcal D_{{\mathds G}_m}$ by the left ideal generated by the so-called hypergeometric operator
$$\prod_{i=1}^n(t\partial_t-\alpha_i)-t\prod_{j=1}^m(t\partial_t-\beta_j).$$
We will denote it by $\mathcal H(\alpha_1,\ldots,\alpha_n;\beta_1,\ldots,\beta_m)$, or in an abridged way, $\mathcal H(\alpha_i;\beta_j)$.
\end{defi}
In this paper we will be mostly concerned with hypergeometric $\mathcal D$-modules of type $(n,0)$.
\begin{rem}\label{rem:BasicHyp}
The excluded type $(n,m)=(0,0)$ corresponds to the punctual delta $\mathcal D_{{\mathds G}_m}$-module on ${\mathds G}_m$ $\mathcal H\left(\emptyset;\emptyset\right)=\mathcal D_{{\mathds G}_m}/(1-t)$.
On the other hand, if we denote the Kummer $\mathcal D$-module $\mathcal D_{{\mathds G}_m}/(t\partial_t-\eta)$ by
$\mathcal K_\eta$, for any fixed complex number $\eta$, then $\mathcal H(\alpha_i;\beta_j) \otimes_{\mathcal O_{{\mathds G}_m}}\mathcal K_\eta\cong \mathcal H(\alpha_i+\eta;\beta_j+\eta)$. In particular, an overall integer shift of the parameters gives us an isomorphic $\mathcal D$-module.
Every hypergeometric $\mathcal D$-module has Euler characteristic -1 (cf. \cite[Lem. 2.9.13]{Ka}). For $n\neq m$, no hypergeometric $\mathcal D$-module of type $(n,m)$ has singularities on ${\mathds G}_m$. If $n>m$ (resp. $m>n$), they have a regular singularity at the origin (resp. infinity) and an irregular singularity at infinity (resp. the origin) of irregularity one and slope $1/|n-m|$ of multiplicity $|n-m|$ (cf. \cite[Prop. 2.11.9]{Ka}). For $n=m$, the hypergeometric $\mathcal D$-modules of type $(n,n)$ are regular, with singularities only at the origin, infinity and 1.
\end{rem}
\begin{prop}[\textbf{Irreducibility}]\label{prop:IrredHyp}
\emph{(cf. \cite[Prop. 2.11.9, 3.2]{Ka})} Let $\mathcal H:=\mathcal H(\alpha_i;\beta_j)$ be a hypergeometric $\mathcal D$-module. It is irreducible if and only if for any pair $(i,j)$ of indices, $\alpha_i-\beta_j$ is not an integer.
\end{prop}
\begin{rem}
Assuming the irreducibility, we have a result which is stronger than the second paragraph of Remark \ref{rem:BasicHyp}. Namely, the isomorphism class of $\mathcal H(\alpha_i;\beta_j)$ depends only on the classes modulo $\mathds Z$ of the $\alpha_i$ and the $\beta_j$ (point 1 of \cite[Prop. 3.2]{Ka}), so we can choose such parameters on a fundamental domain of $\mathds C/\mathds Z$.
\end{rem}
\begin{prop}[\textbf{Rigidity}]\label{prop:RigidHyp}
Let $\mathcal H:=\mathcal H(\alpha_i;\beta_j)$ be an irreducible hypergeometric $\mathcal D$-module of type $(n,m)$, where $n\geq m$, and let $\mathcal M$ be another irreducible $\mathcal D_{{\mathds G}_m}$-module of Euler-Poincaré characteristic -1 which has no singularities outside $\{0,1,\infty\}$. Assume that
\begin{itemize}
\item $\mathcal H\otimes\mathds C((t))\cong\mathcal M\otimes\mathds C((t))$.
\item $\mathcal H\otimes\mathds C((1/t))\cong\mathcal M\otimes\mathds C((1/t))$.
\item If $n=m$, assume further that $\mathcal M$ has a regular singularity at 1.
\end{itemize}
In that case, $\mathcal H$ and $\mathcal M$ are isomorphic.
\end{prop}
\begin{proof}
$\mathcal H$ and $\mathcal M$ being irreducible, both of them coincide with the middle extension of their restriction to ${\mathds G}_m\setminus\{1\}$. Assume first that $n=m$, that is, $\mathcal H$ is regular. Since $\mathcal M$ has characteristic -1 and regular singularities at the origin, one and infinity, by the formula for the Euler characteristic \cite[Thm. 2.9.9]{Ka}, its formal local monodromy at 1 must be a pseudoreflection. Then we can apply [ibid., Rigidity Thm. 3.5.4] and we are done.
If $n>m$, $\mathcal M$, like $\mathcal H$, has a regular singularity at the origin and an irregular singularity at infinity. By the same formula for the Euler characteristic of $j_{\dag+}j^+\mathcal M$ (denoting by $j$ the inclusion ${\mathds G}_m\setminus\{1\}\hookrightarrow{\mathds G}_m$), $\mathcal M$ cannot have more singularities in $\mathds P^1$ apart from zero and infinity. In that case we apply [ibid., Rigidity Thm. bis 3.7.3].
\end{proof}
Consider the case in which $\mathcal H=\mathcal H(\alpha_i;\beta_j)$ is of type $(n,n)$, i.e., such that it is regular.
From the rigidity property of the last Proposition, one concludes by \cite[Cor. 8.1]{Si2} that the restriction
of $\mathcal H$ to ${\mathds G}_m \backslash \{1\}$ underlies a complex polarizable variation of Hodge structures. The next statement, conjectured by Corti and Golyshev (cf. \cite[Conj. 1.4]{CorGol}) and proved by Fedorov (see \cite[Thm. 1]{Fe}), gives important information on its Hodge invariants.
\begin{prop}[\textbf{Hodge numbers (regular case)}]\label{prop:Fedorov}
Let $\mathcal H=\mathcal H(\alpha_i;\beta_j)$ be an irreducible hypergeometric $\mathcal D$-module of type $(n,n)$. Assume that the $\alpha_i$ and the $\beta_j$ are increasingly ordered real numbers, lying in the interval $[0,1)$. Set
$$
\rho(k)=\left|\{i=1,\ldots,n\,:\,\beta_i<\alpha_k\}\right|-k,
$$
for $k=1,\ldots,n$.
Then the Hodge numbers of $\mathcal H$ are, up to an overall shift,
$$
h^p=\left|\rho^{-1}(p)\right|=\left|\{k=1,\ldots,h\,:\, \rho(k)=p\}\right|.
$$
\end{prop}
This last result is the analogous one, in the regular case, to Theorem \ref{thm:HodgeData}, and served as the main motivation to start this project. Notice that this formula slightly differs from the one given in \cite{Fe}. This is because Fedorov considers the dual connection to ours by working with the space of solutions instead of with that of horizontal sections (cf. \cite[p. 10, proof of Lem. 3.6]{Mar18}). Now that we have seen part of the behaviour of classical hypergeometric $\mathcal D$-modules, let us continue with the other family mentioned above.
\begin{defi}\label{def:GKZ}
Let $n\geq m$ two positive integers, and let $d=n-m$. Let $\beta\in\mathds C^d$ be a vector and let $A=(a_{ij})\in\text{M}(d\times n,\mathds Z)$ be an integer matrix.
Consider the $n$-dimensional torus $\mathds G_m^n$ with coordinates $\lambda_1,\ldots,\lambda_n$. We define the Euler operators $E_i=\sum_ja_{ij}\lambda_j\partial_{\lambda_j}$, for $i=1,\ldots,d$, and the toric ideal
$$
I_A:=\left(\partial_\lambda^u-\partial_\lambda^v : Au=Av\right) \subset\mathds C[\partial_{\lambda_1},\ldots,\partial_{\lambda_n}]\subset D_{\AA^n}.
$$
Then, the GKZ-hypergeometric $\mathcal D$-module (or system) is
$$\mathcal M_A^\beta:=\mathcal D_{\mathds G_m^n}/(\mathcal I_A+(E_i-\beta_i:i=1,\ldots,d)_{i=1,\ldots,d}),$$
where $\mathcal I_A$ is the sheafified version of the toric ideal $I_A$.
\end{defi}
Usually the module $\mathcal M_A^\beta$ is defined to be an element in $\textup{Mod}(\mathcal D_{\AA^n})$. However, we will later work
only with the restriction of such an object to $\mathds G_m^n$. In order to avoid the usage of the functor $j^+$ (where $j:\mathds G_m^n\hookrightarrow \AA^n$)
each time that we need to refer to $\mathcal M_A^\beta$, we use this slightly non-standard definition.
A classical hypergeometric $\mathcal D$-module can be considered as a dimensional reduction of a certain GKZ-system. We will describe this procedure in some more detail now,
because it allows us to apply some of the many known results on GKZ-systems to classical hypergeometric $\mathcal D$-modules.
\begin{prop}\label{prop:hypGKZ}
Let $m$ be a positive integer. Let $A\in\operatorname{M}((m-1)\times m,\mathds Z)$ be an integer matrix of rank $m-1$ and take $\kappa\in\mathds C^m$ such that $\kappa_1=0$. Consider the inclusion $\iota:{\mathds G}_m\hookrightarrow\mathds G_m^m$ given by $t\mapsto(t,1,\ldots,1)$, and let $B=(b_1,\ldots,b_m)^{\text{\emph{t}}}\in\mathds Z^m$ be a Gale dual of $A$, that is, an integer column matrix which generates $\ker_\mathds Q A$. Assume moreover that $b_1=1$. Put
$$
\eta:=\prod_{i=1}^mb_i^{b_i}.
$$
Then we have $h_{\eta}^+\mathcal H(\alpha_i;\beta_j)\cong \iota^+\mathcal M_A^{A\kappa}$, where $h_\eta$ is the automorphism of ${\mathds G}_m$ given by $t\mapsto\eta t$, and the unordered sets of parameters $\alpha_i$ and $\beta_j$, counted with multiplicities, are
$$(\alpha_i)=\left(\frac{k-\kappa_j}{b_j}\,:\,b_j>0, k=0,\ldots,b_j-1\right),$$
$$(\beta_i)=\left(\frac{k-\kappa_j}{b_j}\,:\,b_j<0, k=0,\ldots,-b_j-1\right).$$
\end{prop}
\begin{proof}
On one hand, $\mathcal M_A^{A\kappa}$ is not only a GKZ-hypergeometric $\mathcal D$-module, but also the restriction to ${\mathds G}_m^n$ of a lattice basis binomial $\mathcal D_{\AA^m}$-module (cf. \cite[Def. 1.2]{BMW}, noting that the assumption on the columns of $B$ is not needed for the definition). This is because $A$ being of rank $m-1$ implies that the toric ideal $I_A$ coincides with the lattice basis ideal
$$I(B):=\left(\partial_\lambda^{w_+}-\partial_\lambda^{w_-} : w=w_+-w_- \text{ is a column of } B\right).$$
(In fact this holds for any complete intersection ideal, but here the argument is simpler.)
On the other hand, the expression we have given for the parameters of $\mathcal H(\alpha_i;\beta_j)$ follows from applying the definition of Horn hypergeometric $\mathcal D$-modules given in [ibid., Def. 1.1] for a column matrix, up to the same caveat above about the columns on $B$ (in fact normalized ones, but all kinds of Horn $\mathcal D$-modules defined in loc. cit. are equal once restricted to the torus $\mathds G_{m,t}$), and comparing it with Definition \ref{def:ClassicHyp}.
Now let $j:{\mathds G}_m\hookrightarrow\AA^1$ be the canonical inclusion. The isomorphism given in [ibid., Thm. 1.4] relates lattice basis binomial $\mathcal D$-modules to Horn hypergeometric ones. However, due to the previous discussions, we obtain the isomorphism in the statement just by applying $j^+$ to both sides of it.
\end{proof}
Note that the choice of $\kappa_1$ and $b_1$ in the statement of the Proposition force $\alpha_1$ to vanish. However, by Remark \ref{rem:BasicHyp}, any other hypergeometric $\mathcal D$-module can be built from one of this form just by tensoring with a suitable Kummer $\mathcal D$-module.
In our study of Hodge theoretic properties of hypergeometric $\mathcal D_{{\mathds G}_m}$-modules below, we need to go in some sense in the opposite direction: Given sets $\{\alpha_i\}$, $\{\beta_j\}$, we would like to determine a matrix $A$ and a parameter vector $\beta$ such that the module $\mathcal H(\alpha_i;\beta_j)$ can be obtained as an inverse image of the GKZ-system $\mathcal M_A^\beta$. Although such a pair $(A,\beta)$ is not unique, a systematic way of constructing it can be formulated as follows.
\begin{coro}\label{coro:hypGKZ}
Let $\mathcal H(\alpha_i;\beta_j)$ be a hypergeometric $\mathcal D_{{\mathds G}_m}$-module of type $(n,m)$ with $n>0$ and $\alpha_1=0$. Let $A\in\operatorname{M}((m+n-1)\times(n+m),\mathds Z)$ given by
$$A=\left(\begin{array}{c|c|c}
\underline{1}_m & \underline{0}_{m\times(n-1)} & \operatorname{Id}_m\\[3pt]
\hline
& & \vspace{-10pt}\\
\underline{1}_{n-1} & -\operatorname{Id}_{n-1} & \underline{0}_{(n-1)\times m}\end{array}
\right),$$
and let $\beta=(\beta_1,\ldots,\beta_m,\alpha_2,\ldots,\alpha_n)^{\operatorname{t}}$. (Here and later in this paper,
we write $\underline{x}_k$ for a column vector with $k$ rows, where all entries contain the value $x$.) Let $\iota:{\mathds G}_m\rightarrow\mathds G_m^{n+m}$, given by $t\mapsto(t,1\ldots,1)$.Then
$$\mathcal H(\alpha_i;\beta_j)\cong\iota^+\mathcal M_A^\beta.$$
\end{coro}
\begin{proof}
The statement is an easy consequence of the Proposition, taking $B=(1,\overset{(n)}\ldots,1,-1,\overset{(m)}\ldots,-1)^{\operatorname{t}}$ and $\kappa=(0,-\alpha_2,\ldots,-\alpha_n,\beta_1,\ldots,\beta_m)^{\operatorname{t}}$.
\end{proof}
As indicated before, we will see later that the restriction $\alpha_1=0$ is not as strong as it may appear: By tensoring a given hypergeometric $\mathcal D$-module with an appropriate Kummer module, we can always reach this assumption.
We will end this section by explaining how the above construction of GKZ-systems and the dimensional reduction to hypergeometric $\mathcal D_{{\mathds G}_{m,t}}$-modules can be understood at the level of $\mathcal{R}$-modules. Recall (see the introduction) that for a smooth algebraic variety $X$ with local coordinates $(x_1,\ldots,x_n)$ the sheaf $\cR^{\operatorname{int}}_{\AA_z^1\times X}$ is the subsheaf of $\mathcal D_{\AA^1_z\times X}$ locally generated by $z^2\partial_z$ and $(z\partial_{x_i})_{i=1,\ldots, n}$.
\begin{defi}
Let $n\geq m$ two positive integers, and let $d=n-m$. Let $\beta\in\mathds C^d$ be a vector and let $A=(a_{ij})\in\text{M}(d\times n,\mathds Z)$ be an integer matrix.
Consider the affine space ${\mathds G}_m^n$ with coordinates $\lambda_1,\ldots,\lambda_n$, and let $\mathbb L \subset \mathds Z^n$ be the kernel of the linear map $\mathds Z^n\rightarrow \mathds Z^d$ given by left multiplication by the matrix $A$, whose elements will be denoted by $\underline{l}=(l_1,\ldots, l_n)$. Then, the GKZ-hypergeometric $\mathcal{R}$-module is
$$
\widehat{\mathcal M}_{A}^{(\beta_0,\beta)}:=\cR^{\operatorname{int}}_{\AA_z^1\times \mathds G_m^n}/\mathcal I,
$$
where $\beta_0\in\mathds C$ and $\mathcal I$ is generated by
$$\begin{array}{c}
\displaystyle\prod_{j:l_j>0} (z\partial_{\lambda_j})^{l_j}-\prod_{j:l_j<0} (z\partial_{\lambda_j})^{-l_j},\; \underline{l}\in \mathbb L,\\
z^2\partial_z+\lambda_1z\partial_{\lambda_1}+\ldots+\lambda_nz\partial_{\lambda_n}-z\beta_0, \\
\displaystyle\sum_{j=1}^n a_{kj}\lambda_j z\partial_{\lambda_j} - z\beta_k,\; k=1,\ldots,d.
\end{array}
$$
\end{defi}
Note that we can recover the GKZ-hypergeometric $\mathcal D$-module $\mathcal M_{A}^{\beta}$ from Definition \ref{def:GKZ} by restricting $\widehat\mathcal M_A^{(\beta_0,\beta)}$ to $z=1$. In the special case of our original matrix from Corollary \ref{coro:hypGKZ} the generators of $\mathcal I$ are
$$\begin{array}{c}
(z\partial_{\lambda_1})\cdot\ldots\cdot(z\partial_{\lambda_n})- (z\partial_{\lambda_{n+1}})\cdot\ldots\cdot(z\partial_{\lambda_{n+m}}),\\
z^2\partial_z+\lambda_1z\partial_{\lambda_1}+\ldots+\lambda_{n+m}z\partial_{\lambda_{n+m}}-z\beta_0, \\
\lambda_1z\partial_{\lambda_1}+\lambda_{n+i}z\partial_{\lambda_{n+i}}-z\beta_i,\; i=1,\ldots,m,\\
\lambda_1z\partial_{\lambda_1}-\lambda_iz\partial_{\lambda_i}+z\alpha_i,\; i=2,\ldots,n.
\end{array}$$
Moreover, we must also consider the corresponding $\mathcal{R}$-module for hypergeometric $\mathcal D$-modules. Both kinds of $\mathcal{R}$-modules will play a significant role in the proof of Theorem \ref{thm:HypIrrMHM}.
\begin{defi}\label{def:H_Hut}
Let $(n,m)\neq(0,0)$ be a pair of natural numbers, and let $\alpha_1,\ldots,\alpha_n$ and $\beta_1,\ldots,\beta_m$ be elements of $\mathds C$. The (classical) hypergeometric $\mathcal{R}$-module (of type $(n,m)$) associated with the $\alpha_i$ and the $\beta_j$, denoted by $\widehat\mathcal H(\alpha_i;\beta_j)$, is defined as the quotient of $\cR^{\operatorname{int}}_{\AA_z^1\times{\mathds G}_{m,t}}$ by the left ideal generated by
$$
P=z^2\partial_z+(n-m)tz\partial_t+\gamma z \,\text{ and }\,H=\prod_{i=1}^n z(t\partial_t-\alpha_i)-t\prod_{j=1}^m z(t\partial_t-\beta_j),
$$
where $\gamma=-\sum_{i=1}^n \alpha_i+\sum_{j=1}^m\beta_j$.
\end{defi}
The choice of the operator $P$ may seem odd, but as we will see, it is indeed very natural. In fact, we have the following extension of Corollary \ref{coro:hypGKZ} to the realm of $\mathcal{R}$-modules.
\begin{lemma}\label{lem:RhypGKZ}
Let $\widehat\mathcal H(\alpha_i;\beta_j)$ be a classical hypergeometric $\mathcal{R}_{\AA_z^1\times{\mathds G}_{m,t}}$-module of type $(n,m)$ with $n>0$ and $\alpha_1=0$. Let $A\in\operatorname{M}((m+n-1)\times(n+m),\mathds Z)$, $\beta\in\mathds C^{n+m-1}$ and $\iota:{\mathds G}_{m,t}\hookrightarrow\mathds G_m^{n+m}$ be as in the statement of Corollary \ref{coro:hypGKZ}. Then
$$\widehat\mathcal H(\alpha_i;\beta_j)\cong\iota^+\widehat\mathcal M_A^{(0,\beta)}.$$
\end{lemma}
\begin{proof}
The inverse image functor in the category of $\mathcal{R}$-modules is induced by the usual inverse image functor of $\mathcal O$-modules, $(\operatorname{id}_{\AA_z^1}\times\iota)^*$ in this case (cf. \cite[\S2.1.6.2]{Mo13}). Then it is easy to see that
$$
\widehat\mathcal H(\alpha_i;\beta_j)\cong\iota^+\widehat\mathcal M_A^{(0,\beta)}.
$$
Namely, we replace $z\lambda_i\partial_{\lambda_i}$ by $z\lambda_1\partial_{\lambda_1}-z\alpha_i$ if $i=2,\ldots,n$ or by $-z\lambda_1\partial_{\lambda_1}+z\beta_{i-n}$, if $i=n+1,\ldots,n+m$. Since we can invert $\lambda_i$ in $\cR^{\operatorname{int}}_{\AA^1_z\times \mathds G_m^n}$, we
present $\widehat\mathcal M_A^{(0,\beta)}$ as the $\mathcal O_{{\mathds G}_m^{n+m}}$-module $\mathcal O_{{\mathds G}_m^{n+m}}\langle z^2\partial_z,z\lambda_1\partial_{\lambda_1}\rangle/\mathcal J$, where $\mathcal J$ is generated by $$\lambda_{n+1}\cdot\ldots\cdot\lambda_{n+m}\prod_{i=1}^nz(\lambda_1\partial_{\lambda_1}-\alpha_i)- (-1)^m\lambda_1\cdot\ldots\cdot\lambda_n\prod_{i=1}^mz(\lambda_1\partial_{\lambda_1}-\beta_i)\,\text{ and }\, z^2\partial_z+(n-m)z\lambda_1\partial_{\lambda_1}+\gamma z.$$
Now the inverse image by $\iota$ amounts simply to set $\lambda_1=t$ and $\lambda_i=1$ for $i=2,\ldots,{n+m}$ in the generators of the ideal, from which the desired isomorphism follows, up to multiplying $t$ by $-1$.
\end{proof}
We can formulate at this point one of the main results of this paper. Its full proof will occupy the entire next section.
\begin{thm}\label{thm:HypIrrMHM}
Let $\alpha_1,\ldots,\alpha_n$ be real numbers, belonging to the interval $[0,1)$ and increasingly ordered, and let $\gamma=-\sum_{i=1}^n \alpha_i$. Then the $\mathcal{R}_{\AA^1_z\times{\mathds G}_{m,t}}$-module $\widehat\mathcal H:=\widehat\mathcal H(\alpha_i,\emptyset)=\cR^{\operatorname{int}}_{\AA^1_z\times {\mathds G}_{m,t}}/(P,H)$, where
$$
P=z^2\partial_z+ntz\partial_t+\gamma z \,\text{ and }\,H=\prod_{i=1}^n z(t\partial_t-\alpha_i)-t,
$$
underlies an irregular Hodge module, i.e., an object of $\operatorname{IrrMHM}({\mathds G}_{m,t})$. It is the unique
irregular Hodge module whose associated $\mathcal D_{{\mathds G}_{m,t}}$-module is $\mathcal H(\alpha_i;\emptyset)$. Moreover, $\widehat\mathcal H$ can be extended in a unique way to an $\cR^{\operatorname{int}}_{\AA^1_z\times \mathds P^1}$-module, $\widehat\mathcal H_{pr}$, such that it underlies an object of $\operatorname{IrrMHM}\left(\mathds P^1\right)$.
\end{thm}
\begin{proof}[Proof of unicity]
We will give here a proof of the two unicity statements in the above theorem, postponing the proof of the main statement to page \pageref{page:MainProof} below.
Consider any twistor $\mathcal D$-module $\widehat\mathcal H'$ on ${\mathds G}_{m,t}$ whose underlying $\mathcal D_{\mathds G_{m,t}}$-module is $\mathcal H$. Since the functor $\Xi_{\text{DR}}$ is faithful by \cite[Rem. 7.2.9]{Mo13}, we have an injection of Hom groups
$$\operatorname{Hom}_{\operatorname{MTM}(\mathds G_{m,t})}(\widehat\mathcal H,\widehat\mathcal H')\hookrightarrow\operatorname{Hom}_{\mathcal D_{\mathds G_{m,t}}}(\mathcal H,\mathcal H).$$
But $\mathcal H$ is irreducible, so its only endomorphism is the identity and then, a twistor $\mathcal D$-module underlying $\mathcal H$ is unique, if it exists.
On the other hand, let $j:\mathds G_{m,t}\hookrightarrow\mathds P^1$ be the canonical inclusion and consider the $\mathcal D_{\mathds P^1}$-module $\mathcal H_{pr}:=j_{\dag+}\mathcal H$. It is an irreducible holonomic $\mathcal D_{\mathds P^1}$-module, because so is $\mathcal H$ by Proposition \ref{prop:IrredHyp}. Then it gives rise to a unique pure integrable twistor $\mathcal D$-module $\widehat\mathcal H_{pr}$ on $\mathds P^1$ by \cite[Thm. 1.4.4]{Mo5} and \cite[Rem. 1.40]{Sa15}. In addition, its underlying $\mathcal D_{\mathds P^1}$-module $\mathcal H_{pr}$ is rigid by virtue of Proposition \ref{prop:RigidHyp}. As a consequence, we can invoke \cite[Thm. 0.7]{Sa15} and claim that such twistor $\mathcal D$-module on $\mathds P^1$ is in fact an object of $\operatorname{IrrMHM}(\mathds P^1)$. Take now $\widehat\mathcal H':=j^+\widehat\mathcal H_{pr}$, which is an irregular mixed Hodge module whose underlying $\mathcal D_{\mathds G_{m,t}}$-module is $\mathcal H$, by \cite[Prop. 14.1.24]{Mo13}. The we must have, as was just shown, $\widehat{\mathcal H}'\cong \widehat{\mathcal H}$, so that the extension $\widehat{\mathcal H}_{pr}$ of $\widehat{\mathcal H}$ is unique, as claimed.
\end{proof}
\label{page:Roadmap}
The main point in the above theorem is that $\widehat{\mathcal H}$ underlies an irregular mixed Hodge module. Since the proof of this fact is rather long, and will be carried out in the next section through various intermediate results, we would like to orient the reader by giving here an overview
of these steps. We will restrict the sketch to the case where $\alpha_1=0$, this is also the first (and main) step in the
actual proof below on page \pageref{page:MainProof}. The general case can be rather easily deduced from this special one by considering Kummer $\mathcal D$- resp. $\mathcal{R}$-modules.
The first point is to realise $\widehat{\mathcal H}$ in a geometric way. For this purpose, consider the following two
families of Laurent polynomials
$$
f(y_1,\ldots,y_{n-1},\lambda_1,\ldots,\lambda_n):= -\lambda_1 \cdot y_1\cdot\ldots\cdot y_{n-1}-\frac{\lambda_2}{y_1}-\ldots-\frac{\lambda_n}{y_{n-1}}
$$
and
$$
{\,'\!}f(y_1,\ldots,y_{n-1},t):=-t\cdot y_1\cdot\ldots\cdot y_{n-1}-\frac{1}{y_1}-\ldots-\frac{1}{y_{n-1}}.
$$
where $y_k,\lambda_i, t\in \mathds G_m$. Write $\iota: {\mathds G}_{m,t}\hookrightarrow \mathds G_m^n$, $t\mapsto (t,1,\ldots,1)$, so that we
have the cartesian diagram
$$
\begin{tikzcd}
\mathds G_m^{n-1}\times {\mathds G}_{m,t} \ar{rr} \ar[swap]{dd}{{\,'\!}f\times \pi_2} & & \mathds G_m^{n-1}\times \mathds G_m^n \ar{dd}{f\times \pi_2} \\ \\
\AA^1_{\lambda_0}\times {\mathds G}_{m,t} \ar{rr}{\operatorname{id}_{\AA^1_{\lambda_0}}\times \iota} && \AA^1_{\lambda_0}\times \mathds G_m^n
\end{tikzcd}
$$
where we denote the coordinate on the affine line corresponding to the value of $f$ resp. of ${\,'\!}f$ by $\lambda_0$,
for reasons that will become clear later.
We consider the so-called twisted cohomology groups associated to the morphisms $f$ and ${\,'\!}f$. It can be shown (see Proposition \ref{prop:TwdeRham} below) that
$$
\widehat{\mathcal M}^{(0,\alpha)}_A\cong\mathcal H^{n-1}\left(\pi_{2,*}\Omega_{\mathds G_m^{n-1}\times \mathds G_m^n/\mathds G_m^n}^{\bullet+d}[z],z\left(d-\kappa(\alpha)\wedge\right)-df\wedge\right),
$$
where $(0,\alpha)=(0,\alpha_1,\alpha_2,\ldots,\alpha_n)=(0,0,\alpha_2,\ldots,\alpha_n)$,
where $\kappa(\alpha)=\sum_{j=1}^{n-1} \alpha_{j+1} dy_j/y_j$ and $A$ is the matrix from Corollary \ref{coro:hypGKZ} for the
case $m=0$.
Moreover, since the twisted cohomology groups involve complexes of relative differential forms, we have
$$
\begin{array}{c}
\displaystyle \iota^+ \mathcal H^{n-1}\left(\pi_{2,*}\Omega_{\mathds G_m^{n-1}\times \mathds G_m^n/\mathds G_m^n}^{\bullet+d}[z],z\left(d-\kappa(\alpha)\wedge\right)-df\wedge\right) \\ \\
\cong
\displaystyle \mathcal H^{n-1}\left(\pi_{2,*}\Omega_{\mathds G_m^{n-1}\times {\mathds G}_{m,t}/{\mathds G}_{m,t}}^{\bullet}[z],z\left(d-\kappa(\alpha)\wedge\right)-d{\,'\!}f\wedge\right),
\end{array}
$$
so that by using Lemma \ref{lem:RhypGKZ} we obtain an isomorphism of $\cR^{\operatorname{int}}_{\AA^1_z\times{\mathds G}_{m,t}}$-modules
\begin{equation}\label{eq:IdentRMod}
\widehat{\mathcal H}
\cong
\mathcal H^{n-1}\left(\pi_{2,*}\Omega_{\mathds G_m^{n-1}\times {\mathds G}_{m,t}/{\mathds G}_{m,t}}^{\bullet}[z],z\left(d-\kappa(\alpha)\wedge\right)-d{\,'\!}f\wedge\right).
\end{equation}
As a second step, we will realize the right hand side of the above isomorphism in a different way. Namely, write
${\,'\!}\varphi:=({\,'\!}f,\pi_2):\mathds G_m^{n-1}\times{\mathds G}_{m,t}\rightarrow\AA^1_{\lambda_0}\times{\mathds G}_{m,t}$ and consider the direct image complex
${\,'\!}\varphi_+\mathcal O_{\mathds G_m^{n-1}}^\alpha\in \text{D}_{\text{rh}}^\text{b}(\mathcal D_{\AA^1_{\lambda_0}\times{\mathds G}_{m,t}})$, where
$\mathcal O_{\mathds G_m^{n-1}}^\alpha=\mathcal D_{\mathds G_m^{n-1}}/(y_j\partial_{y_j}+\alpha_{j+1}+1)_{j=1,\ldots,n-1}$. We are interested
in the top cohomology of this complex. Standard techniques for the calculation
of direct images of $\mathcal D$-modules show that it is given by
$$
M:=\frac{\pi_{2,*}\Omega_{\mathds G_m^{n-1}\times {\mathds G}_{m,t}/{\mathds G}_{m,t}}^{n-1}[\partial_{\lambda_0}]}{(d-\partial_{\lambda_0} \cdot d{\,'\!}f\wedge)\pi_{2,*}\Omega_{\mathds G_m^{n-1}\times {\mathds G}_{m,t}/{\mathds G}_{m,t}}^{n-2}[\partial_{\lambda_0}]}
$$
We will use a variant of the Fourier-Laplace transformation (called localized partial Fourier-Laplace transformation,
and denoted by $\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}$,
see Definition \ref{def:FL} and Definition \ref{def:plocFL} below) exchanging the operator $\partial_{\lambda_0} \cdot $
into $z^{-1} \cdot $, the operator $\lambda_0 \cdot$ into $z^2\partial_z \cdot $, and localizing along $z=\infty$. Then we have
an isomorphism of $\mathcal D_{\AA^1_z\times {\mathds G}_{m,t}}$-modules
$$
\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}(M) =
\frac{\pi_{2,*}\Omega_{\mathds G_m^{n-1}\times {\mathds G}_{m,t}/{\mathds G}_{m,t}}^{n-1}[z^\pm]}{(z\cdot d- d{\,'\!}f\wedge)\pi_{2,*}\Omega_{\mathds G_m^{n-1}\times {\mathds G}_{m,t}/{\mathds G}_{m,t}}^{n-2}[z^\pm]}
\cong
\widehat{\mathcal H}[z^\pm] \supset \widehat{\mathcal H}.
$$
One of the main points of the proof in the next section is to give a good description of the image of $\widehat{\mathcal H}$
inside $\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}(M)$ under this isomorphism. One such description is given by the isomorphism of $\cR^{\operatorname{int}}_{\AA^1_z\times {\mathds G}_{m,t}}$-modules in the displayed formula \eqref{eq:IdentRMod}. However, we cannot, a priori, obtain any Hodge theoretic
information on $\widehat{\mathcal H}$ from \eqref{eq:IdentRMod}. On the other hand, we know that $M$ underlies an algebraic complex mixed Hodge module on $\AA^1_{\lambda_0 \times {\mathds G}_{m,t}}$ (since it is the direct image of such an object on $\mathds G_m^{n-1}$), and hence it comes equipped with a certain good filtration $F^H_\bullet M$ (the Hodge filtration).
There is a general procedure, explained below in Definition \ref{def:G0F} and Lemma \ref{lem:MHMIntoIrrMHMbyFL}, which constructs,
given a filtered $\mathcal D_{\AA_{\lambda_0}\times {\mathds G}_{m,t}}$-module $(N,F_\bullet)$,
a $\cR^{\operatorname{int}}_{\AA^1_z\times {\mathds G}_{m,t}}$-module called $G_0^F \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} N$ such that its localisation
$G_0^F \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} N \otimes_{\mathcal O_{\AA^1_z\times {\mathds G}_{m,t}}} \mathcal O_{\AA^1_z\times {\mathds G}_{m,t}}[z^{-1}]$ equals
$\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} N$. Then we show in Theorem \ref{thm:EqualFourierFilt} that
$$
\widehat{\mathcal H} \cong G_0^{F^H} \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M
$$
up to a shift of the Hodge filtration. Actually, the proof is not that direct, since we have
to identify $\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}(M)$ with the localized partial Fourier-Laplace transformation of some other $\mathcal D_{\AA^1_{\lambda_0}\times {\mathds G}_{m,t}}$-module (called $M_{\dag+}$), which underlies
a pure polarizable Hodge module. It is constructed by taking a compactification
of ${\,'\!}f$, i.e., a projective morphism defined on a quasi-projective (usually singular)
variety constructed from the toric compactification of $\mathds G_m^{n-1}$ inside $\mathds P^n$.
Then $M_{\dag+}$ is obtained as the direct image under this projective morphism of
a certain intersection cohomology module. Now it is known (see \cite[Cor. 0.5]{Sa15}) that if
$M_{\dag+}$ underlies a pure polarizable Hodge module, the $\cR^{\operatorname{int}}_{\AA^1_z\times {\mathds G}_{m,t}}$-module
$G_0^{F^H}\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}M_{\dag+}$ underlies an irregular Hodge module,
which finishes the proof. Notice that the proof of the identification $\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}(M)\cong
\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}(M_{\dag+})$ is derived from a similar isomorphism for the direct images of the
morphisms $\varphi=(f,\operatorname{id}_{\mathds G_m^n})$ resp. its compactification, rather than for ${\,'\!}\varphi$, and is done via
the formalism of Radon transformations for regular holonomic $\mathcal D$-modules (in the same way as in \cite{Reich2}
and \cite{ReiSe2, ReiSe3}).
\section{Hodge modules and Fourier-Laplace transformation}
Let $\alpha_1,\ldots,\alpha_n$ be real numbers, and consider the hypergeometric $\mathcal D_{{\mathds G}_m}$-module $\mathcal H=\mathcal H(\alpha_i;\emptyset)$.
As we have mentioned before, the goal of this section is to prove Theorem \ref{thm:HypIrrMHM} above, showing that the $\mathcal{R}$-module $\widehat\mathcal H:=\widehat\mathcal H(\alpha_i;\emptyset)$ from Definition \ref{def:H_Hut} underlies an object of $\operatorname{IrrMHM}({\mathds G}_m)$ (the abelian category of exponential Hodge modules as defined in \cite{Sa15}, see the introduction). We have already indicated several times
that we will use the GKZ-hypergeometric $\mathcal{R}$-module $\widehat\mathcal M_A^{(0,\alpha)}$ for the matrix $A$ from corollary \ref{coro:hypGKZ},
but where $m=0$. However, we will start with a more general situation, and specify the assumptions we need when going on with the proof.
Let $d<n$ be two positive integers, and take a parameter vector $\beta\in\mathds C^d$. For the Hodge theoretic questions we are interested in, only real parameter vectors are relevant, but we will work with this
more general setting until Remark \ref{rem:realExponents} below.
Let $A=(\underline{a}_1,\ldots,\underline{a}_n)\in \text{M}(d\times n,\mathds Z)$ be an integer matrix satisfying the following:
\begin{assump}\label{assump:AssMatrix}
$\mbox{}$
\begin{enumerate}[(i)]
\item $\mathds Z A =\mathds Z^d$, here $\mathds Z A:=\sum_{i=1}^n \mathds Z \underline{a}_i$,
\item Let $\Delta:=\operatorname{Conv}(\underline{a}_1,\ldots,\underline{a}_n)$
be the convex hull in $\mathds R^d$ of the vectors given by the columns of the matrix $A$. Then for any proper face $\Gamma\subset \Delta$ we require
that the set $\{\underline{a}_i \,|\, \underline{a}_i\in \Gamma\}$ is part of a $\mathds Q$-basis of $\mathds Q^d$.
\item The origin lies in the interior of $\Delta$.
\end{enumerate}
\end{assump}
\begin{rem}\label{rem:AssMatrix}
\begin{enumerate}[(i)]
\item These assumptions are in particular satisfied if $\underline{a}_1,\ldots,\underline{a}_n$ are the primitive integral generators
of the rays of the fan $\Sigma$ defining a toric Fano orbifold $X_\Sigma$, since in this case it is known (see \cite[Lem. 3.2.1 and \S~3.5]{CK}) that
$\Sigma$ is the union of the cones over the proper faces of $\Delta$, so that assumption (ii) is satisfied by the fact that the cones of $\Sigma$ are simplicial. Moreover, for Fano toric varieties the origin is the \emph{only} integer point in the interior of $\Delta$, so (iii) obviously holds. In any case, we see that these conditions are satisfied
for the example
\begin{equation}\label{eq:matAProjSpace}
A=
\begin{pmatrix}
1 & -1 & 0 & 0 &\ldots & 0 \\
1 & 0 & -1 & 0 & \ldots & 0 \\
\vdots &\ldots \\
1 & 0 & 0 & 0 & \ldots & -1
\end{pmatrix}
\in \text{M}\left((n-1) \times n, \mathds Z\right),
\end{equation}
since these are the generators of the rays of the fan of $\mathds P^{n-1}$. As we have seen in Corollary \ref{coro:hypGKZ}, this is the matrix
we have to look at when we want to express the classical hypergeometric $\mathcal D$-module of type $(n,0)$ and where $\alpha_0=0$ as an inverse image of the GKZ-system $\mathcal M_A^\beta$
where $\beta=\alpha:=(\alpha_2,\ldots, \alpha_n)^{\text{t}}\in \mathds R^{n-1}$.
\item
Assumption (iii) from above implies in particular that there is a relation $\underline{l}=(l_1,\ldots,l_n) \in \textup{ker}(A)\subset \mathds Z^n$ such
that $l_i>0$ for $i=1,\ldots, n$. It follows then from assumption (i) that the semi-group $\mathds N A=\sum_{i=1}^{n} \mathds N \underline{a}_i$ equals $\mathds Z^d$ (since for any $\underline{c}\in \mathds Z^d$, a linear combination
$\underline{c}=\sum_{i=1}^{n} n_i \underline{a}_i$ with integer coefficients $n_i$ can be turned into a combination
with positive coefficents by adding the vector $\underline{0}=\sum_{i=1}^{n} l_i \underline{a}_i$ sufficiently many times). This fact will be used later (see the proof of Proposition \ref{prop:TwdeRham}).
\end{enumerate}
\end{rem}
Let $S_1={\mathds G}_m^d=\operatorname{Spec}(\mathds C[y_1^\pm,\ldots,y_d^\pm])$ and $S_2={\mathds G}_m^n=\operatorname{Spec}(\mathds C[\lambda_1^\pm,\ldots,\lambda_n^\pm])$ be two algebraic tori, and consider the affine space $V=\AA^{n+1}$ with coordinates $\lambda_0,\lambda_1,\ldots,\lambda_n$. Let $V^\vee$ be the dual space with coordinates $w_0,w_1,\ldots,w_n$, and we also set $\tau:=-w_0$ and $z:=\tau^{-1}$. We decompose $V=\AA^1_{\lambda_0}\times W$, and consider $S_2\subset W$ as an open subset.
Consider the following family of Laurent polynomials
\begin{equation}\label{eq:TwdeRham}
\begin{array}{rcl}
\varphi: S_1 \times S_2 & \longrightarrow & \AA^1_{\lambda_0}\times S_2 \\
\left(\underline{y},\underline{\lambda}\right) & \longmapsto & \displaystyle \left(-\sum_{i=1}^n \lambda_i \underline{y}^{\underline{a}_i},\lambda_1,\ldots,\lambda_n\right)
\end{array},
\end{equation}
which in the case of the matrix from equation \eqref{eq:matAProjSpace} becomes
\begin{equation}\label{eq:TwdeRham-concrete}
\varphi(y_1,\ldots,y_{n-1},\lambda_1,\ldots,\lambda_n)=\left(-\lambda_1 \cdot y_1\cdot\ldots\cdot y_{n-1}-\frac{\lambda_2}{y_1}-\ldots-\frac{\lambda_n}{y_{n-1}},\lambda_1,\ldots,\lambda_n\right).
\end{equation}
Write $f:S_1\times S_2\rightarrow \AA_{\lambda_0}^1$ for the composition of $\varphi$ with the first projection $\AA_{\lambda_0}^1\times S_2\rightarrow\AA^1_{\lambda_0}$. Similarly, for any fixed $\underline{\lambda}\in S_2$,
we write $f_{\underline{\lambda}}:=f_{|S_1\times\{\underline{\lambda}\}}:S_1\rightarrow \AA^1_{\lambda_0}$ for the restriction of $f$ to the parameter value $\underline{\lambda}$.
Let us first quote the following statement from \cite[Lemma 2.8.]{ReiSe}. Since the input date in loc. cit. are fans
of toric varieties, we will copy the proof here to make it fit the assumptions above. Recall (see \cite{Kouch}) that
a Laurent polynomial $f_{\underline{\lambda}}=\sum_{i=1}^{n} \lambda_i \underline{y}^{\underline{a}_i}$ is called
convenient if $0$ lies in the interior of $\Delta$ and non-degenerate if
for all proper faces $\delta\subset \operatorname{Conv}(0,\underline{a}_1,\ldots,\underline{a}_n)$ not containing the origin, the Laurent polynomial $f^\delta_{\underline{\lambda}} =
\sum_{i:\underline{a}_i\in \delta} \lambda_i \underline{y}^{\underline{a}_i}$ has no critical points in $S_1$.
Notice that for matrices $A$ satisfying assumption (iii) from above, this last condition is equivalent to asking that $f_{\underline{\lambda}}^\delta$ is non-singular for
all proper faces $\delta\subset \Delta$.
\begin{lemma}\label{lem:NonDegen}
The Laurent polynomial $f_{\underline{\lambda}}:S_1\rightarrow \AA^1_z$ is non-degenerate and convenient for any $\underline{\lambda}\in S_2$.
\end{lemma}
\begin{proof}
Obviously $f_{\underline{\lambda}}$ is convenient by assumption (iii) from above.
Let $\delta\subset \Delta$ be a face of codimension $d+1-l$, with $l=1,\ldots, d$.
Let $\{i_1,\ldots,i_l\}\subset \{1,\ldots,n\}$ such that $\{\underline{a}_i\in\delta\}=\{\underline{a}_{i_1},\ldots, \underline{a}_{i_l}\}$,
notice that because of assumption (ii), we cannot have more than $l$ vectors in a face of dimension $l-1$.
Since the vectors
$\underline{a}_{i_1}, \ldots, \underline{a}_{i_l}$ are linearly independent over $\mathds Q$,
the matrix
$$
C:=\begin{pmatrix}
a_{i_1 1} & \ldots & a_{i_l 1} \\
\vdots & \vdots & \vdots \\
a_{i_1 d} & \ldots & a_{i_l d} \\
\end{pmatrix}
$$
has full rank (equal to $l$) and hence the system
$$
C\cdot
\begin{pmatrix}
\lambda_{i_1} \underline{y}^{\underline{a}_{i_1}} \\
\vdots \\
\lambda_{i_l} \underline{y}^{\underline{a}_{i_l}}
\end{pmatrix} = 0,
$$
which is the system of critical point equations $(y_k\partial_{y_k} f^\delta_{\underline{\lambda}} =0)_{k=1,\ldots,d}$,
has no nontrivial solution; the trivial one $\lambda_i \cdot \underline{y}^{\underline{a}_i}=0$ for all $i\in \{i_1,\ldots,i_l\}$ is not valid since $\underline{\lambda}\in S_2$ and we are looking for solutions $\underline{y}\in S^1$. Hence
$f_{\underline{\lambda}}^\delta$ is non-singular on $S_1$, and so $f_{\underline{\lambda}}$ is non-degenerate.
\end{proof}
From this we can deduce
the following statement, which is a variant of
\cite[Lem. 2.13]{ReiSe}. However, we will give the proof here for the convenience of the reader.
\begin{lemma}
$\widehat{\mathcal M}_{A}^{(\beta_0,\beta)}$ is locally $\mathcal O_{\AA^1_z\times S_2}$-free of rank $n!\cdot\operatorname{vol}(\Delta)$ (considering the normalized volume in $\mathds R^n$ such that $[0,1]^n$ has volume one). For the case of the matrix in equation \eqref{eq:matAProjSpace}, this rank
equals $n$.
\end{lemma}
\begin{proof}
There is an isomorphism of $\mathcal O_{\AA^1_z\times S_2}$-modules (or even of $\mathcal{R}_{\AA^1_z\times S_2}$-modules)
$$
\widehat{\mathcal M}_{A}^{(\beta_0,\beta)}\cong\frac{\mathcal{R}_{\AA^1_z\times S_2}}{
\left(\prod_{j:l_j>0} (z\partial_{\lambda_j})^{l_j}-\prod_{j:l_j<0} (z\partial_{\lambda_j})^{-l_j}\right)_{l\in\mathbb L}
+\left(\sum_{j=1}^n a_{kj}\lambda_j z\partial_{\lambda_j} - z\beta_k\right)_{k=1,\ldots,d}
},
$$
so it suffices to prove the statement for the module on the right hand side of this equation.
We consider the filtration induced on it by the filtration
on $\mathcal{R}_{\AA^1_z\times S_2}$ for which $z\partial_{\lambda_i}$ has degree $1$ and any element of $\mathcal O_{\AA^1_z\times S_2}$ has degree
zero. The graded module with respect to this filtration is a sheaf on $\AA^1_z\times T^* S_2$, and we first need to show
that its support lies in the zero section, i.e., in the subspace $\AA^1_z\times S_2$. Notice that the symbols
of the operators in the ideal
$\left(\prod_{j:l_j>0} (z\partial_{\lambda_j})^{l_j}-\prod_{j:l_j<0} (z\partial_{\lambda_j})^{-l_j}\right)_{l\in\mathbb L}
+\left(\sum_{j=1}^n a_{kj}\lambda_j z\partial_{\lambda_j} - z\beta_k\right)_{k=1,\ldots,d}$ with respect to the
filtration of $\mathcal{R}_{\AA^1_z\times S_2}$ defined above are the same as the symbols
of the operators of the usual hypergeometric ideal
$\left(\prod_{j:l_j>0} \partial_{\lambda_j}^{l_j}-\prod_{j:l_j<0} \partial_{\lambda_j}^{-l_j}\right)_{l\in\mathbb L}
+\left(\sum_{j=1}^n a_{kj}\lambda_j \partial_{\lambda_j} - \beta_k\right)_{k=1,\ldots,d}$ with respect to the
(usual) order filtration on $\mathcal D_{S_2}$. Hence by the arguments of \cite[Lem. 3.1 to Lem. 3.3]{Adolphson},
we obtain that the variety cut out by the symbols of the operators in
$\left(\prod_{j:l_j>0} (z\partial_{\lambda_j})^{l_j}-\prod_{j:l_j<0} (z\partial_{\lambda_j})^{-l_j}\right)_{l\in\mathbb L}
+\left(\sum_{j=1}^n a_{kj}\lambda_j z\partial_{\lambda_j} - z\beta_k\right)_{k=1,\ldots,d}$ is $\AA^1_z\times S_2$,
notice that here the fact that $f_{\underline{\lambda}}$ is non-degenerate for all $\underline{\lambda}\in S_2$
(i.e., the statement of the last lemma) plays a crucial role.
From $\textup{supp}(\textup{gr}(\widehat{\mathcal M}^{(\beta_0,\beta)}_A))\subseteq \AA^1_z\times S_2$ one deduces as in ordinary $\mathcal D$-module theory that $\widehat{\mathcal M}_{A}^{(\beta_0,\beta)}$ is
$\mathcal O_{\AA^1_z\times S_2}$-coherent.
Now the restriction $\widehat{\mathcal M}_A^{(0,\beta)}/z\cdot \widehat{\mathcal M}_A^{(0,\beta)}$ is isomorphic
to the Jacobian algebra $\textup{Jac}(f)=\mathcal O_{S_1\times S_2}/(\partial_{y_1} f, \ldots, \partial_{y_d} f)$
(see \cite[Lem. 2.12]{ReiSe}), and that the latter has rank equal to $n!\cdot \textup{vol}(\Delta)$ (see \cite[Thm. 1.16]{Kouch}).
Moreover, the localized object $\widehat{\mathcal M}_A^{(0,\beta)}\otimes_{\mathcal O_{\AA^1_z\times S_2}} \mathcal O_{\AA^1_z\times S_2}[z^{-1}]$
has a $\mathcal D_{\AA^1_z\times S_2}[z^{-1}]$-module structure, and is $\mathcal O_{\AA^1_z\times S_2}[z^{-1}]$-coherent, hence
$\mathcal O_{\AA^1_z\times S_2}[z^{-1}]$-free. Its rank can also be calculated as the holonomic rank of ordinary GKZ-systems,
see \cite[Prop. 2.7 (3)]{ReiSe}, and equals $n!\cdot\operatorname{vol}(\Delta)$.
This shows that the module $\widehat{\mathcal M}^{(\beta_0,\beta)}_A$ itself is $\mathcal O_{\AA^1_z\times S_2}$-free of the same rank
$n!\cdot\operatorname{vol}(\Delta)$.
\end{proof}
For any complex number $\beta$, recall that the Kummer $\mathcal D$-module of parameter $\beta$ is by defintion the quotient $\mathcal K_\beta:=\mathcal D_{{\mathds G}_{m,t}}/(t\partial_t-\beta)$. We will also use in this section $\mathcal{R}$-modules arising from such $\mathcal D$-modules. Here is the precise definition.
\begin{defi}
For any complex number $\beta$, we define the Kummer $\mathcal{R}$-module of parameter $\beta$ as the cyclic $\cR^{\operatorname{int}}_{\AA^1_z\times {\mathds G}_{m,t}}$-module
$$\widehat\mathcal K_{\beta}:=\cR^{\operatorname{int}}_{\AA^1\times {\mathds G}_{m,t}}/(z^2\partial_z,zt\partial_t-z\beta).$$
\end{defi}
\begin{rem}\label{rem:KummerHodge}
Although both kinds of Kummer modules can be defined for any complex value of their parameters, in the end we will be interested only in the real case to make use of their Hodge properties. Indeed, since both have no singularities at ${\mathds G}_{m,t}$, if $\mathcal K_\beta$ were a complex Hodge module it would be in fact a complex variation of Hodge structures, and by (the first part of) the proof of \cite[Lem. 4.5]{Sch}, $\beta$ ought to be real.
On the other hand, $\widehat\mathcal K_\beta$ is clearly the Rees module of $\mathcal K_\beta$ together with the trivial filtration $F_\bullet$ such that $F_k=0$ for $k<0$ and $F_k=\mathcal K_\beta$ for $k\geq0$. As described in \cite[Prop. 13.5.4]{Mo13} and \cite[Thm. 0.2]{Sa15}, it gives rise to an integrable pure twistor $\mathcal D$-module on ${\mathds G}_{m,t}$, which belongs as well to $\operatorname{IrrMHM}({\mathds G}_m)$. It is also described as a harmonic bundle at \cite[\S2.1.9]{Mo13}.
\end{rem}
\begin{defi}\label{def:Oalpha}
For any smooth complex algebraic variety $X$, and for any $\beta\in\mathds C^d$, we will denote by $\mathcal O_{S_1\times X }^\beta$ the $\mathcal D_{S_1\times X }$-module corresponding to the structure sheaf of $S_1 \times X$ twisted by $\underline{y}^{-1-\beta}$, that is,
$$\mathcal O_{S_1\times X }^\beta:=\frac{\mathcal D_{S_1}}{\left(y_k\partial_{y_k}+\beta_k+1\,:\, k=1,\ldots,d\right)}\boxtimes\mathcal O_ X =:\mathcal O_{S_1}^\beta\boxtimes\mathcal O_ X .$$
\end{defi}
Note that for any other $\beta'\in\mathds C^d$ such that $\beta-\beta'\in\mathds Z^d$, $\mathcal O_{S_1\times X }^\beta\cong\mathcal O_{S_1\times X }^{\beta'}$. These modules underly complex Hodge modules if and only if the components of the parameter vector are real numbers, since they are the corresponding exterior products of the Kummer modules $\mathcal K_{-\beta_1},\ldots,\mathcal K_{-\beta_d}$ and $\mathcal O_ X $.
With these notations, the following result is a special case of
\cite[Prop. 3.21]{ReiSe2}, taking into account the twist of $\mathcal O_{S_1\times S_2}$ by $\underline{y}^{-1-\beta}$. However, we prefer
to give a direct proof here, which is a simplified variant of the corresponding statement in \cite[Prop. E.6]{Mo15}.
Notice that the idea of this approach goes back to the so-called ``better behaved GKZ-systems'' of Borisov-Horja (see \cite{BorHor}).
\begin{prop}\label{prop:TwdeRham}
There exists an isomorphism of $\cR^{\operatorname{int}}_{\AA^1_z\times S_2}$-modules
$$
\mathcal H^0\left(\pi_{2,*}\Omega_{S_1\times S_2/S_2}^{\bullet+d}[z],z\left(d-\kappa(\beta)\wedge\right)-df\wedge\right) \longrightarrow \widehat{\mathcal M}_A^{(0,\beta)}
$$
for any $\beta\in\mathds C^d$, given by sending $\omega:=\prod_{j=1}^d dy_j/y_j$ to $[1]\in\widehat{\mathcal M}_A^{(0,\beta)}$, where
we write $\kappa(\beta)$ for $\sum_{j=1}^d \beta_j dy_j/y_j$ and $\pi_2$ for the the second canonical projection $S_1\times S_2\rightarrow S_2$.
\end{prop}
\begin{proof}
We will construct a third module $\mathcal Q/\mathcal K$, and show that both the module $\widehat{\mathcal M}_A^{(0,\beta)}$ and the module $\mathcal H^0\left(\pi_{2,*}\Omega_{S_1\times S_2/S_2}^{\bullet+d}[z],z\left(d-\kappa(\beta)\wedge\right)-df\wedge\right)$ are isomorphic to it.
For this purpose, define the free $\mathcal O_{\AA^1_z\times S_2}$-module
$$
\mathcal Q:=\bigoplus_{\underline{c}\in \mathds Z^d} \mathcal O_{\AA^1_z\times S_2} \cdot e(\underline{c}),
$$
where $e(\alpha)$ is a symbol representing a generator of $\mathcal Q$. We put a $\cR^{\operatorname{int}}_{\AA^1_z\times S_2}$-module structure on $\mathcal Q$ by letting
$$
\begin{array}{rcl}
z \partial_{\lambda_i} e(\underline{c}) & := & e(\underline{c}+\underline{a}_i), \\ \\
z^2\partial_z e(\underline{c}) &:= & \displaystyle -\sum_{i=1}^{n} \lambda_i \cdot z \partial_{\lambda_i} e(\underline{c}).
\end{array}
$$
Since we have $\mathds N A = \mathds Z^d$ (see Remark \ref{rem:AssMatrix}, 2.), we conclude from the first of these equations that $\mathcal Q$ is a cyclic $\cR^{\operatorname{int}}_{\AA^1_z\times S_2}$-module with generator $e(\underline{0})$.
Moreover, we consider the $\cR^{\operatorname{int}}_{\AA^1_z\times S_2}$-submodule $\mathcal K$ of $\mathcal Q$ generated by
$$
\left(\displaystyle \sum_{i=1}^{n} a_{ki} \lambda_i\cdot z\partial_{\lambda_i} + z(c_k-\beta_k)\right)\cdot e(\underline{c})\quad\quad\forall\underline{c}\in\mathds Z^d, \;\forall k=1,\ldots,d.
$$
Then we claim that there is an $\cR^{\operatorname{int}}_{\AA^1_z\times S_2}$-isomorphism
$$
\phi:\widehat{\mathcal M}^{(0,\beta)}_A \stackrel{\cong}{\longrightarrow} \mathcal Q/\mathcal K.
$$
sending $[1]$ to $e(\underline{0})$.
It is clear that $\phi$ is well defined since all operators occurring in the denominator in
the definition of $\widehat{\mathcal M}^{(0,\beta)}_A$ act by zero in $\mathcal Q/\mathcal K$: The operators $\prod_{j:l_j>0} (z\partial_{\lambda_j})^{l_j}-\prod_{j:l_j<0} (z\partial_{\lambda_j})^{-l_j}$ act by zero
already on $\mathcal Q$ (as $\underline{l}\in \mathbb L$);
similarly, $z^2\partial_z+\lambda_1z\partial_{\lambda_1}+\ldots+\lambda_nz\partial_{\lambda_n}$ acts by zero on $\mathcal Q$ because of the
definition of the action of $z^2\partial_z$, and
$\sum_{j=1}^n a_{kj}\lambda_j z\partial_{\lambda_j} - z\beta_k,\; k=1,\ldots,d$ is a generator of $\mathcal K$, so its class is obviously zero
in the quotient $\mathcal Q/\mathcal K$.
An inverse map $\mathcal Q/\mathcal K \rightarrow \widehat{\mathcal M}_A^{(0,\beta)}$ is defined as follows: For any $\underline{c} \in \mathds N^d$, choose a representation
$\underline{c}=\sum_{i=1}^{n} n_i \underline{a}_i$, with $n_i\in\mathds N$. Then we map $e(\underline{c})$ to the class
of $\prod_{i=1}^{n} (z\partial_{\lambda_i})^{n_i}$ in $\widehat{\mathcal M}_A^{(0,\beta)}$. This is well defined: If we take another representation $\underline{c}=\sum_{i=1}^{n} n'_i \underline{a}_i$, then $(n_i-n'_i)_{i=1,\ldots,n}\in\mathds Z^n$ lies in $\mathbb L$,
showing that
$$
\displaystyle \prod_{i:n_i>n'_i} (z\partial_{\lambda_i})^{n_i-n'_i}-\prod_{i:n'_i>n_i} (z\partial_{\lambda_i})^{n'_i-n_i} = 0 \in \widehat{\mathcal M}^{(0,\beta)}_A,
$$
from what it follows that
$$
\displaystyle \prod_{i=1}^n (z\partial_{\lambda_i})^{n_i}=\prod_{i=1}^n (z\partial_{\lambda_i})^{n'_i}\in \widehat{\mathcal M}^{(0,\beta)}_A.
$$
Moreover, elements of $\mathcal K$ obviously go to zero in $\widehat{\mathcal M}^{(0,\beta)}_A$. It is also clear that this map is inverse to $\phi$.
In order to identify $\mathcal Q/\mathcal K$ with the twisted de Rham cohomology module, notice that the complex
$\left(\pi_{2,*}\Omega_{S_1\times S_2/S_2}^{\bullet+d}[z],z\left(d-\kappa(\beta)\wedge\right)-df\wedge\right)$ is concentrated
in degrees $-d$ to $0$, so we need to compute its top cohomology, i.e., the quotient
\begin{equation}\label{eq:FLGM-system}
\frac{\pi_{2,*}\Omega_{S_1\times S_2/S_2}^{d}[z]}{\left(z\left(d-\kappa(\beta)\wedge\right)-df\wedge\right)\pi_{2,*}\Omega_{S_1\times S_2/S_2}^{d-1}[z]}
\end{equation}
Since we have $\mathds C[\mathds Z^d]\cong H^0(S_1, \mathcal O_{S_1})$, there is an obvious identification of $\mathcal O_{\AA^1_z\times S_2}$-modules,
$$
\mathcal Q \cong \pi_{2,*}\Omega^d_{S_1\times S_2/S_2}[z]
$$
sending $e(\underline{c})$ to $\underline{y}^{\underline{c}}\cdot \omega$.
Now it is easy to see (cf. the proofs of \cite[Prop. E.4 and E.6]{Mo15}) that the image of
$$
\left(z\left(d-\kappa(\beta)\wedge\right)-df\wedge\right)\pi_{2,*}\Omega_{S_1\times S_2/S_2}^{d-1}[z]
$$
can be
identified under this isomorphism with the submodule $\mathcal K$ of $\mathcal Q$. Moreover, one checks that the $\cR^{\operatorname{int}}_{\AA^1_z\times S_2}$-module
structures on the quotient \eqref{eq:FLGM-system} and the module $\mathcal Q/\mathcal K$ are compatible, e.g., we have
$z\partial_{\lambda_i} \omega = -(\partial_{\lambda_i} f) \omega=\underline{y}^{\underline{a}_i}\omega$, accordingly with $(z\partial_{\lambda_i})\cdot e(\underline{0})
=e(\underline{a}_i)$.
Combining the two isomorphisms $\mathcal Q/\mathcal K \cong
\mathcal H^0\left(\pi_{2,*}\Omega_{S_1\times S_2/S_2}^{\bullet+d}[z],z\left(d-\kappa(\beta)\wedge\right)-df\wedge\right)$ and
$\widehat{\mathcal M}_A^{(0,\beta)} \cong \mathcal Q/\mathcal K$ we obtain the desired one
$$
\mathcal H^0\left(\pi_{2,*}\Omega_{S_1\times S_2/S_2}^{\bullet+d}[z],z\left(d-\kappa(\beta)\wedge\right)-df\wedge\right) \longrightarrow \widehat{\mathcal M}_A^{(0,\beta)}
$$
which sends $\omega$ to $[1]$.
\end{proof}
In the sequel, we need to consider an extension of the map $\varphi:S_1\times S_2\rightarrow \AA^1_{\lambda_0}\times S_2$ to a projective morphism. For that purpose,
we will construct a partial compactification of $S_1\times S_2$ by looking at a toric compactification
of $S_1$. More precisely, consider the embedding
\begin{equation}\label{morphism:g}
\begin{array}{rcl}
g:S_1 & \hookrightarrow & \mathds P\left(V^\vee\right)=\mathds P^n \\
\underline{y} & \longmapsto & (w_0:\ldots:w_n)=\left(1:\underline{y}^{\underline{a}_1}:\ldots: \underline{y}^{\underline{a}_n}\right)
\end{array}
\end{equation}
and put $X:=\overline{\text{Im}(g)}$. Consider the graph $\Gamma_f\subset S_1\times\AA^1_{\lambda_0}\times S_2$, and let $\Gamma X$ be the closure
of $\Gamma_f$ in $X\times\AA^1\times S_2$.
Then we have $\Gamma X\subset Z^*$, where
$$
\begin{tikzcd}
Z^*:= \left\{\sum_{i=0}^n \lambda_i\cdot w_i=0\right\}\ar[hook]{r}{i_P} & \mathds P^n\times \AA^1_{\lambda_0}\times S_2=:P
\end{tikzcd}
$$
is the universal hyperplane.
We thus have the commutative diagram
\begin{equation}\label{eq:CompactDiagram}
\begin{tikzcd}
S_1\times S_2 \ar{rd}{\varphi} \ar[hook]{r} \ar[bend left=35]{rr}{k} & \Gamma X \ar{d}{\overline{\varphi}} \ar[hook]{r} & Z^* \ar[swap]{ld}{p_2} \ar[hook]{r}{i_P} & P, \ar{lld}{p_2}\\
& \AA^1\times S_2&
\end{tikzcd}
\end{equation}
where the map $S_1\times S_2 \hookrightarrow \Gamma X$ is the composition of the isomorphism $S_1\times S_2 \stackrel{\cong}{\rightarrow}\Gamma_f$ with $\Gamma_f\hookrightarrow\Gamma X$ and the map $\Gamma X \hookrightarrow Z^*$ is the closed embedding
mentioned above. Notice that $\overline{\varphi}$ is projective, and restricts to $\varphi$ on $S_1\times S_2$, i.e.,
it is the extension of $\varphi$ we were looking for.
We need also the following important geometric property of the morphisms $\varphi$ and $\overline{\varphi}$.
Recall (see \cite[\S8]{Sa2}) that for a smooth affine variety $U$, a regular function $h:U\rightarrow \AA^1$ with isolated
critical points is called cohomologically tame if there is a partial
compactification $j:U\hookrightarrow\overline{U}$ (i.e. $\overline{U}$ is quasi-projective) and an extension of $h$ to a projective morphism $\overline{h}:\overline{U}\rightarrow \AA^1$ such that the sheaf $\mathbf R j_* \mathds Q_U$ has no vanishing cycles with respect to $\overline{h}$ outside of $U$,
i.e., such that for any $c\in \AA^1$, we have
$$
\textup{supp}(\psi_{\overline{h}-c}(\mathbf R j_* \mathds Q_U)) \subset U.
$$
We call a morphism $H:\mathcal X \rightarrow \mathcal{S}$ on a quasi-projective
variety $\mathcal X$ stratified smooth if there is a locally finite stratification
by locally
closed smooth subvarieties such that the restriction of $H$ to any strata has no critical points.
\begin{lemma}\label{lem:StratSmooth}
We have the following properties of the partial compactifications defined above:
\begin{enumerate}
\item For any parameter value $\underline{\lambda}\in S_2$, the morphism $f_{\underline{\lambda}}:S_1\rightarrow \AA^1_{\lambda_0}$ is cohomologically tame.
\item The morphism $\overline{\varphi}:\Gamma X \rightarrow \AA^1\times S_2$ is stratified smooth on its boundary $\Gamma X\setminus(S_1\times S_2) $. \item Consider the composition $k':S_1\times S_2 \hookrightarrow P$ of the map $k:S_1\times S_2\hookrightarrow Z^*$ with
the canonical closed embedding $i_P:Z^*\hookrightarrow P$. Then for any $\beta\in \mathds C^d$ and for $\star\in\{+,\dag\}$, the module $(k')_\star \mathcal O^\beta_{S_1\times S_2}$ is non-characteristic with respect to $p_2$ along the boundary $\overline{\operatorname{im}(k')}\backslash\operatorname{im}(k')$, i.e., its characteristic variety satisfies $\textup{char}(k_\star \mathcal O^\beta_{S_1\times S_2}) \cap (\mathds P^n\times T^*(\AA^1_{\lambda_0}\times S_2))_{|T^*(P\backslash\operatorname{im}(k'))} \subset P\backslash\operatorname{im}(k')$.
\end{enumerate}
\end{lemma}
\begin{proof}
\begin{enumerate}
\item According to Lemma \ref{lem:NonDegen}, $f_{\underline{\lambda}}$ is non-degenerate and convenient for any $\underline{\lambda}\in S_2$. It then follows from \cite[Lem. 3.4]{DeLoe} that $f_{\underline{\lambda}}$ is cohomologically tame, but since the notations in loc. cit. differ considerably
from our situation, we recall the proof: We will show that the extension $\overline{f}_{\underline{\lambda}}:\Gamma X^{\underline{\lambda}}:=(\Gamma X)\cap(\mathds P^n\times\AA^1_{\lambda_0}\times\{\underline{\lambda}\})\rightarrow \AA^1_{\lambda_0}$ which is the restriction of $\overline{\varphi}$ over $\AA^1_{\lambda_0}\times\{\underline{\lambda}\}$ has no vanishing cycles at infinity.
Recall that the projective toric variety $X$ is stratified by $X=\bigcup_{\delta\subset \Delta} X_\delta$, where $\Delta$ is the convex hull in $\mathds R^d$ of the columns of the matrix $A$, $\delta$ is a face of $\Delta$, and $X_\delta$ is a torus orbit associated with the face $\delta$ (cf., for instance, \cite[Prop. 5.1.9]{GKZbook}). We obtain an induced stratification $(\Gamma X_\delta)_{\delta\in\Delta}$ of $\Gamma X$ and an induced stratification $(\Gamma X^{\underline{\lambda}}_\delta)_{\delta\in\Delta}$ of the restriction $\Gamma X^{\underline{\lambda}}$.
Then the smoothness of the restriction $(\overline{f}_{\underline{\lambda}})_{|\Gamma X^{\underline{\lambda}}_\delta}$ follows from the smoothness of the Laurent polynomial $f^\delta_{\underline{\lambda}}=\sum_{i:\underline{a}_i\in\delta} \lambda_i \underline{y}^{\underline{a}_i}$, which has no critical points
since $f_{\underline{\lambda}}$ is non-degenerate (see Lemma \ref{lem:NonDegen}). Hence we see that $\overline{f}_{\underline{\lambda}}$ is
stratified smooth on its boundary, i.e., outside $\Gamma X^{\underline{\lambda}}_\Delta = (\Gamma X \backslash \Gamma_f)\cap(\mathds P^n\times\AA^1_{\lambda_0}\times\{\underline{\lambda}\}) \cong S_1$. Then it follows from \cite[Prop. 4.2.8]{Di} that for any constructible complex $\mathcal F^\bullet$ on $\Gamma X^{\underline{\lambda}}$ (with respect to the stratification $(\Gamma X^{\underline{\lambda}}_\delta)_{\delta\subset \Delta}$) we have $\psi_{\overline{f}_{\underline{\lambda}}-c} \mathcal F^\bullet_{|(\Gamma X^{\underline{\lambda}} \backslash \Gamma X^{\underline{\lambda}}_\Delta)}=0$ for any $c\in \AA^1_{\lambda_0}$. Hence $\textup{supp}(\psi_{\overline{f}_{\underline{\lambda}}-c} \mathcal F^\bullet) \subset \Gamma X^{\underline{\lambda}}_\Delta \cong S_1$, and so $f_{\underline{\lambda}}$ is cohomologically tame since we can apply this to the case where $\mathcal F^\bullet = \mathbf R j_* \mathds Q_{S_1}$, $j:S_1\cong \Gamma X^{\underline{\lambda}}_\Delta \hookrightarrow
\Gamma X^{\underline{\lambda}}$ being the canonical open embedding.
\item The same proof as in (1) applies, i.e., the restriction $\overline{\varphi}_{|\Gamma X_\delta}:\Gamma X_\delta\rightarrow
\AA^1_{\lambda_0}\times S_2$ is non-singular for all $\delta \subsetneq \Delta$.
\item We have $\textup{char}((k')_\star\mathcal O_{S_1\times S_2}^\beta) \subset
\bigcup_{\delta\in\Delta} T^*_{\Gamma X_\delta}P$. The fact that $\overline{\varphi}_{|\Gamma X_\delta}$ is smooth (for $\delta\subsetneq \Delta$)
means exactly that the fibres of $p_2:P\rightarrow \AA^1_{\lambda_0}\times S_2$ are transversal to $\Gamma X_\delta$. As
the conormal bundle to these fibres is precisely the space $\mathds P^n\times T^*(\AA^1_{\lambda_0}\times S_2)$, we obtain
$(\mathds P^n\times T^*(\AA^1_{\lambda_0}\times S_2))\cap \Gamma X_\delta \subset \mathds P^n\times \AA^1_{\lambda_0}\times S_2$, for
all $\delta\subsetneq \Delta$, and so we have $\textup{char}(k_\star \mathcal O^\beta_{S_1\times S_2}) \cap (\mathds P^n\times T^*(\AA^1_{\lambda_0}\times S_2))_{|T^*(P\backslash\operatorname{im}(k'))} \subset P\backslash\operatorname{im}(k')$,
as required.
\end{enumerate}
\end{proof}
In order to achieve the comparison results of this section we need to use several variants of the Fourier-Laplace transformations; let us recall here the definitions.
\begin{defi}\label{def:FL}
Let $Y$ be a smooth algebraic variety, $U$ be a finite-dimensional complex vector space and $U'$ its dual vector space. Denote by $\mathcal E$ the trivial vector bundle $\tau:U\times Y\rightarrow Y$ and by $\mathcal E'$ its dual.
Write $\operatorname{can}:U\times U'\rightarrow\AA^1$ for the canonical morphism defined by $\operatorname{can}(a,\varphi)=\varphi(a)$. This extends to a function $\operatorname{can}:\mathcal E\times_Y\mathcal E'\rightarrow\AA^1$. Define $\mathcal L:=\mathcal O_{\mathcal E\times_{Y}\mathcal E'}\cdot e^{-\operatorname{can}}$, the free rank one module with differential given by the product rule. Consider also the canonical projections $p_1:\mathcal E\times_{Y}\mathcal E'\rightarrow\mathcal E$, $p_2:\mathcal E\times_{Y}\mathcal E'\rightarrow\mathcal E'$. The partial Fourier-Laplace transformation is then defined by
$$\operatorname{FL}_{Y}(\bullet):=p_{2,+}\left(p_1^+(\bullet)\otimes_{\mathcal O_{\mathcal E\times_{Y}\mathcal E'}}^\L\mathcal L\right).$$
\end{defi}
If the base $Y$ is a point we recover the usual Fourier-Laplace transformation and we will simply write $\operatorname{FL}$. Notice that although this functor is defined at the level of derived categories, it is $t$-exact in the derived category of bounded complexes of $\mathcal D$-modules with holonomic cohomologies, i.e., induces a functor $\operatorname{FL}_Y:\operatorname{Mod}_\text{h}(\mathcal D_\mathcal E)\rightarrow \operatorname{Mod}_\text{h}(\mathcal D_{\mathcal E'})$.
We also need the following variant of the Fourier-Laplace transformation.
\begin{defi}\label{def:plocFL}
Keep the notations of the previous definition, and assume moreover that $U$ and $U'$ are one-dimensional, with respective coordinates $t$ and $\tau$. Put $z=\tau^{-1}$, and denote by $j_\tau:\mathds{G}_{m,\tau}\hookrightarrow\AA^1_\tau$ and $j_z:\mathds{G}_{m,\tau}\hookrightarrow\AA^1_z=\mathds P^1_\tau\setminus\{\tau = 0\}$ the canonical embeddings. Then the localized partial Fourier-Laplace transformation with respect to $\tau$ is defined by
$$\operatorname{FL}^{\operatorname{loc}}_{Y}:=(j_z\times\operatorname{id}_Y)_+(j_\tau\times\operatorname{id}_Y)^+\operatorname{FL}_{Y}.$$
\end{defi}
Our next aim is to compare the twisted de Rham cohomology of the family $\varphi:S_1\times S_2\rightarrow \AA^1_{\lambda_0}\times S_2$, i.e., the
left-hand side of the isomorphism of Proposition \ref{prop:TwdeRham} with an object derived from a certain intersection cohomology $\mathcal D$-module on $Z^*$.
Recall that for a smooth algebraic variety $Y$, and an open subvariety $j:U\hookrightarrow Y$, we call intersection cohomology module with coefficients in some $\mathcal D_U$-module $\mathcal N$ the intermediate extension $j_{\dag+}\mathcal N:=\operatorname{im}(j_\dag \mathcal N\rightarrow j_+\mathcal N)$. Its name comes from the fact that, if $\mathcal N$ is smooth and corresponds to a local system $\mathcal L$ on $U$ under the Rieman-Hilbert correspondence, $j_{\dag+}\mathcal N$ corresponds to the intersection cohomology complex on $Y$ with coefficients in $\mathcal L$, $\mathit{IC}(Y,\mathcal L)$.
Now is when we can properly state and prove the next comparison result of this section. Recall that we take a matrix $A\in\text{M}(d\times n,\mathds Z)$
satisfying the assumptions \ref{assump:AssMatrix} and a parameter vector $\beta\in \mathds C^d$. Recall that $Z^*=\left\{\sum_{i=0}^n w_i \lambda_i =0\right\}\subset P=\mathds P^n\times \AA^1_{\lambda_0}\times S_2$ denotes the universal hyperplane, the map $k$, introduced in diagram (\ref{eq:CompactDiagram}), is
$$
\begin{array}{rcl}
k:S_1\times S_2 & \longrightarrow & Z^* \\
(\underline{y},\underline{\lambda}) & \longmapsto & ((1:\underline{y}^{\underline{a}_1}:\ldots:\underline{y}^{\underline{a}_n}),
(-\sum_{i=1}^{n}\lambda_i \underline{y}^{\underline{a}_1},\lambda_1,\ldots,\lambda_n))
\end{array}
$$
and $p_2$ is the restriction of the canonical projection from $P$ to $\AA^1\times S_2$ to the subspace $Z^*$.
\begin{prop}\label{prop:IsoAfterFourier}
In the above situation, we have the following isomorphism of $\mathcal D_{\AA^1_z\times S_2}$-modules:
$$
\operatorname{FL}^{\operatorname{loc}}_{S_2}\mathcal H^0p_{2,+}k_{\dag+}\mathcal O_{S_1\times S_2}^\beta\stackrel{\sim}{\longrightarrow}\operatorname{FL}^{\operatorname{loc}}_{S_2}\mathcal H^0\varphi_+\mathcal O_{S_1\times S_2}^\beta.
$$
Moreover, this isomorphism is induced from the canonical morphism $k_{\dag+}\mathcal O_{S_1\times S_2}^\beta\hookrightarrow k_+\mathcal O_{S_1\times S_2}^\beta$ by applying the functor $\operatorname{FL}^{\operatorname{loc}}_{S_2}\mathcal H^0 p_{2,+}$.
\end{prop}
Before entering into the proof of this Proposition, we will need to state some facts about Radon transformations
for $\mathcal D$-modules. We follow \cite[\S~2]{Reich2}. Recall that $V$ and $V^\vee$ are dual affine spaces of dimension $n+1$ with coordinates $w_0,\ldots,w_n$ and $\lambda_0,\ldots,\lambda_n$ respectively.
\begin{defi}
Denote by $Z\subset\mathds P(V^\vee)\times V$ the universal hyperplane with equation $\sum_{i=0}^nw_i\lambda_i=0$ and by $U:=(\mathds P(V^\vee)\times V)\setminus Z$ its complement. Consider the following commutative diagram:
$$\xymatrix{ && U \ar[drr]^{\pi_2^U} \ar[dll]_{\pi_1^U} \ar@{^(->}[d]^{j_U}&& \\ \mathds P(V^\vee) && \mathds P(V^\vee) \times V \ar[ll]_{\pi_1} \ar[rr]^{\pi_2} && V. \\ && Z \ar[ull]^{\pi_1^Z} \ar@{^(->}[u]_{i_Z} \ar[rru]_{\pi_2^Z} &&}$$
The Radon transformations are functors from $\text{D}^\text{b}(\mathcal D_{\mathds P(V^\vee)})$ to $\text{D}^\text{b}(\mathcal D_V)$ given by
\begin{align}
\mathcal{R} & := \pi^Z_{2,+}\pi_1^{Z,+}\cong\pi_{2,+}i_{Z,+}i_{Z}^+\pi_1^+, \notag \\
\mathcal{R}^\circ & := \pi^U_{2,+}\pi_1^{U,+}\cong\pi_{2,+}j_{U,+}j^+_U\pi_1^+, \notag \\
\mathcal{R}^\circ_c & :=\pi^U_{2,\dag}\pi_1^{U,+}\cong\pi_{2,+}j_{U,\dag}j^+_U\pi_1^+, \notag \\
\mathcal{R}_{cst} & :=\pi_{2,+}\pi_1^+. \notag
\end{align}
\end{defi}
\begin{prop}\label{prop:triangleRadon}
Let $g$ be as in (\ref{morphism:g}). Then, for every $\beta\in\mathds C^d$, we have the following two exact sequences of regular holonomic $\mathcal D_V$-modules, which are dual to each other:
$$0\longrightarrow\mathcal H^{-1}\mathcal{R}_{cst}g_+ \mathcal O_{S_1}^\beta\longrightarrow\mathcal H^0\mathcal{R} g_+\mathcal O_{S_1}^\beta\longrightarrow\mathcal H^0\mathcal{R}^\circ_cg_+\mathcal O_{S_1}^\beta\longrightarrow\mathcal H^0\mathcal{R}_{cst}g_+\mathcal O_{S_1}^\beta\lra0,$$
$$0\longrightarrow\mathcal H^0\mathcal{R}_{cst}g_\dag\mathcal O_{S_1}^{-\beta}\longrightarrow\mathcal H^0\mathcal{R}^\circ g_\dag\mathcal O_{S_1}^{-\beta}\longrightarrow\mathcal H^0\mathcal{R} g_\dag\mathcal O_{S_1}^{-\beta}\longrightarrow\mathcal H^1\mathcal{R}_{cst}g_\dag\mathcal O_{S_1}^{-\beta}\lra0.$$
Moreover, the $\mathcal D_V$-modules $\mathcal H^i\mathcal{R}_{cst}g_\star \mathcal O_{S_1}^\beta$, for $i\in \{-1,0,1\}$ and $\star\in\{+,\dag\}$, that appear in the above sequences are $\mathcal O_V$-free. Consequently, for any $\beta\in\mathds C^d$, calling $j_{V^*}$ the canonical inclusion $V^*:=\AA^1_{\lambda_0}\times S_2\hookrightarrow V$, we have isomorphisms of $\mathcal D_{\AA^1_z\times S_2}$-modules
$$\begin{array}{ccc}
\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R}^\circ_c g_+\mathcal O_{S_1}^\beta & \cong & \operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R} g_+\mathcal O_{S_1}^\beta\\[3pt]
\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R}^\circ g_\dag\mathcal O_{S_1}^\beta & \cong & \operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R} g_\dag\mathcal O_{S_1}^\beta
\end{array}.$$
\end{prop}
\begin{proof}
Following the notation of the previous definition, since $Z$ is smooth, the excision triangle (\hspace{-.5pt}\cite[Prop. 1.7.1]{Hotta}) corresponding to the diagram $U\hookrightarrow\mathds P(V^\vee)\times V\leftarrow Z$ gives rise to the following triangles of Radon transformations for any $\mathcal M\in\text{D}_{\text{c}}^\text{b}(\mathcal D_{\mathds P(V^\vee)})$:
\begin{align}
\mathcal{R}_{cst}\mathcal M\longrightarrow\mathcal{R}^\circ\mathcal M\longrightarrow\mathcal{R}\mathcal M\longrightarrow, \label{eq:Radontri1}\\
\mathcal{R}\mathcal M\longrightarrow\mathcal{R}^\circ_{c}\mathcal M\longrightarrow\mathcal{R}_{cst}\mathcal M\longrightarrow \label{eq:Radontri2},
\end{align}
where the second triangle is dual to the first.
Note that $\mathds D\mathcal O_{S_1}^\beta\cong\mathcal O_{S_1}^{-\underline{1}-\beta}\cong\mathcal O_{S_1}^{-\beta}$. It suffices then to show the existence of the first exact sequence of the statement of the proposition and the fact that the $\mathcal H^i\mathcal{R}_{cst}g_\star \mathcal O_{S_1}^\beta$ are constant. The existence of the exact sequences here follows by just a variation of \cite[Prop. 2.8]{Reich2}, but considering the twist by $\underline{y}^{-1-\beta}$ of $\mathcal O_{S_1}$. That needs in turn [ibid., Prop. 2.5, 2.7, Lem. 2.6], but almost every argument is functorial and anyway they can be easily adapted to our context. The constancy of $\mathcal H^i\mathcal{R}_{cst}g_\star\mathcal O_{S_1}^{\beta}$ can be proved as the second point of [ibid., Lem. 2.7].
\end{proof}
\begin{proof}[Proof of Proposition \ref{prop:IsoAfterFourier}]
Call $p_1$ the restriction to $Z^*$ of the projection $\mathds P^n\times\AA_{\lambda_0}^1\times S_2\rightarrow\mathds P^n$, abusing a bit of the notation.
Consider the cartesian diagram
$$
\xymatrix{\ar @{} [dr] |{\Box} S_1\times S_2 \ar[d]_{k} \ar[r]^{\pi_1} & S_1 \ar[d]^{g}\\
Z^* \ar[r]_{p_1} & \mathds P^n}.
$$
By base change, we have that
\begin{equation}\label{eq:BaseChange1}
k_+\mathcal O_{S_1\times S_2}^\beta\cong p_1^+g_+\mathcal O_{S_1}^\beta
\end{equation}
for any $\beta\in\mathds C^d$. Now, since $p_1$ is smooth, we have the analogous isomorphism $k_\dag\mathcal O_{S_1\times S_2}^\beta\cong p_1^+g_\dag\mathcal O_{S_1}^\beta$ for every $\beta$ as well. Now note that because of $p_1$ being non-characteristic, it is easy to show (cf. the proof of the third point of \cite[Prop. 2.22]{ReiSe2}) that for every $\beta$
\begin{equation}\label{eq:BaseChange2}
k_{\dag+}\mathcal O_{S_1\times S_2}^\beta\cong p_1^+g_{\dag+}\mathcal O_{S_1}^\beta.
\end{equation}
Consider now the commutative diagram
$$\xymatrix{ & Z^* \ar[dl]_{p_1} \ar[r]^{p_2} \ar[d]^{j_{Z^*}} & V^* \ar[d]^{j_{V^*}}\\
\mathds P^n & Z \ar[l]^{\pi_1^Z} \ar[r]_{\pi_2^Z} & V},$$
where the square is also cartesian. By applying base change again, we obtain the natural transformations of functors from $\text{D}_{\text{c}}^\text{b}(\mathcal D_{\mathds P^n})$ to $\text{D}_{\text{c}}^\text{b}(\mathcal D_{V^*})$
\begin{equation}\label{eq:NatTr}
p_{2,+}p_1^+\cong p_{2,+}j_{Z^*}^+\pi_1^{Z,+}\cong j_{V^*}^+\pi_{2,+}^Z\pi_1^{Z,+}=j_{V^*}^+\mathcal{R}.
\end{equation}
Therefore, applying $p_{2,+}$ to isomorphisms \eqref{eq:BaseChange1} and \eqref{eq:BaseChange2} (and taking into account
that $\varphi=p_2\circ k$, see diagram \eqref{eq:CompactDiagram}) we obtain
\begin{equation}\label{eq:MIC_Project}
\varphi_+\mathcal O^\beta_{S_1 \times S_2} \cong p_{2,+}k_{+}\mathcal O_{S_1\times S_2}^\beta\cong j_{V^*}^+\mathcal{R} g_{+}\mathcal O_{S_1}^\beta,
\quad\textup{and}\quad
p_{2,+}k_{\dag+}\mathcal O_{S_1\times S_2}^\beta\cong j_{V^*}^+\mathcal{R} g_{\dag+}\mathcal O_{S_1}^\beta,
\end{equation}
for any $\beta\in\mathds C^d$.
We need now to relate the various Radon transformations with the Fourier-Laplace transformation $\operatorname{FL}: \operatorname{Mod}_{\text{h}}(\mathcal D_{V^\vee})\rightarrow\operatorname{Mod}_{\text{h}}(\mathcal D_V)$. This is possible due to the fundamental result of d'Agnolo and Eastwood \cite[Prop. 1]{AE}. We quote the formulation from the proof of \cite[Lem. 2.12]{ReiSe2}. Let $Bl_0\left(V^\vee\right)\subset\mathds P^n\times V^\vee$ be the blow-up of $V^\vee$ at the origin and consider the commutative diagram
$$\xymatrix{ T:=\mathds G_m\times S_1 \ar [r]^{h} \ar [dr]^{\tilde{h}} \ar[dd]_{\pi_T} & V^\vee & Bl_0(V^\vee) \ar[l]_p \ar[ddl]^{q}\\
& V^\vee\setminus\{0\} \ar[u]_{j_0} \ar[d]_{\pi} & \\
S_1 \ar[r]^{g} & \mathds P^n &},$$
where $\pi$ is the canonical morphism $V^\vee\setminus\{0\}\rightarrow\mathds P(V^\vee)$, $\pi_T$ is the second projection, and $h$ and $\tilde{h}$ are given by $(y_0,\underline{y})\mapsto (y_0,y_0\underline{y}^{\underline{a}_1},\ldots,y_0\underline{y}^{\underline{a}_d})$. Then we have the natural transformations
\begin{equation}\label{eq:NatTr2}
\mathcal{R}^\circ_cg_+\cong\operatorname{FL} h_+\pi_T^+\,\text{ and }\,\mathcal{R}^\circ g_\dag\cong\operatorname{FL} h_\dag\pi_T^+,
\end{equation}
of functors from $\operatorname{Mod}_{\text{h}}(\mathcal D_{S_1})$ to $\operatorname{Mod}_{\text{h}}(\mathcal D_V)$. Notice that although
in general $\mathcal{R}^\circ_c$ and $\mathcal{R}^\circ$ are not exact, so the compositions $\mathcal{R}^\circ_c g_+$ and $\mathcal{R}^\circ g_\dag$ are precisely due to the above isomorphisms.
Applying $\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+$ to the natural transformations in (\ref{eq:NatTr2}) we obtain the following ones of functors from $\operatorname{Mod}_{\text{h}}(\mathcal D_{S_1})$ to $\operatorname{Mod}_{\text{h}}(\mathcal D_{\AA^1_z\times S_2})$:
\begin{equation}\label{eq:RadonFourier}
\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R}^\circ_c g_+\cong\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\operatorname{FL} h_+\pi^+\,\text{ and }\,\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R}^\circ g_\dag\cong\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\operatorname{FL} h_\dag\pi^+
\end{equation}
We are now closer to the isomorphism of the statement; let us rewrite in a different way the functors above to obtain it. Namely,
$$\operatorname{FL}^{\operatorname{loc}}_{S_2}j_{V^*}^+\operatorname{FL}\cong j_{V^*}^+\operatorname{FL}^{\operatorname{loc}}_W\operatorname{FL}\cong j_{V^*}^+(j_z\times\operatorname{id}_W)_+(j_\tau\times\operatorname{id}_W)^+\operatorname{FL}_W\operatorname{FL}\cong
j_{V^*}^+(j_z\times\operatorname{id}_W)_+(j_\tau\times\operatorname{id}_W)^+\operatorname{FL}_{\AA^1_{w_0}}.$$
From the third of the assumptions \ref{assump:AssMatrix} we know that we can decompose the morphism $h$ as
$$\begin{tikzcd}
h:T \ar[hook]{r}{h_1} & \mathds{G}_{m,w_0}\times W^\vee \ar[hook]{rr}{j_\tau\times\operatorname{id}_{W^\vee}} &&
\AA^1_{w_0}\times W^\vee=V^\vee
\end{tikzcd},$$
where $h_1$ is a closed embedding (cf. \cite[Prop. 2.1 (1), proof of Thm. 2.4, p. 213]{ReiSe}). (Recall that $w_0=-\tau$.) It follows that
$$(j_\tau\times\operatorname{id}_W)^+\operatorname{FL}_{\AA^1_{w_0}}h_+\cong\operatorname{FL}_{\AA^1_{w_0}}(j_\tau\times\operatorname{id}_{W^\vee})^+h_+\cong
\operatorname{FL}_{\AA^1_{w_0}}(j_\tau\times\operatorname{id}_{W^\vee})^+(j_\tau\times\operatorname{id}_{W^\vee})_+h_{1,+}\cong\operatorname{FL}_{\AA^1_{w_0}}h_{1,+}.$$
Summarizing, we obtain that
$$\operatorname{FL}^{\operatorname{loc}}_{S_2}j_{V^*}^+\operatorname{FL} h_\star\cong j_{V^*}^+(j_z\times\operatorname{id}_W)\operatorname{FL}_{\AA^1_{w_0}}h_{1,+},$$
where $\star\in\{+,\dag\}$, because $h_{1,+}=h_{1,\dag}$ for $h_1$ is proper. In particular,
we have $\operatorname{FL}^{\operatorname{loc}}_{S_2}\circ j_{V^*}^+ \circ \operatorname{FL} \circ h_+ \cong \operatorname{FL}^{\operatorname{loc}}_{S_2}\circ j_{V^*}^+ \circ \operatorname{FL} \circ h_\dag$. As a consequence, we can claim using the isomorphisms in (\ref{eq:RadonFourier}) that
$$\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R}^\circ_cg_+\cong\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R}^\circ g_\dag,$$
and so, from Proposition \ref{prop:triangleRadon} and applying this last natural transformation to $\mathcal O_{S_1}^\beta$,
$$\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R} g_{\dag+}\mathcal O_{S_1}^\beta\cong\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R} g_+\mathcal O_{S_1}^\beta.$$
In conclusion, we finally obtain, by using the isomorphisms from (\ref{eq:MIC_Project}) as well as the exactness
of the functor $\operatorname{FL}^{\operatorname{loc}}_{S_2}$, that
$$
\operatorname{FL}_{S_2}^{\operatorname{loc}}\mathcal H^0p_{2,+}k_{\dag+}\mathcal O_{S_1\times S_2}^\beta\cong \operatorname{FL}_{S_2}^{\operatorname{loc}}\mathcal H^0\varphi_+\mathcal O_{S_1\times S_2}^\beta.
$$
The last statement is an easy consequence of isomorphisms in (\ref{eq:NatTr}) and (\ref{eq:MIC_Project}), noting that
$$\operatorname{FL}^{\operatorname{loc}}_{S_2}\mathcal H^0p_{2,+}k_{\dag+}\mathcal O_{S_1\times S_2}^\beta\cong\operatorname{FL}^{\operatorname{loc}}_{S_2}\mathcal H^0j_{V^*}^+\mathcal{R} g_{\dag+}\mathcal O_{S_1}^\beta\cong\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R} g_+\mathcal O_{S_1}^\beta\cong\operatorname{FL}_{S_2}^{\operatorname{loc}}\mathcal H^0\varphi_+\mathcal O_{S_1\times S_2}^\beta$$
is induced from the canonical morphism $g_{\dag+}\mathcal O_{S_1}^\beta\hookrightarrow g_+\mathcal O_{S_1}^\beta$ via $\operatorname{FL}_{S_2}^{\operatorname{loc}}j_{V^*}^+\mathcal{R}$.
\end{proof}
Consider again the space $P=\mathds P^n\times(\AA^1_{\lambda_0}\times S_2)$, together with the canonical closed embedding
$i_P:Z^* \hookrightarrow P$. We have the diagram
$$
\begin{tikzcd}
Z^* \ar{d}{p_2} \ar[hook]{r}{i_P} & P \ar{ld}{p_2} \\
\AA^1_{\lambda_0}\times S_2
\end{tikzcd},
$$
where we denote the restriction of the projection $p_2:P\rightarrow \AA^1_{\lambda_0}\times S_2$ to $Z^*$ by
the same letter (as was done before).
Since $i_P$ is proper, we have
$$
\begin{array}{c}
\mathcal H^0p_{2,+}k_{\dag+}\mathcal O_{S_1\times S_2}^\beta \cong \mathcal H^0p_{2,+}(i_P\circ k)_{\dag+}\mathcal O_{S_1\times S_2}^\beta
\quad
\text{ and }
\\\\
\mathcal H^0\varphi_+\mathcal O_{S_1\times S_2}^\beta
\cong \mathcal H^0p_{2,+}k_+\mathcal O_{S_1\times S_2}^\beta \cong
\mathcal H^0p_{2,+}(i_P\circ k)_+\mathcal O_{S_1\times S_2}^\beta.
\end{array}
$$
so that we can also write the morphism
$\mathcal H^0p_{2,+}k_{\dag+}\mathcal O_{S_1\times S_2}^\beta\longrightarrow\mathcal H^0\varphi_+\mathcal O_{S_1\times S_2}^\beta$
from the proof of Proposition \ref{prop:IsoAfterFourier} as
\begin{equation}\label{eq:MorphismPhiBeforeReduction}
\mathcal H^0p_{2,+}(i_P\circ k)_{\dag+}\mathcal O_{S_1\times S_2}^\beta\longrightarrow
\mathcal H^0p_{2,+}(i_P\circ k)_+\mathcal O_{S_1\times S_2}^\beta.
\end{equation}
In order to proceed, we will have to take into account certain group actions on the spaces $S_1\times S_2$,
$P$ and $\AA^1_{\lambda_0}\times S_2$ as well as some equivariance properties
of the various sheaves of modules on these spaces. For the reader's convenience, we recall some facts from
\cite[\S~2.4]{ReiSe2}.
We consider the action of $S_1$ on $S_2$ given by
$$
\begin{array}{rcl}
\mu:S_1\times S_2 & \longrightarrow & S_2 \\ \\
(y_1,\ldots,y_d,\lambda_1,\ldots,\lambda_n) & \longmapsto & (\underline{t}^{-\underline{a}_1}\lambda_1,\ldots,\underline{t}^{-\underline{a}_n}\lambda_n),
\end{array}
$$
inducing the following three:
$$
\begin{array}{rcl}
S_1\times \left(S_1\times S_2\right) & \longrightarrow & S_1 \times S_2 \\ \\
(\underline{t},(y_1,\ldots,y_d,\lambda_1,\ldots,\lambda_n)) & \longmapsto & (t_1 y_1,\ldots,t_d y_d,\underline{t}^{-\underline{a}_1}\lambda_1,\ldots,\underline{t}^{-\underline{a}_n}\lambda_n),
\end{array}
$$
$$
\begin{array}{rcl}
S_1\times P & \longrightarrow & P= \mathds P^n\times(\AA^1_{\lambda_0}\times S_2) \\ \\
(\underline{t},((w_0:\ldots:w_n),\lambda_0,\lambda_1,\ldots,\lambda_n)) & \longmapsto & ((w_0:\underline{t}^{\underline{a}_1} w_1:
\ldots:\underline{t}^{\underline{a}_n} w_n),\lambda_0, \underline{t}^{-\underline{a}_1}\lambda_1,\ldots,\underline{t}^{-\underline{a}_n}\lambda_n),
\end{array}
$$
$$
\begin{array}{rcl}
S_1\times \left(\AA^1_{\lambda_0} \times S_2\right) & \longrightarrow & \AA^1_{\lambda_0} \times S_2 \\ \\
(\underline{t},(\lambda_0,\lambda_1,\ldots,\lambda_n)) & \longmapsto & (\lambda_0, \underline{t}^{-\underline{a}_1}\lambda_1,\ldots,\underline{t}^{-\underline{a}_n}\lambda_n).
\end{array}
$$
It is easy to see that all these four actions are free, basically because so $\mu$ is
and have smooth geometric quotients. These are described
by the following result, which we cite from \cite[§2.4]{ReiSe2}. For a free action of an algebraic group $G$ on a smooth variety $X$ admitting a geometric quotient, we write $X/G$ for such quotient.
\begin{prop}
In the above situation, put ${'\!}S:=({\mathds G}_{m,t})^{n-d}$. Then the geometric quotients
$(S_1\times S_2)/S_1$, $P/S_1$
and $(\AA^1_{\lambda_0}\times S_2)/S_1$ are given, respectively, by the spaces
$$
S_1\times {'\!}S, \; {'\!}P:=\mathds P^n\times \AA^1_{\lambda_0} \times {'\!}S, \;\text{ and }
\AA^1_{\lambda_0}\times {'\!}S.
$$
There is a canonical embedding ${'\!}S \hookrightarrow S_2$ inducing embeddings (all denoted by $\iota$)
$$
\begin{array}{rcl}
S_1\times {'\!}S & \hookrightarrow &S_1\times S_2,\\
{'\!}P & \hookrightarrow &P=\mathds P^n\times \AA^1_{\lambda_0} \times S_2,\\
S_1\times \AA^1_{\lambda_0} \times {'\!}S & \hookrightarrow &S_1\times \AA^1_{\lambda_0} \times S_2.
\end{array}
$$
\end{prop}
In the sequel, we will always consider ${'\!}S$ as a subvariety of $S_1$ (as well as
${'\!}P$ as a subvariety of $P$ etc.).
There is a more direct description of the construction of ${'\!}S$ resp. of the embedding $\iota$ which we recall for the readers convenience. Namely, let $B$ a Gale dual of $A$ (that is, an integer matrix $B\in\text{M}(n\times (n-d),\mathds Z)$ whose columns generate $\ker_\mathds Q(A)$; see Proposition \ref{prop:hypGKZ}). Then we have the split exact sequence of abelian groups
$$
0\longrightarrow\mathds Z^{n-d}\stackrel{B\cdot}{\longrightarrow}\mathds Z^n\stackrel{-A\cdot}{\longrightarrow}\mathds Z^d\lra0.
$$
By applying the functor $\text{Hom}_{\mathds Z}(\bullet,{\mathds G}_m)$ to that sequence, we get the exact sequence of algebraic groups
$$
(1)\longrightarrow S_1={\mathds G}_m^d \longrightarrow S_2={\mathds G}_m^n \longrightarrow{\mathds G}_m^{n-d}\longrightarrow(1),
$$
where the first nontrivial morphism is just $\mu(\bullet,\underline{1})$. From this it follows that the torus ${\mathds G}_m^{n-d}$ can be canonically
identified with the geometric quotient $S_2/S_1$. Since this exact sequence of algebraic tori also splits, we can chose a section $\iota:{'\!}S = S_2/S_1\hookrightarrow S_2$, and this choice corresponds exactly to the one in \cite[§2.4]{ReiSe2}.
We define
reduced versions of the maps $\varphi$ and $i_P\circ k$ by the cartesian diagrams
$$
\begin{tikzcd}
S_1 \times S_2 \ar{rr}{\varphi} & & \AA^1_{\lambda_0}\times S_2 \\ \\
S_1 \times {'\!}S \ar[hook]{uu}{\iota} \ar{rr}{{\,'\!}\varphi} && \AA^1_{\lambda_0}\times {'\!}S \ar[hook]{uu}{\iota}
\end{tikzcd}
\quad\quad
\text{and}
\quad\quad
\begin{tikzcd}
S_1 \times S_2 \ar{rr}{i_P\circ k} & & P \\ \\
S_1 \times {'\!}S \ar[hook]{uu}{\iota} \ar{rr}{l} && {'\!}P\ar[hook]{uu}{\iota}
\end{tikzcd}
$$
The mapping ${\,'\!}\varphi: S_1\times {'\!}S\rightarrow \AA^1_{\lambda_0}\times {'\!}S$ is a family of Laurent polynomials
parametrized by ${'\!}S$, and we denote by ${\,'\!}f:S_1\times {'\!}S\rightarrow \AA^1_{\lambda_0}$ its first component.
In order to illustrate these statements, consider the main case of interest, where we have
$$
A=
\begin{pmatrix}
1 & -1 & 0 & 0 &\ldots & 0 \\
1 & 0 & -1 & 0 & \ldots & 0 \\
\vdots &\ldots \\
1 & 0 & 0 & 0 & \ldots & -1
\end{pmatrix}
\in \text{M}\left((n-1) \times n, \mathds Z\right).
$$
Then $d=n-1$, ${'\!}S=\mathds G_{m,t}$ and we can choose
$$
\begin{array}{rcl}
\iota: {'\!}S={\mathds G}_{m,t} & \longrightarrow & S_2 = {\mathds G}_m^n\\ \\
t & \longmapsto & (t,1,\ldots,1).
\end{array}
$$
Then we have (see also the explanation on page \pageref{page:Roadmap})
\begin{equation}\label{eq:LaurPolPn}
\begin{array}{rcl}
{\,'\!}\varphi:S_1\times \mathds G_{m,t} & \longrightarrow & \AA^1_{\lambda_0}\times \mathds G_{m,t} \\ \\
(y_1,\ldots,y_{n-1},t) & \longmapsto & \left(-\frac{1}{y_1}-\ldots-\frac{1}{y_{n-1}}-t\cdot y_1\cdot\ldots\cdot y_{n-1}, t \right)
\end{array}
\end{equation}
Going back to the situation of a general matrix $A\in \text{M}(d\times n,\mathds Z)$ satisfying the assumptions
\ref{assump:AssMatrix}, we state the following result, inspired from \cite{ReiSe2}, showing that $\iota$ behaves well with respect
to all modules in question.
To simplify our notation we will write
$$
M_{\dag+,S_2}:=\mathcal H^0 p_{2,+} (i_P\circ k)_{\dag\,+}\mathcal O^\beta_{S_1\times S_2}
\quad\quad
\text{and}
\quad\quad
M_{S_2}:=\mathcal H^0\varphi_+\mathcal O^\beta_{S_1\times S_2} =
\mathcal H^0 p_{2,+} (i_P\circ k)_+\mathcal O^\beta_{S_1\times S_2}
,$$
and analogously,
$$
M_{\dag+}:=\mathcal H^0 {'\!}p_{2,+} l_{\dag\,+}\mathcal O^\beta_{S_1\times {'\!}S}
\quad\quad
\text{and}
\quad\quad
M:=\mathcal H^0{\,'\!}\varphi_+\mathcal O^\beta_{S_1\times {'\!}S} =
\mathcal H^0 p_{2,+} l_+\mathcal O^\beta_{S_1\times {'\!}S},
$$
where we write ${'\!}p_2:{'\!}P=\mathds P^n\times\AA^1_{\lambda_0}\times {'\!}S\rightarrow \AA^1_{\lambda_0}\times {'\!}S$
(to distinguish this projection from the one to $\AA^1_{\lambda_0}\times S_2$ considered above).
\begin{prop}\label{prop:IsoAfterFourierRed}
We have a morphism of $\mathcal D_{\AA^1_{\lambda_0}\times {'\!}S}$-modules
$$
\phi:M_{\dag +} \longrightarrow M
$$
inducing an isomorphism of $\mathcal D_{\AA^1_z\times {'\!}S}$-modules
$$
\operatorname{FL}^{\operatorname{loc}}_{{'\!}S} M_{\dag +}\cong
\operatorname{FL}^{\operatorname{loc}}_{{'\!}S} M.
$$
Moreover, both modules $M$ and $M_{\dag+}$ are non-characteristic with respect to the projection ${'\!}p:{'\!}P\rightarrow \AA^1_{\lambda_0}\times {'\!}S$ along the subspace ${'\!}P\, \backslash\, {'\!}P^*$, where ${'\!}P^*=\AA^n\times(\AA_{\lambda_0}^1\times {'\!}S)$.
\end{prop}
\begin{proof}
It has been shown in {\cite[Prop. 2.22., Lem. 6.4.]{ReiSe2}} that the morphism $\iota:\AA^1_{\lambda_0}\times {'\!}S\hookrightarrow \AA^1_{\lambda_0}\times S_2$ is non-characteristic for
the modules $M_{\dag +,S_2}$ and $M_{S_2}$. Consequently,
we obtain the morphism of $\mathcal D_{\AA^1_{\lambda_0}\times {'\!}S}$-modules
$$
\phi:M_{\dag +} \longrightarrow M
$$
by applying $\iota^+$ to the morphism
$$
M_{\dag +,S_2} = \mathcal H^0 p_{2,+} (i_P\circ k)_{\dag\,+}\mathcal O^\beta_{S_1\times S_2}
\longrightarrow \mathcal H^0\varphi_+\mathcal O^\beta_{S_1\times S_2} =
\mathcal H^0 p_{2,+} (i_P\circ k)_+\mathcal O^\beta_{S_1\times S_2} = M_{S_2}
$$
(see \eqref{eq:MorphismPhiBeforeReduction})
Since the functors $\operatorname{FL}^{\operatorname{loc}}_{S_2}$ resp.
$\operatorname{FL}^{\operatorname{loc}}_{{'\!}S}$ commute with $\iota$, we obtain the isomorphism
$\operatorname{FL}^{\operatorname{loc}}_{{'\!}S} M_{\dag +}\cong \operatorname{FL}^{\operatorname{loc}}_{{'\!}S} M$.
Finally, the fact that $\iota$ is non-characteristic for $M_{\dag +,S_2}$ and $M_{S_2}$
yields the last statement using Lemma
\ref{lem:StratSmooth}.
\end{proof}
\begin{rem}\label{rem:realExponents}
From now on we will assume that the $\beta_i$ are real numbers, since we will use some Hodge theoretic constructions,
which are not valid for arbitrary complex $\beta_i$, as commented in Remark \ref{rem:KummerHodge}.
\end{rem}
We start by introducing certain auxiliary filtrations on the $\mathcal D$-modules considered above which are not a priori
Hodge filtrations but have an explicit description. We will see later that it is sufficient to consider these
filtrations to extract the Hodge theoretic information we need.
Recall that an easy calculation decomposing ${\,'\!}\varphi$ as a graph embedding followed by a projection shows that the direct image complex ${\,'\!}\varphi_+\mathcal O_{S_1\times {'\!}S}^\beta$ can be represented by
$$
\Big({\,'\!}\varphi_*\Omega^{\bullet+d}_{S_1\times {'\!}S/{'\!}S}[\partial_{\lambda_0}], d-\kappa(\beta)\wedge-(d{\,'\!}f\wedge)\otimes \partial_{\lambda_0}\Big),
$$
where ${\,'\!}f$ is still the first component of ${\,'\!}\varphi$.
We consider the filtration on each ${\,'\!}\varphi_*\Omega^{l+d}_{S_1\times {'\!}S/{'\!}S}[\partial_{\lambda_0}]$ given by
\begin{equation}\label{eq:FiltDirectImageComp}
F_{k+l}{\,'\!}\varphi_*\Omega^{l+d}_{S_1\times {'\!}S/{'\!}S}[\partial_{\lambda_0}]=\sum_{i=0}^{k+l}{\,'\!}\varphi_*\Omega^{l+d}_{S_1\times {'\!}S/{'\!}S}\partial_{\lambda_0}^i.
\end{equation}
One easily checks that this filtration is compatible with the differential, so that we obtain the filtered complex
$$
\begin{array}{c}
F_k\Big({\,'\!}\varphi_*\Omega^{\bullet+d}_{S_1\times {'\!}S/{'\!}S}[\partial_{\lambda_0}], d-(\kappa(\beta)\wedge)-(d{\,'\!}f\wedge)\otimes \partial_{\lambda_0}\Big):=\\
\Big(F_{k+\bullet}{\,'\!}\varphi_*\Omega^{\bullet+d}_{S_1\times {'\!}S/{'\!}S}[\partial_{\lambda_0}], d-(\kappa(\beta)\wedge)-(d{\,'\!}f\wedge)\otimes \partial_{\lambda_0}\Big).
\end{array}
$$
\begin{defi}
We call the induced filtration $F_\bullet \mathcal H^i{\,'\!}\varphi_+\mathcal O_{S_1\times {'\!}S}^\beta$ on the cohomology sheaves $\mathcal H^i{\,'\!}\varphi_+\mathcal O_{S_1\times {'\!}S}^\beta$ the \emph{Brieskorn filtration}.
\end{defi}
Notice that for $i=0$, $k=0$ and $\beta=0$ the filtration step $F_k \mathcal H^0{\,'\!}\varphi_+\mathcal O_{S_1\times {'\!}S}^\beta =F_0 M$
is exactly the module $M_0$ considered in \cite{Sa2} and was called Brieskorn lattice there
because it was defined similarly to the case of isolated hypersurface singularities (see \cite{Brie}).
On the other hand, it is well-known that $l_{\dag+}\mathcal O_{S_1\times {'\!}S}^\beta$ carries a filtration $F^Hl_{\dag+}\mathcal O_{S_1\times {'\!}S}^\beta$ such that $\left(l_{\dag+}\mathcal O_{S_1\times {'\!}S}^\beta, F^H\right)$ underlies a pure polarizable complex Hodge module of weight $n=\dim(S_1)+\dim({'\!}S)$, in particular, an element of $\operatorname{MHM}({'\!}P,\mathds C)$.
Since ${'\!}p_2$ is projective, the direct image $M_{\dag +}=\mathcal H^0 {'\!}p_{2,+}l_{\dag+}\mathcal O_{S_1\times {'\!}S}^\beta$ also carries a Hodge filtration $F^H\mathcal H^0 {'\!}p_{2,+}l_{\dag+}\mathcal O_{S_1\times {'\!}S}^\beta$ such that $\left(M_{\dag +},F^H\right)$ underlies a pure polarisable complex Hodge module (see the first point of \cite[Thm. 1]{Saito1}).
We consider the shifted filtration $F^{H_{sh}}_\bullet M_{\dag +}:=F^H_{\bullet-d} M_{\dag +}$. The next step is to compare this filtration to the Brieskorn filtration on $M$ via the morphism $\phi$. We will show in the next lemma that $\phi$ is filtered.
Notice that since the Brieskorn filtration has a priori no Hodge properties, we cannot simply deduce this result
from the functorial properties of mixed Hodge modules.
\begin{lemma}\label{lem:InclusionHodgeFilt}
Consider again the morphism
$\phi:M_{\dag +} \longrightarrow M$ from Proposition \ref{prop:IsoAfterFourierRed}
which yields
an isomorphism of $\mathcal D_{\AA^1_z\times {'\!}S}$-modules after applying the functor $\operatorname{FL}^{\operatorname{loc}}_{{'\!}S}$.
Then $\phi$ is filtered with respect to the shifted Hodge filtration on $M_{\dag+}$ and with respect
to the Brieskorn filtrations on $M$, i.e., for every $k\in\mathds Z$, we have the inclusion
$$
\phi\left(F^{H_{sh}}_k M_{\dag +} \right)\subset F_k M.
$$
\end{lemma}
\begin{proof}
Recall that ${'\!}P^*=\AA^n\times(\AA_{\lambda_0}^1\times {'\!}S)$ is the complement in ${'\!}P$ of the divisor
$w_0=0$. Then
the map $l$ can be decomposed into a closed embedding
$l_1:S_1\times {'\!}S \hookrightarrow {'\!}P^*$ and an open embedding $l_2: {'\!}P^*\hookrightarrow {'\!}P$.
Here again the fact that $l_1$ is closed follows from the third assumption in \ref{assump:AssMatrix}.
We can further decompose $l_1$ as $l_1=l_0\circ i_{{\,'\!}\varphi}$, where $i_{{\,'\!}\varphi}$ is the graph embedding
of ${\,'\!}\varphi$.
More precisely,
we have the following diagram:
\begin{equation}\label{eq:CompactDiagram-2}
\begin{tikzcd}
S_1\times {'\!}S \ar[swap]{rrdd}{{\,'\!}\varphi} \ar[hook]{r}{i_{{\,'\!}\varphi}} \ar[swap,bend left=35]{rr}{l_1}
\ar[bend left=35]{rrr}{l}& S_1\times(\AA^1_{\lambda_0}\times {'\!}S) \ar[hook]{r}{l_0} \ar{rdd}{{'\!}p_2}&
{'\!}P^*=\AA^n\times(\AA^1_{\lambda_0}\times {'\!}S) \ar{dd}{{'\!}p_2} \ar[hook]{r}{l_2}& {'\!}P=\mathds P^n\times(\AA^1_{\lambda_0}\times {'\!}S) \ar{ldd }{{'\!}p_2} \\ \\
& & \AA^1_{\lambda_0}\times {'\!}S&
\end{tikzcd},
\end{equation}
where we denote by slight abuse of notation all projections to the last coordinates by ${'\!}p_2$.
Recall that $M_{\dag+}=\mathcal H^0 {'\!}p_{2,+} l_{\dag\,+}\mathcal O^\beta_{S_1\times {'\!}S}$ and $M=\mathcal H^0{\,'\!}\varphi_+\mathcal O^\beta_{S_1\times {'\!}S}
=\mathcal H^0{'\!}p_{2,+} l_{1,+}\mathcal O^\beta_{S_1\times {'\!}S}$.
Notice that the Hodge filtration $F^H_\bullet M_{\dag +}$
is induced from the filtration $F^H_\bullet \text{DR}^{\bullet+n}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}(l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta)$
on the relative de Rham complex, where
\begin{equation}\label{eq:HodgeFiltdeRham1}
F^H_k \text{DR}^{\bullet+n}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}(l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta)
:=\left(\ldots\longrightarrow \Omega^{n+l}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}\otimes F^H_{k+n+l} l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta \longrightarrow \ldots \right)
\end{equation}
by the first point of \cite[Thm. 1]{Saito1}.
On the other hand, we have the isomorphism of $\mathcal D_{\AA^1_{\lambda_0}\times {'\!}S}$-modules
$$
\mathcal H^0{'\!}p_{2,*} \text{DR}^{n+\bullet}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}\left(l_{1, +}\mathcal O_{S_1\times {'\!}S}^\beta\right) \cong M
$$
as the above diagram shows, just by the definition of $\mathcal H^0{'\!}p_{2,+}$.
The Hodge filtration $F_\bullet^H$ on the module $l_{1, +}\mathcal O_{S_1\times {'\!}S}^\beta$ can be explicitly written down, due to the fact that $l_1$ is a closed embedding (in particular, the filtered module
$(l_{1, +}\mathcal O_{S_1\times {'\!}S}^\beta, F_\bullet^H)$ underlies a pure Hodge module), and then one checks that the shifted Brieskorn filtration $F_\bullet[-d]$ on the module $M$ (see formula \eqref{eq:FiltDirectImageComp} for the definition of the Brieskorn filtration) is induced
from the filtration
\begin{equation}\label{eq:HodgeFiltdeRham2}
F_k^H \text{DR}^{\bullet+n}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}(l_{1, +}\mathcal O_{S_1\times {'\!}S}^\beta)
:=\left(\ldots\longrightarrow \Omega^{n+l}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}\otimes F^H_{k+n+l} l_{1, +}\mathcal O_{S_1\times {'\!}S}^\beta \longrightarrow \ldots \right).
\end{equation}
Notice once again that we cannot deduce from this description that the Brieskorn filtration $F_\bullet M$ (or its shifted version $F^\bullet[-d] M$)
has any Hodge properties since the map ${'\!}p_2:{'\!}P^* \rightarrow \AA^1_{\lambda_0}\times {'\!}S$ is not projective
(and in particular the filtration from formula \eqref{eq:FiltDirectImageComp} on the direct image complex ${\,'\!}\varphi_+\mathcal O_{S_1\times {'\!}S}^\beta$ is not necessarily strict).
We will now show that the induced morphism on global sections
$$
\phi:\Gamma(\AA^1_z\times {'\!}S, M_{\dag +})\longrightarrow \Gamma(\AA^1_z\times {'\!}S, M)
$$
is filtered, i.e. sends the $\Gamma(\AA^1_z\times {'\!}S, \mathcal O_{\AA^1_z\times {'\!}S,})$-submodule
$\Gamma(\AA^1_z\times {'\!}S,F_k^{H_{sh}} M_{\dag +})$ to $\Gamma(\AA^1_z\times {'\!}S,F_k M)$. This is obviously equivalent
to the statement of the proposition since $\AA^1_z\times {'\!}S$ is affine.
We have (denoting $a:\AA^1_z\times {'\!}S \rightarrow \{pt\}$)
$$
\begin{array}{rcl}
\Gamma(\AA^1_z\times {'\!}S, M_{\dag +}) &=& a_* M_{\dag +} =
a_* \mathcal H^0 R ('p_2)_* \text{DR}^{n+\bullet}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}(l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta)
\\ \\ &=&
H^0 R (a\circ {'p}_2)_* \text{DR}^{n+\bullet}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}(l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta)
=H^0
\mathbf R\Gamma \left({'\!}P,\text{DR}^{n+\bullet}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}\left(l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta\right)\right)
\end{array}
$$
and similarly
$$
\begin{array}{rcl}
\Gamma(\AA^1_z\times {'\!}S, M_+) &=& a_* M_+ =
a_* \mathcal H^0 R ('p_2)_* \text{DR}^{n+\bullet}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}(l_{1,+}\mathcal O_{S_1\times {'\!}S}^\beta)
\\ \\ &=&
H^0 R (a\circ {'p}_2)_* \text{DR}^{n+\bullet}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}(l_{1,+}\mathcal O_{S_1\times {'\!}S}^\beta)
=H^0
\mathbf R\Gamma \left({'\!}P^*,\text{DR}^{n+\bullet}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}\left(l_{1,+}\mathcal O_{S_1\times {'\!}S}^\beta\right)\right) \\ \\
&=&H^0\Gamma \left({'\!}P^*,\text{DR}^{n+\bullet}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}\left(l_{1,+}\mathcal O_{S_1\times {'\!}S}^\beta\right)\right)
\end{array}
$$
(for the last equality, we use that ${'\!}P^*$ is affine, in contrast to ${'\!}P$).
Now notice that the morphism $\phi:\Gamma(\AA^1_z\times {'\!}S, M_{\dag +})\longrightarrow \Gamma(\AA^1_z\times {'\!}S, M)$
is induced from
\begin{align*}
\mathbf R\Gamma \left({'\!}P,\text{DR}^{n+\bullet}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}\left(l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta\right)\right)
& \rightarrow
\mathbf R\Gamma\left({'\!}P^*,\text{DR}^{n+\bullet}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}\left(l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta\right) \right)\\
& \cong
\mathbf R\Gamma\left({'\!}P^*,\text{DR}^{n+\bullet}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}\left(l_{1,\dag+}\mathcal O_{S_1\times {'\!}S}^\beta\right) \right)\\
& \cong
\mathbf R\Gamma\left({'\!}P^*,\text{DR}^{n+\bullet}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}\left(l_{1,+}\mathcal O_{S_1\times {'\!}S}^\beta\right) \right)\\
& \cong
\Gamma\left({'\!}P^*,\text{DR}^{n+\bullet}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}\left(l_{1,+}\mathcal O_{S_1\times {'\!}S}^\beta\right) \right),
\end{align*}
where the first morphism is simply given by restricting sections
of $l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta$ from ${'\!}P$ to ${'\!}P^*$ and the isomorphisms are due to the fact that $l$ restricted to ${'\!}P^*$ is $l_1$, which is proper and affine.
Obviously, the restriction of the Hodge filtration on the module $l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta$ is
the Hodge filtration on the module $l_{1,\dag +}\mathcal O_{S_1\times {'\!}S}^\beta=l_{1,+}\mathcal O_{S_1\times {'\!}S}^\beta$.
Since, as has been discussed before, the filtration
$F^H_k \text{DR}^{\bullet+n}_{{'\!}P/\AA_{\lambda_0}^1\times {'\!}S}(l_{\dag +}\mathcal O_{S_1\times {'\!}S}^\beta)$ induces
$F^H_\bullet M_{\dag +}$ and the filtration $F_k^H \text{DR}^{\bullet+n}_{{'\!}P^*/\AA_{\lambda_0}^1\times {'\!}S}(l_{1, +}\mathcal O_{S_1\times {'\!}S}^\beta)$ induces $F_\bullet[-d] M$, we conclude that
$\phi:\Gamma(\AA^1_z\times {'\!}S, M_{\dag +})\rightarrow \Gamma(\AA^1_z\times {'\!}S, M)$ sends
$\Gamma(\AA^1_z\times {'\!}S,F_k^H M_{\dag +})$ to $\Gamma(\AA^1_z\times {'\!}S,F_k[-d] M)$, or, equivalently,
$\Gamma(\AA^1_z\times {'\!}S,F_k^{H_{sh}} M_{\dag +})$ to $\Gamma(\AA^1_z\times {'\!}S,F_k M)$, as required.
\end{proof}
In general, the filtrations on $M_{\dag +}$ and $M$ are not equal, simply because the underlying $\mathcal D_{\AA^1_{\lambda_0} \times {'\!}S}$-modules are not equal. They become equal after localized partial Fourier transformation as we have shown in Proposition \ref{prop:IsoAfterFourier}. First we will explain that these transformations can be performed at the
filtered level and how the last result can be interpreted in this context.
We will use a general procedure which produces from a filtered $\mathcal D_{\AA^1_{\lambda_0}\times {'\!}S}$-module $(N,F_\bullet)$ a lattice $G^{F_\bullet}_0$ inside $\operatorname{FL}^{\operatorname{loc}}_{{'\!}S}N$, i.e., an $\mathcal O_{\AA^1_z\times {'\!}S}$-module which generates $\operatorname{FL}^{\operatorname{loc}}_{{'\!}S}N$ over $\mathcal D_{\AA^1_z\times {'\!}S}$.
l
\begin{defi}\label{def:G0F}(cf. \cite[\S1.d]{Sa8}, \cite[\S A.1]{Sa14})
Let $X$ be a smooth affine variety and let $(N,F_\bullet)$ be a filtered $\mathcal D_{\AA_s^1\times X}$-module, which we identify with its module of global sections. Consider the algebraic microlocalization
$$N[\partial_s^{-1}]:=\mathds C[s]\langle\partial_s,\partial_s^{-1}\rangle\otimes_{\mathds C[s]\langle\partial_s\rangle}N.$$
By letting act $\tau$ as $-\partial_s$ and $\partial_\tau$ as $s$, we consider $N[\partial_s^{-1}]$ as a $\mathcal D_X[\tau,\tau^{-1}]\langle\partial_\tau \rangle$-module (which actually coincides with $\operatorname{FL}^{\operatorname{loc}}_X N$). Let now $\wh{\operatorname{loc}}$ be the natural localization morphism $\wh{\operatorname{loc}}:N\rightarrow N[\partial_s^{-1}]$. Then we define
\begin{equation}\label{eq:DefBrieskorn}
G^{F_\bullet}_0\operatorname{FL}^{\operatorname{loc}}_X N:=\sum_{j\geq 0}\partial_s^{-j}\wh{\operatorname{loc}}(F_j N),
\end{equation}
notice that then $G^{F_\bullet}_0\operatorname{FL}^{\operatorname{loc}}_X N$ has naturally the structure of a $\cR^{\operatorname{int}}_{\AA_z^1\times X}$-module. We also put
for any $k\in\mathds Z$
$$G^{F_\bullet}_k\operatorname{FL}^{\operatorname{loc}}_X N:=z^k\cdot G^{F_\bullet}_0\operatorname{FL}^{\operatorname{loc}}_X N=\sum_{j\geq 0}\partial_s^{-(j+k)}\wh{\operatorname{loc}}(F_j N)=\sum_{j\geq 0}\partial_s^{-j}\wh{\operatorname{loc}}(F_{j+k} N).$$
\end{defi}
There is an interpretation of this construction as a Fourier-Laplace transformation
for $\cR^{\operatorname{int}}_{\AA_z^1\times\AA^1_s\times X}$-modules as explained in \cite[Rem. A.3]{Sa14}. Using this interpretation, one can show the following fact.
\begin{lemma}\label{lem:MHMIntoIrrMHMbyFL}
Let $(N,F_\bullet)$ be a filtered $\mathcal D_{\AA_s^1\times X}$-module underlying an element in $\operatorname{MHM}(\AA^1_s\times X, \mathds C)$ (the abelian category of complex mixed Hodge modules). Then the $\cR^{\operatorname{int}}_{\AA^1_z\times X}$-module $G_0^{F_\bullet} \operatorname{FL}^{\operatorname{loc}}_X(N)$
underlies an element of $\operatorname{IrrMHM}(X)$.
\end{lemma}
\begin{proof}
We first define the algebraic Fourier-Laplace transformation for integrable $\mathcal{R}$-modules as in \cite[Defs. 3.2, 3.7]{SevCastReich}. Consider the following diagram:
$$
\begin{tikzcd}
\AA^1_s\times X \ar[hook]{rr}{j} \ar{ddrr}{q}&& \mathds P^1_s\times X \ar{dd}{\overline{q}} \\ \\
&&X
\end{tikzcd},
$$
where $j$ is the canonical open embedding and $q$ and $\bar{q}$ the respective second projections. Let $\mathcal A^{s/z}_{\textup{aff}}$ the $\mathcal{R}_{\AA^1_z \times \AA_s \times X}$-module $\mathcal O_{\AA^1_z \times \AA_s \times X}$ equipped with the $z$-connection $zd+ds$. Then for an algebraic $\cR^{\operatorname{int}}_{\AA^1_z\times \AA^1_s\times X}$-module $\mathcal N$,
we put
$$
\operatorname{FL}^{\mathcal{R}}_X(\mathcal N):=\mathcal H^0 q_+\left(\mathcal N\otimes \mathcal A^{s/z}_{\textup{aff}}\right)
\in \textup{Mod}(\cR^{\operatorname{int}}_{\AA^1_z\times X}).
$$
Let $D$ be the reduced divisor $(\mathds P^1_s\backslash \AA^1_s)\times X$. Then $\mathcal A^{s/z}_*:= j_* \mathcal A^{s/z}_{\textup{aff}}$ carries a natural structure of an $\mathcal{R}_{\AA^1_z \times \mathds P^1_s \times X}(*D)$-module. Let $\mathcal E_*^{s/z}$ be the analytification of $\mathcal A^{s/z}_*$.
As in the case of $\mathcal D$-modules, there is the notion of strict specializability and $V$-filtration for $\cR^{\operatorname{int}}$-modules; check \cite[\S 2.1.2]{Mo13} for more details.
Since the meromorphic function $s\in \mathcal O_{\mathds P^1_s\times X}(*D)$ extends evidently to a map $\mathds P^1_s\times X \rightarrow \mathds P^1_s$ whose reduced pole divisor $D$ is a line, thanks to \cite[Lem. 3.1]{Sa14} (using that, according to their notation, $P_{\textup{red}}=D$ and $\mathbf{e}=1$) we have that $\mathcal E_*^{s/z}$ is coherent not only over $\mathcal{R}_{\AA^1_z \times \mathds P^1_s \times X}$ but over $V_0\mathcal{R}_{\AA^1_z \times \mathds P^1_s \times X}$ too. Then, by \cite[\S 2.1.2]{Mo13} we know that $\mathcal E_*^{s/z}$ is automatically specializable along $D$ and its corresponding $V$-filtration is trivial. Therefore, by construction, $\mathcal E^{s/z}:=\mathcal E_*^{s/z}[*D]=\mathcal E_*^{s/z}$ (cf. [ibid., \S 3.1.2]). We then know by \cite[Prop. 3.3]{Sa14} that $\mathcal E^{s/t}$ underlies an algebraic, integrable
pure twistor $\mathcal D$-module $\mathcal T^{t/z}$ on $\AA^1_s\times X$. (Cf. \cite[\S 1.6.a]{Sa15} for another discussion on this issue.)
Now suppose that $\mathcal N$ underlies an algebraic, integrable mixed twistor $\mathcal D$-module $\mathscr{N}=(\mathcal N',\mathcal N,C)\in\operatorname{MTM}_{\textup{alg}}^{\textup{int}}(\AA^1_s\times X)$, then we can define
its relative Fourier-Laplace transform
$$
\operatorname{FL}^{\textup{MTM}}_X(\mathscr{N}) := \mathcal H^0 q_* (\mathcal N\otimes \mathcal T^{s/z})
\in \operatorname{MTM}_{\textup{alg}}^{\textup{int}}(X).
$$
For notational convenience, for any $\mathcal{R}$-triple $\mathscr{K}=(\mathcal K',\mathcal K,C)$ we define the forgetful
functor $\textup{For}(\mathscr{K}):=\mathcal K$. Then we have a comparison formula, the proof of which is completely
analogous to \cite[Prop. 3.5]{SevCastReich}:
Let $\mathscr{N}$ be an element in $\operatorname{MTM}_{\textup{alg}}^{\textup{int}}(\AA^1_s\times X)$, then there is an isomorphism
of $\mathcal{R}_{\AA^1_z\times X}$-modules:
\begin{equation}\label{eq:FLCompar}
\textup{For}(\operatorname{FL}^{\operatorname{MTM}}_X(\mathscr{N})) \cong z^{-1}\operatorname{FL}^{\mathcal{R}}_X(\textup{For}(\mathscr{N})).
\end{equation}
In other words, if $\mathcal N$ is an $\mathcal{R}_{\AA^1_z\times \AA^1_s\times X}$-module underlying an algebraic, integrable mixed twistor $\mathcal D$-module on $\AA^1_s\times X$, then
the (shifted) relative algebraic Fourier-Laplace transform $z^{-1}\operatorname{FL}^{\mathcal{R}}_X(\mathcal N)$ underlies an element of $\operatorname{MTM}_{\textup{alg}}^{\textup{int}}(X)$.
Now let us suppose that we are given a filtered $\mathcal D_{\AA^1_s\times X}$-module $(N,F_\bullet)$
underlying a complex mixed Hodge module on $\AA^1_s\times X$. Then its Rees module
$\mathcal{R}_F \mathcal N$ is an algebraic $\mathcal{R}_{\AA^1_z\times \AA^1_s\times X}$-module and underlies an element $\mathscr{N}$ in $\operatorname{MTM}_{\text{alg}}^{\text{int}}(\AA^1_s\times X)$ as well as in $\operatorname{IrrMHM}(\AA^1_s\times X)$. Since all the functors
entering in the definition of $\operatorname{FL}_X^{\operatorname{MTM}}$ preserve the category of irregular Hodge modules by \cite[Cor. 0.5.]{Sa15},
we know by the above comparison result (i.e. by formula \eqref{eq:FLCompar}) that $z^{-1}\operatorname{FL}^{\mathcal{R}}_X(\mathcal{R}^{F} N)$ underlies an irregular Hodge module on $X$. Now, by \cite[Rem. A.3]{Sa14} (noting the argument there is valid for the partial transformation as well), we can identify $\operatorname{FL}^{\mathcal{R}}_X(\mathcal{R}^{F} N)$ with $zG_0^{F_\bullet} \operatorname{FL}^{\operatorname{loc}}_X(N)$, so that
$$
G_0^{F_\bullet} \operatorname{FL}^{\operatorname{loc}}_X(N)\cong z^{-1}\operatorname{FL}^{\mathcal{R}}_X(\mathcal{R}^{F} N).
$$
This shows that $G_0^{F_\bullet} \operatorname{FL}^{\operatorname{loc}}_X(N)$ underlies an irregular Hodge module on $X$,
as required.
\end{proof}
With these definitions at hand, we have the following consequence of Lemma \ref{lem:InclusionHodgeFilt}:
\begin{coro}
In the above situation, we have
$$
G^{F^{H_{sh}}_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{'\!}S} M_{\dag +}\subset G^{F_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{'\!}S} M
$$
\end{coro}
\begin{proof}
This is a direct consequence of the definition in formula \eqref{eq:DefBrieskorn}, taking into account
Lemma \ref{lem:InclusionHodgeFilt} and the fact that the filtered morphism $\phi$ induces an isomorphism
of $\mathcal D_{\AA^1_z\times {'\!}S}$-modules by applying the functor $\operatorname{FL}^{\operatorname{loc}}_{{'\!}S}$.
\end{proof}
From now on, we will specify the above situation to our main example, where the matrix $A$ is given by
$$
A=
\begin{pmatrix}
1 & -1 & 0 & 0 &\ldots & 0 \\
1 & 0 & -1 & 0 & \ldots & 0 \\
\vdots &\ldots \\
1 & 0 & 0 & 0 & \ldots & -1
\end{pmatrix}.
$$
In particular, we have $d=n-1$, and ${'\!}S = \mathds G_{m,t}$.
We still write $M_{\dag +}=\mathcal H^0 p_{2,+} l_{\dag\,+}\mathcal O^\beta_{S_1\times \mathds G_{m,t}}$ and $M=\mathcal H^0{\,'\!}\varphi_+ \mathcal O^\beta_{S_1\times \mathds G_{m,t}}$.
We seek
to improve the inclusion of the last corollary to an equality of lattices
inside the $\mathcal D_{\AA^1_z \times \mathds G_{m,t}}$-modules
$\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} (M_{\dag +})
\cong
\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} (M)$.
We will follow an argument from the proof of \cite[Lem. 4.7]{Sa8}. In order to do so, we have to make more explicit
the structure of the module $\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}(M)\cong\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}(M_{\dag\,+})$,
which is done by the next lemma.
\begin{lemma}
\begin{enumerate}
\item
The singular locus
$\Sigma:=\text{Sing}(M)=\text{Sing}(\mathcal H^0\varphi_+ \mathcal O^\beta_{S_1\times \mathds G_{m,t}})$
is given by
$$
\Sigma=\bigcup_{\xi\in\mu_n} \{(n\cdot \xi\cdot t',t)\} \subset \AA^1_{\lambda_0} \times \mathds G_{m,t},
$$
where $t'$ is an $n$-th root of $t$, chosen without loss of generality.
\item
Write $D:=\{0\}\times \mathds G_{m,t}\subset \AA^1_z\times \mathds G_{m,t}$. Then
$\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} (M)$ is
$\mathcal O_{\AA^1_z\times \mathds G_{m,t}}(*D)$-locally free of rank $n$.
\item
Consider the sheaf
$\widehat{\mathcal O}_{\AA^1_z\times \mathds G_{m,t}}$, which is the formal completion of $\mathcal O_{\AA^1_z\times \mathds G_{m,t}}$ along
the divisor $\{0\}\times \mathds G_{m,t}$. Then we have a decomposition (as sheaves on $\{0\}\times\mathds G_{m,t}$)
$$
\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}(M)
\otimes_{\mathcal O_{\AA^1_z\times \mathds G_{m,t}}(*D)} \widehat{\mathcal O}_{\AA^1_z\times \mathds G_{m,t}}(*D)
\cong \bigoplus_{\xi\in\mu_n} \widehat{\mathcal E}_\xi \otimes \widehat{\mathcal N}_{\alpha_\xi}
$$
where $\widehat{\mathcal E}_\xi:=(\widehat{\mathcal O}_{\AA^1_z\times \mathds G_{m,t}}(*D), d-d(n \cdot \xi \cdot t'/z))$ and
$\widehat{\mathcal N}_{\alpha_\xi}=(\widehat{\mathcal O}_{\AA^1_z\times \mathds G_{m,t}}(*D), d+\alpha_\xi dz/z)$, with $\alpha_\xi\in \mathds C$.
\end{enumerate}
\end{lemma}
\begin{proof}
\begin{enumerate}
\item
It is well known that the singular locus of a Gauss-Manin system, i.e., of the top-cohomology
of the direct image complex $\varphi_+ \mathcal M$, is nothing but the discriminant of the morphism $\varphi$
provided that the module $\mathcal M$ is smooth (which is the case here, since $\mathcal M=\mathcal O^\beta_{S_1\times \mathds G_{m,t}})$.
Recall (see formula \eqref{eq:LaurPolPn}) that ${\,'\!}\varphi(y_1,\ldots,y_{n-1},t)=\left(\frac{1}{y_1}+\ldots+\frac{1}{y_{n-1}}+t\cdot y_1\cdot\ldots\cdot y_{n-1}, t \right)$.
One easily checks (see, e.g., \cite[\S 1.B.]{DS2}) that a point $(y_1,\ldots,y_{n-1})\in S_1$ is critical if and only if $y_1=\ldots=y_{n-1}=:y$ and $y^n\cdot t=1$ (and that all critical points are Morse). Then the critical values are as indicated.
\item This is a direct consequence of the second point of \cite[Thm. 1.11]{DS}, since by the discussion above the singular locus $\Sigma$ satisfies the assumption (NC) of loc. cit. It is also known that the rank of
$\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}(M)$
equals the global Milnor number
of $\varphi$, i.e., the numbers of critical points, which is $n$.
\item
This follows from \cite[Ch. III, Thm. 5.7]{Sa4}, since the critical values of $\varphi$, i.e., the eigenvalues
of the pole part of $z^2\nabla_z$, are distinct for any $t\in \mathds G_{m,t}$.
\end{enumerate}
\end{proof}
With these preparations, we can state the next result. As has been explained at the end of section \ref{sec:reduction} from page \pageref{page:Roadmap} on, it is the main step to show that the $\cR^{\operatorname{int}}_{\AA^1_z\times {\mathds G}_{m,t}}$-module $\widehat{\mathcal H}$ underlies
a mixed Hodge module (that is, the content of Theorem \ref{thm:HypIrrMHM}). The explicit description of $\widehat{\mathcal H}$ as a cyclic quotient by two operators can be rather easily identified with the object $G^{F_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M$, as we will see below in the proof of Theorem \ref{thm:HypIrrMHM}, whereas the Hodge theoretic property we want (i.e., the fact that
it is an object in $\operatorname{IrrMHM}({\mathds G}_{m,t})$) holds for $G^{F^{H_{sh}}_\bullet}_0
\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M_{\dag +}$. Hence we need to identify these two
$\cR^{\operatorname{int}}_{\AA^1_z\times{\mathds G}_{m,t}}$-modules.
\begin{thm}\label{thm:EqualFourierFilt}
In the above situation, we have
$$
G^{F^{H_{sh}}_\bullet}_0
\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M_{\dag +} =
G^{F_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M.
$$
\end{thm}
\begin{proof}
We have already proved the inclusion
$$
G^{F^{H_{sh}}_\bullet}_0
\operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M_{\dag +} \subset
G^{F_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M
$$
of $\mathcal O_{\AA^1_z\times \mathds G_{m,t}}$-modules. Since both sheaves coincide outside the divisor
$D=\{0\}\times \mathds G_{m,t}$, and since
$\widehat{\mathcal O}_{\AA^1_z\times \mathds G_{m,t}}$ is $\mathcal O_{\left(\AA^1_z\times \mathds G_{m,t},D\right)}$-flat,
it is therefore sufficient to show that
$$
G^{F^{H_{sh}}_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M_{\dag +} \otimes \widehat{\mathcal O}_{\AA^1_z\times \mathds G_{m,t}}
=
G^{F_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M
\otimes \widehat{\mathcal O}_{\AA^1_z\times \mathds G_{m,t}}.
$$
This follows as in the proof of \cite[Lem. 4.7]{Sa8}: Using the formal
decomposition result from the last Lemma, both modules can be interpreted as microlocal filtered direct images under ${{'\!}p}_2$
of two modules which coincide on ${'\!}P^*$. In these direct images, the contributions from ${'\!}P\backslash {'\!}P^*$
vanish by the last statement of Proposition \ref{prop:IsoAfterFourierRed} and Lemma \ref{lem:StratSmooth} (notice that inside $P=\mathds P^n \times \AA^1_{\lambda_0} \times S_2$,
we have ${'\!}P^*\cap \Gamma X \cong S_1 \times {'\!}S$ where we see ${'\!}S$ as a subspace of $S_2$ via the embedding $\iota$), and therefore both modules are equal.
\end{proof}
We are finally able to complete the proof of Theorem \ref{thm:HypIrrMHM}. It remains
to show that the $\cR^{\operatorname{int}}_{\AA^1_z\times{\mathds G}_{m,t}}$-module
$$
\widehat{\mathcal H} = \frac{\cR^{\operatorname{int}}_{\AA^1_z\times{\mathds G}_{m,t}}}{\left( z^2\partial_z+(n-m)tz\partial_t+z(n \alpha_1-\sum_{i=2}^n \alpha_i), \prod_{i=1}^n z(t\partial_t-\alpha_i)-t
\right)}
$$
associated to
the purely irregular hypergeometric $\mathcal D_{{\mathds G}_{m,t}}$-module $\mathcal H(\alpha_i,\emptyset)$ underlies
an object of the category $\operatorname{IrrMHM}({\mathds G}_{m,t})$.
\label{page:MainProof}
\begin{proof}[End of the proof of theorem \ref{thm:HypIrrMHM}]
Let us assume first that $\alpha_1=0$, denote by $\alpha$ the vector $(\alpha_2,\ldots,\alpha_n)$ and put $\alpha_0:=0$.
From Lemma \ref{lem:RhypGKZ} and Proposition \ref{prop:TwdeRham} we conclude that
\begin{align*}
\widehat\mathcal H& \cong \iota^+ \mathcal H^0\left(\pi_{2,*}\Omega_{S_1\times S_2/S_2}^{\bullet+d}[z],z\left(d-\kappa(\alpha)\wedge\right)-df\wedge\right) \\
& \cong \mathcal H^0\left(\pi_{2,*}\Omega_{S_1\times {\mathds G}_{m,t}/{\mathds G}_{m,t}}^{\bullet+d}[z],z\left(d-\kappa(\alpha)\wedge\right)-d{\,'\!}f\wedge\right),
\end{align*}
recall that ${\,'\!}f$ is the first component of ${\,'\!}\varphi$, as written in (\ref{eq:LaurPolPn}). Finally, it is easy to see from Definition \ref{def:G0F} that we have
$$
\mathcal H^0\left(\pi_{2,*}\Omega_{S_1\times {\mathds G}_{m,t}/{\mathds G}_{m,t}}^{\bullet+d}[z],z\left(d-\kappa(\alpha)\wedge\right)-d{\,'\!}f\wedge\right)
\cong
G^{F_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} \mathcal H^0 {\,'\!}\varphi_+ \mathcal O^\alpha_{S_1\times {\mathds G}_{m,t}}
=
G^{F_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}} M.
$$
Since by Theorem \ref{thm:EqualFourierFilt} we can further conclude
$$
\widehat\mathcal H\cong G^{F^{H_{sh}}_\bullet}_0 \operatorname{FL}^{\operatorname{loc}}_{{\mathds G}_{m,t}}M_{\dag +},
$$
we obtain that $\widehat\mathcal H$ underlies an element of $\operatorname{IrrMHM}(\mathds G_{m,t})$ by Lemma \ref{lem:MHMIntoIrrMHMbyFL} (recall that $M_{\dag +}$ underlies a pure polarizable complex Hodge module).
Restricting $\widehat\mathcal H$ to $z=1$ we get the original $\mathcal D_{\mathds G_{m,t}}$-module $\mathcal H(\alpha_i;\emptyset)$.
Assume now that $\alpha_1\neq0$. The tensor product of $\cR^{\operatorname{int}}_{\AA_z^1\times \mathds G_{m,t}}$-modules $\widehat\mathcal H\otimes_{\mathcal O_{\AA_z^1\times\mathds G_{m,t}}}\widehat\mathcal K_{-\alpha_1}$ gives rise to the corresponding tensor product of twistor $\mathcal D$-modules on $\mathds G_{m,t}$. This product can be presented as $\widehat\mathcal H(\alpha'_i;\emptyset)$, where $\alpha'_i=\alpha_i-\alpha_1$ for every $i$. Reasoning as above, since $\alpha'_1=0$, such tensor product is an irregular mixed Hodge module. Since $\widehat\mathcal K_{\alpha_1}$ is the faithful image of a mixed Hodge module on $\mathds G_{m,t}$, the tensor product with it preserves the condition of being in $\operatorname{IrrMHM}(\mathds G_{m,t})$ due to \cite[Cor. 0.5]{Sa15}, and so is the case of our original $\cR^{\operatorname{int}}_{\AA_z^1\times \mathds G_{m,t}}$-module
$$\widehat\mathcal H\cong\widehat\mathcal H(\alpha'_i;\emptyset)\otimes_{\mathcal O_{\AA_z^1\times\mathds G_{m,t}}}\widehat\mathcal K_{\alpha_1}.$$
\end{proof}
\section{The irregular Hodge filtration}
In this section we will prove the second main result of this paper. Let us recall the notations used above. For a positive integer number $n$, and $\alpha_1,\ldots,\alpha_n$ real numbers, we consider the hypergeometric $\mathcal D_{\mathds G_{m,t}}$-module $\mathcal H=\mathcal H(\alpha_i;\emptyset)$ and its associated twistor $\mathcal D$-module $\widehat\mathcal H$ on $\mathds G_{m,t}$ (we will denote by the same symbol the underlying hypergeometric $\cR^{\operatorname{int}}_{\AA_z^1\times\mathds G_{m,t}}$-module). From \cite[Thm. 0.7]{Sa15} and Theorem \ref{thm:HypIrrMHM} we know that there exists a unique irregular Hodge filtration of $\mathcal H$. We provide it in Theorem \ref{thm:HodgeData} below.
Let $\widehat\mathcal M$ a twistor $\mathcal D$-module on $X$, and call its associated $\mathcal{R}_{\AA_z^1\times X}$-module the same way. If the $\mathcal{R}$-module $\widehat\mathcal M$ is integrable, good and well-rescalable (\hspace{-.5pt}\cite[Def. 2.19]{Sa15}), we can define the irregular Hodge filtration of the underlying $\mathcal D_X$-module (say $\mathcal M$) following [ibid., Def. 2.22].
In our particular context, let us use the following notation (cf. \cite[Not. 2.1]{Sa15}) for the sake of brevity: We will write $\mathcal X:=\AA_z^1\times \mathds G_{m,t}$, ${}^\theta\!\mathcal X=\mathcal X\times\mathds{G}_{m,\theta}$, ${}^\tau\!\mathcal X=\mathcal X\times\AA_\tau^1$ and ${}^\tau\! \mathcal X_0=\mathcal X\times\{\tau=0\}$, where $\theta=1/\tau$.
Let us summarize the process we follow to achieve our goal. We must first consider the rescaling of $\widehat\mathcal H$: this is the inverse image ${}^\theta\!\widehat\mathcal H:=\mu^*\mathcal H$ (as $\mathcal O_{{}^\theta\!\mathcal X}$-module), endowed with a natural action of $\cR^{\operatorname{int}}_{{}^\theta\!\mathcal X}$ as depicted in \cite[2.4]{Sa15} (note that $\theta=\tau^{-1}$), where $\mu$ is the morphism given in [ibid., Not. 2.1] by
$$\begin{array}{rrcl}
\mu:&{}^\theta\!\mathcal X&\rightarrow&\mathcal X\\
&(z,t,\theta)&\mapsto&(z\theta,t).
\end{array}$$
This is done right below. Then we have to invert $\theta$ to obtain an $\cR^{\operatorname{int}}_{{}^\tau\!\mathcal X}(*{}^\tau\! \mathcal X_0)$-module ${}^\tau\!\widehat\mathcal H$, to work in the context of \cite[\S 2.3]{Sa15}. Finally, the irregular Hodge filtration is obtained from a suitable $V$-filtration along the divisor $\tau=0$ defined on ${}^\tau\!\widehat\mathcal H$, which is called ${}^\tau\! V$-filtration (the new symbol ${}^\tau\! V$ is to make clear the variety over which we are working; note the same convention in [ibid.], from Remark 2.20 on). We will actually \emph{define} a filtration on ${}^\tau\!\widehat\mathcal H$ in Definition \ref{defi:tauVfilt}, and then prove that it equals the ${}^\tau\! V$-filtration in Proposition \ref{prop:tauVfiltr}, following \cite[\S 2.1.2]{Mo13}.
\begin{prop}\label{prop:rescaling}
Recall that we could write $\widehat\mathcal H$ as the $\cR^{\operatorname{int}}_{\mathcal X}$-module $\cR^{\operatorname{int}}_{\mathcal X}/(P,H)$, where $P$ and $H$ were, respectively,
$$z^2\partial_z+nzt\partial_t+\gamma z\,\text{ and }\,\prod_{i=1}^nz(t\partial_t-\alpha_i)-t,$$
for certain value of $\gamma$. Then, ${}^\theta\!\widehat\mathcal H=\cR^{\operatorname{int}}_{{}^\theta\!\mathcal X}/(P,{}^\theta\! R,{}^\theta\! H)$, with $P$ as before and
$${}^\theta\! R=z^2\partial_z-z\theta\partial_\theta\,\text{ and }\,{}^\theta\! H=\prod_{i=1}^nz\theta(t\partial_t-\alpha_i)-t.$$
\end{prop}
\begin{proof}
The morphism $\mu$ can be decomposed as $p\circ\phi$, where $p$ is the canonical projection from ${}^\theta\!\mathcal X$ to $\mathcal X$ and $\phi$ is the automorphism of ${}^\theta\!\mathcal X$ given by $(z,t,\theta)\mapsto(z\theta,t,\theta)$. Then, in the category of $\mathcal O_{{}^\theta\!\mathcal X}$-modules we have that
$$\mu^*\widehat\mathcal H\cong\phi^*p^*\widehat\mathcal H\cong\phi^*\cR^{\operatorname{int}}_{{}^\theta\!\mathcal X}/(z\theta\partial_\theta, P,H(z,t,\partial_t))\cong\cR^{\operatorname{int}}_{{}^\theta\!\mathcal X}/(z^2\partial_z-z\theta\partial_\theta,P,H(z\theta,t,\partial_t)),$$
by the chain rule.
What remains now is to prove the compatibilities of \cite[2.4]{Sa15} among the actions of $\cR^{\operatorname{int}}_{{}^\theta\!\mathcal X}$ on $\cR^{\operatorname{int}}_{{}^\theta\!\mathcal X}/(P,{}^\theta\! R,{}^\theta\! H)$, seen as $\mu^*\widehat\mathcal H=\mu^{-1}\widehat\mathcal H\otimes_{\mu^{-1}\mathcal O_{\mathcal X}}\mathcal O_{{}^\theta\!\mathcal X}$.
They are just a consequence of the presence of $z^2\partial_z-z\theta\partial_\theta$ in the ideal with which we take the quotient in $\mu^*\widehat\mathcal H$ and how $z$, $z\partial_i$ or $z^2\partial_z$ act on both factors of the tensor product. For instance, if we multiply by $z$ at the right-hand one is the same as if we multiply by $z\theta$ at the left-hand one.
\end{proof}
\begin{rem}\label{rem:chi}
Let $i_{\tau=z}$ be the inclusion $\mathds{G}_{m,z}\times\mathds G_{m,t}\hookrightarrow{}^\theta\!\mathcal X$ given by $(z,t)\mapsto(z,t,\tau)$. Note that, according to the fourth point of \cite[Lem. 2.5]{Sa15}, we must have $i_{\tau=z}^*{}^\theta\!\widehat\mathcal H\cong\pi^{0,+}\mathcal H$ as $\mathcal{R}_{\mathds{G}_{m,z}\times\mathds G_{m,t}}$-modules, with $\pi^0$ being the projection $\mathds{G}_{m,z}\times\mathds G_{m,t}\rightarrow \mathds G_{m,t}$. Indeed, we have
\begin{align*}
i_{\tau=z}^*{}^\theta\!\widehat\mathcal H = \cR^{\operatorname{int}}_{{}^\theta\!\mathcal X}/(P,{}^\theta\! R,{}^\theta\! H,\theta z-1)
& \cong
\mathcal O_{\mathds{G}_{m,\theta}\times \AA^1_z\times \mathds G_{m,t}}\langle zt\partial_t\rangle/(H_1,\theta z-1) \\ \\
& \cong
\mathcal O_{\mathds{G}_{m,\theta}\times \mathds{G}_{m,z} \times \mathds G_{m,t}}\langle zt\partial_t\rangle/(H_1,\theta -z^{-1}) \\ \\
& \cong
\mathcal O_{\mathds{G}_{m,z}\times \mathds G_{m,t}}\langle zt\partial_t\rangle/(H_1) \\ \\
& \cong \mathcal O_{\mathds{G}_{m,z}\times \mathds G_{m,t}} \otimes_{\mathcal O_{\mathds G_{m,t}}} \mathcal H \cong\pi^{0,+}\mathcal H,
\end{align*}
where $H_1$ is the result of replacing $z$ by 1 at the expression for $H$.
\end{rem}
As said above, in order to continue, we must pass from ${}^\theta\!\mathcal X$ to ${}^\tau\!\mathcal X$. Therefore, we invert $\theta$ and extend $\tau$ to the affine line to get a $\cR^{\operatorname{int}}_{{}^\tau\!\mathcal X}(*{}^\tau\! \mathcal X_0)$-module. In other words, call $\operatorname{inv}:\mathds{G}_{m,\theta}\rightarrow\mathds{G}_{m,\tau}$ the inversion operator $\theta\mapsto\theta^{-1}=\tau$ and $j:\mathds{G}_{m,\tau}\hookrightarrow\AA_{\tau}^1$ the canonical inclusion. From now on, we will denote by ${}^\tau\!\widehat\mathcal H$ the $\cR^{\operatorname{int}}_{{}^\tau\!\mathcal X}(*{}^\tau\! \mathcal X_0)$-module $(\operatorname{id}_{\mathcal X}\times(j\circ\operatorname{inv}))_*{}^\theta\!\widehat\mathcal H$. By virtue of Proposition \ref{prop:rescaling} we can write ${}^\tau\!\widehat\mathcal H$ as the $\cR^{\operatorname{int}}_{{}^\tau\!\mathcal X}(*{}^\tau\! \mathcal X_0)$-module ${}^\tau\!\widehat\mathcal H=\cR^{\operatorname{int}}_{{}^\tau\!\mathcal X}(*{}^\tau\! \mathcal X_0)/(P,{}^\tau\! R,{}^\tau\! H)$, with $P$ as before and
$${}^\tau\! R=z^2\partial_z+z\tau\partial_\tau\,\text{ and }\,{}^\tau\! H=\prod_{i=1}^n\frac{z}{\tau}(t\partial_t-\alpha_i)-t.$$
\begin{lemma}\label{lem:ConnHypResc}
For each $k=0,\ldots,n-1$, let $Q_k$ be the operator
$$Q_k=(-n)^k\prod_{j=1}^k\frac{z}{\tau}(t\partial_t-\alpha_j),$$
where the empty product must be understood as one. Then the $Q_k$ form a basis of ${}^\tau\!\widehat\mathcal H$ as an $\mathcal O_{{}^\tau\!\mathcal X}(*{}^\tau\! \mathcal X_0)$-module. The integrable connection arising from the $\cR^{\operatorname{int}}_{{}^\tau\!\mathcal X}(*{}^\tau\! \mathcal X_0)$-module structure associated with ${}^\tau\!\widehat\mathcal H$ has the following matrix expression with respect to that basis:
$$\nabla\underline Q=\underline Q\left(\left(\tau A_0+zA_\infty\right)\frac{dz}{z^2}+\left(-\tau A_0+zA'_\infty\right)\frac{dt}{nzt}-\left(\tau A_0+zA_\infty\right)\frac{d\tau}{z\tau}\right),$$
where $A_0$, $A'_\infty$ and $A_\infty$ are the matrices
$$A_0=\left(\begin{array}{cccc}
0& & & (-n)^nt\\
1&\ddots& & 0\\
&\ddots&0&\vdots\\
& & 1& 0\end{array}\right),\,A'_\infty=\operatorname{diag}(n\alpha_1,\ldots,n\alpha_n)$$
$$\text{\emph{and }}\,A_\infty=\operatorname{diag}(0,1,\ldots,n-1)-\gamma I_n-A'_\infty.$$
\end{lemma}
\begin{proof}
We can use the expressions for ${}^\tau\! R$ and $P$ to replace the classes of $z\tau\partial_\tau$ and $z^2\partial_z$, respectively, in terms of $zt\partial_t$. If we extend for a moment the definition of the $Q_k$ for values of $k$ greater than $n-1$ taking $Q_k:=\left(z\tau^{-1}t\partial_t\right)^{k-n+1}Q_{n-1}$, we see that ${}^\tau\!\widehat\mathcal H$ is generated as a $\mathcal O_{{}^\tau\!\mathcal X}(*{}^\tau\! \mathcal X_0)$-module by the $Q_k$, for $k\geq0$ (since it is obviously generated by the powers of $zt\partial_t$, and those can be expressed by the $Q_k$). If we focus now at the degree in $zt\partial_t$ of the generators, we can use ${}^\tau\! H$ to get rid of any $Q_k$ with $k\geq n$. Since $\deg_{zt\partial_t}Q_k=k$, they must be linearly independent over $\mathcal O_{{}^\tau\!\mathcal X}(*{}^\tau\! \mathcal X_0)$ and so they are a basis.
Let now $k<n-1$. Then from the relation $-nz/\tau(t\partial_t-\alpha_{k+1})Q_k=Q_{k+1}$ we can write that $nzt\partial_tQ_k=-\tau Q_{k+1}+nz\alpha_{k+1}Q_k$. Now if $k=n-1$, then
$$-nz/\tau(t\partial_t-\alpha_n)Q_{n-1}=(-n)^n\prod_{j=1}^nz/\tau(t\partial_t-\alpha_j)=(-n)^nt.$$
This gives us the second summand of the formula above in the statement.
The first one is a consequence of the last one and the fact that the class of $z^2\partial_z+z\tau\partial_\tau$ vanishes in ${}^\tau\!\widehat\mathcal H$; let us show the expression for the latter.
Take again $k<n-1$. Then,
$$z\tau\partial_\tau Q_k=(-n)^kz\tau\partial_\tau \tau^{-k}\prod_{j=1}^kz(t\partial_t-\alpha_j)=(-n)^kz(-k\tau^{-k}+\tau^{-k+1}\partial_\tau) \prod_{j=1}^kz(t\partial_t-\alpha_j)=$$
$$=-kzQ_k+Q_kz\tau\partial_\tau=-kzQ_k+Q_kz(nt\partial_t+\gamma)=z(nt\partial_t+\gamma-k)Q_k=-\tau Q_{k+1}+z(n\alpha_{k+1}+\gamma-k)Q_k.$$
The analogous calculation for $k=n-1$ gives us that $z\tau\partial_\tau Q_{n-1}=-\tau(-n)^nt+z(n\alpha_n+\gamma-(n-1))Q_{n-1}$.
\end{proof}
\begin{defi}\label{defi:tauVfilt}
For each $\alpha\in\mathds R$, let us define the following subsets of ${}^\tau\!\widehat\mathcal H$:
$${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H:=\left\{\sum_{k=0}^{n-1}f_k\tau^{\nu_{k}}Q_k\,:\, f_k\in\mathcal O_{{}^\tau\!\mathcal X}\text{ , }\,\max(k-n\alpha_{k+1}-\gamma-\nu_k)\leq\alpha\right\},$$
$${}^\tau\! U_{<\alpha}{}^\tau\!\widehat\mathcal H:=\left\{\sum_{k=0}^{n-1}f_k\tau^{\nu_k}Q_k\,:\, f_k\in\mathcal O_{{}^\tau\!\mathcal X}\text{ , }\,\max(k-n\alpha_{k+1}-\gamma-\nu_k)<\alpha\right\}.$$
\end{defi}
\begin{rem}\label{rem:tauVfilt}
Note that the ${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H$ form an increasing filtration of ${}^\tau\!\widehat\mathcal H$, indexed by the real numbers but with a discrete set of jumping numbers, such that $\tau{}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H={}^\tau\! U_{\alpha-1}{}^\tau\!\widehat\mathcal H$ for any $\alpha$. The graded piece associated with $\alpha$ is $\operatorname{Gr}_\alpha^{{}^\tau\! U}{}^\tau\!\widehat\mathcal H={}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H/{}^\tau\! U_{<\alpha}{}^\tau\!\widehat\mathcal H$.
In the definition of the ${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H$ all the exponents $\nu_k$ of the powers of $\tau$ accompanying the $f_kQ_k$ satisfy that $\nu_k\geq-\alpha+k-n\alpha_{k+1}-\gamma$. Therefore, we can define the steps of the filtration in an alternative way, as the free $\mathcal O_{{}^\tau\!\mathcal X}$-modules of finite rank
$${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H=\bigoplus_{k=0}^{n-1}\mathcal O_{{}^\tau\!\mathcal X}\cdot\tau^{\nu_{\alpha}(k)}Q_k,$$
where $\nu_\alpha(k)=\lceil-\alpha+k-\gamma-n\alpha_{k+1}\rceil$.
With this expression it is easy to see that ${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H/(\tau-z){}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H$ is the $z$-graded free $\mathcal O_{\mathcal X}$-module $\bigoplus_k\mathcal O_{\mathcal X}z^{\nu_\alpha(k)}\bar{Q}_k$, where
$$\bar{Q}_k=(-n)^k\prod_{j=1}^k(t\partial_t-\alpha_j),$$
and that the graded pieces $\text{Gr}_\alpha^{{}^\tau\! U}{}^\tau\!\widehat\mathcal H$ are
$$\text{Gr}_\alpha^{{}^\tau\! U}{}^\tau\!\widehat\mathcal H=\bigoplus_{k=0}^{n-1}\mathcal O_{\mathcal X}\cdot\tau^{\nu_{\alpha}(k)}Q_k,$$
which are strict $\mathcal{R}_{\mathcal X}$-modules.
\end{rem}
Recall that as in the case of $\mathcal D$-modules, we have a notion of strict specializability and $V$-filtration for $\cR^{\operatorname{int}}$-modules. In the setting under consideration we recall that we will use ${}^\tau\! V$ to denote the canonical $V$-filtration of a $\cR^{\operatorname{int}}_{{}^\tau\!\mathcal X}$-module. We recall as well the reference \cite[\S 2.1.2]{Mo13} for more details.
\begin{prop}\label{prop:tauVfiltr}
Assume the $\alpha_i$ lie in the interval $[0,1)$, increasingly ordered. Then, ${}^\tau\!\widehat\mathcal H$ is strictly $\mathds R$-specializable along ${}^\tau\! \mathcal X_0$ and its ${}^\tau\! V$-filtration is in fact given by the ${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H$.
\end{prop}
\begin{proof}
First of all we will see that ${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H$ is the ${}^\tau\! V$-filtration of ${}^\tau\!\widehat\mathcal H$, following \cite[\S\S 2.1.2.1, 2.1.2.2]{Mo13}. Apart from what we already shown at the remark above, what remains then is showing conditions iii' and v of [ibid., \S 2.1.2] and prove that the ${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H$ are coherent $V_0\mathcal{R}_{\mathcal X}$-modules. We will start by the second condition. We will consider then the mappings $\mathfrak{p},\mathfrak{e}$ given by
$$\begin{array}{rcl}
(\mathfrak{p},\mathfrak{e}):\mathds R\times\mathds C&\longrightarrow&\mathds R\times\mathds C\\
(\beta,\omega)&\longmapsto&(\beta+2\Re(z\bar\omega),-\beta z+\omega-\bar{\omega}z^2)\end{array}.$$
We ought to see now that the operator $z\tau\partial_\tau-\mathfrak{e}(\beta,\omega)$ is nilpotent on the graded pieces $\operatorname{Gr}_\alpha^{{}^\tau\! U}{}^\tau\!\widehat\mathcal H$ only for a finite amount of $(\beta,\omega)\in\mathcal K:=\{\beta+2\Re(z_0\bar\omega)=\alpha\}$, for any value $z_0$ of $z$. Moreover, ${}^\tau\!\widehat\mathcal H$ will be strictly $\mathds R$-specializable if those $(\beta,\omega)$ belong in fact to $\mathds R\times\{0\}$ (cf. \cite[\S 1.3.a]{Sa15}).
Take then $(\beta,\omega)\in\mathcal K$ and $f\tau^\nu Q_k\in{}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H$, with $f\in\mathcal O_{{}^\tau\!\mathcal X}$. We must have that $k-n\alpha_{k+1}-\gamma-\nu\leq\alpha$. Assume that $k<n-1$. Thanks to Lemma \ref{lem:ConnHypResc} we know that
$$(z\tau\partial_\tau-\mathfrak{e}(\beta,\omega))f\tau^\nu Q_k=\big(z\tau\partial_\tau+(\nu+n\alpha_{k+1}+\gamma-k+\beta)z-\omega+\bar{\omega}z^2\big)(f)\tau^\nu Q_k-\tau^{\nu+1}Q_{k+1}.$$
Recall that the $\alpha_i$ are increasingly ordered. Thus $f\tau^{\nu+1}Q_{k+1}$ lives in ${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H$, for
$$k+1-n\alpha_{k+2}-\gamma-\nu-1\leq\left((k+1)-n\alpha_{k+2}-\gamma)- (k-n\alpha_{k+1}-\gamma)\right)-1+\alpha\leq\alpha.$$
Now we should look at what happens to the class of $f\tau^{\nu+1}Q_{k+1}$ in the $\alpha$-graded piece of ${}^\tau\!\widehat\mathcal H$.
Note that $\left[f\tau^\nu Q_k\right]\neq0$ if and only if $\nu+n\alpha_{k+1}+\gamma-k+\alpha=0$, so
$$(z\tau\partial_\tau-\mathfrak{e}(\beta,\omega))f\tau^\nu Q_k=\big(z\tau\partial_\tau+(\beta-\alpha)z-\omega+\bar{\omega}z^2\big)(f)\tau^\nu Q_k-\tau^{\nu+1}Q_{k+1}=$$
$$=\big(z\tau\partial_\tau-2\Re(z_0\bar\omega)z-\omega+\bar{\omega}z^2\big)(f)\tau^\nu Q_k-\tau^{\nu+1}Q_{k+1}.$$
Now notice that $\tau$ divides $\tau\partial_\tau(f)$, so in fact $z\tau\partial_\tau(f)\tau^\nu Q_k\in{}^\tau\! U_{\alpha-1}{}^\tau\!\widehat\mathcal H$ and then we can further reduce our expression to
$$(z\tau\partial_\tau-\mathfrak{e}(\beta,\omega))f\tau^\nu Q_k=(-\omega-2\Re(z_0\bar\omega)z+\bar{\omega}z^2)f\tau^\nu Q_k-\tau^{\nu+1}Q_{k+1}.$$
On the other hand, $\tau^{\nu+1}Q_{k+1}$ does not vanish either in $\operatorname{Gr}_\alpha^{{}^\tau\! U} {}^\tau\!\widehat\mathcal H$ if and only if $\alpha_{k+2}=\alpha_{k+1}$. Indeed, we know that $\nu+n\alpha_{k+1}+\gamma-k+\alpha=0$, so doing the same as before, $k+1-n\alpha_{k+2}-\gamma-\nu-1=\alpha+n(\alpha_{k+2}-\alpha_{k+1})$ and the claim follows. Furthermore, in order to $(z\tau\partial_\tau-\mathfrak{e}(\beta,\omega))$ to vanish, we should impose that $\omega=0$, just by looking at the coefficients of the powers of $z$ in the expression for $f$.
Now if $k=n-1$, then everything would be the same as before except $-\tau^{\nu+1}Q_{k+1}$, which becomes $-(-n)^nt\tau^{\nu+1}$, whose class vanishes obviously in the graded piece under consideration.
In conclusion, $(z\tau\partial_\tau-\mathfrak{e}(\beta,\omega))^lf\tau^\nu Q_k$ can only vanish in $\operatorname{Gr}_\alpha^{{}^\tau\! U}{}^\tau\!\widehat\mathcal H$ if $\alpha=\beta$ (and then $\omega=0$), and does not do so until we get to an index $k+l$ such that $\alpha_{k+l}$ is strictly bigger than $\alpha_k$. Since there is a finite set of indexes, $(z\tau\partial_\tau+\alpha z)$ is nilpotent, of nilpotency index $n$ at most.
Condition iii' in \cite[\S 2.1.2.2]{Mo13} is equivalent to $z\tau\partial_\tau{}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H\subseteq{}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H$, using that ${}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H=\tau{}^\tau\! U_{\alpha+1}{}^\tau\!\widehat\mathcal H$, and such claim is a consequence from an argument very similar to the proof of condition v above. Finally, since $V_0\mathcal{R}_{\mathcal X}=\mathcal O_{{}^\tau\!\mathcal X}\langle z\partial_t,z\tau\partial_\tau\rangle$, it is clear from the computations above and the alternative expression for the filtration steps in Remark \ref{rem:tauVfilt} that they are cyclic $V_0\mathcal{R}_{\mathcal X}$-modules, and then coherent.
Summing up and noting that all the calculation was in fact independent of $z_0$, ${}^\tau\!\widehat\mathcal H$ is strictly $\mathds R$-specializable along ${}^\tau\! \mathcal X_0$.
\end{proof}
Finally, we are able to state and prove our main result.
\begin{thm}\label{thm:HodgeData}
Let as before $\alpha_1,\ldots,\alpha_n$ be real numbers in $[0,1)$, increasingly ordered, and put $\mathcal H=\mathcal H(\alpha_i,\emptyset)$. For each $k=1,\ldots,n$, set $\rho(k)=-n\alpha_k+k$. Then the jumping numbers of the irregular Hodge filtration of $\mathcal H$ are, up to an overall real shift, the numbers $\rho(k)$. The irregular Hodge numbers are the multiplicities of those jumping numbers, or in other words, the nonzero values of $|\rho^{-1}(x)|$, for $x$ real.
Moreover, recall that $\nu_\alpha(k)=\lceil -\alpha+k-\gamma-n\alpha_{k+1}\rceil$, and that the operators $\bar{Q}_k$, for $i=0,\ldots,n-1$, were defined as
$$\bar{Q}_k=(-n)^k\prod_{i=1}^k(t\partial_t-\alpha_i).$$
Then, the irregular Hodge filtration $F^{\operatorname{irr}}_\bullet\mathcal H$ is given by
$$F^{\operatorname{irr}}_{\alpha+j}\mathcal H=\bigoplus_{k:j\geq\nu_\alpha(k)}\mathcal O_X\bar{Q}_k.$$
\end{thm}
\begin{proof}
Since we know that $\widehat\mathcal H$ underlies an object in $\operatorname{IrrMHM}(\mathds G_{m,t})$ by Theorem \ref{thm:HypIrrMHM},
we conclude by \cite[Def. 2.52]{Sa15} that $\widehat\mathcal H$ is well-rescalable (as defined in [ibid., Def. 2.19]) and so we apply [ibid., Def. 2.22]. From Remark \ref{rem:tauVfilt}, we have
$$i_{\tau=z}^*{}^\tau\! V_\alpha{}^\tau\!\widehat\mathcal H={}^\tau\! V_\alpha{}^\tau\!\widehat\mathcal H/(\tau-z){}^\tau\! V_\alpha{}^\tau\!\widehat\mathcal H=\bigoplus_k\mathcal O_{\mathcal X}z^{\nu_\alpha(k)}\bar{Q}_k,$$
which is $z$-graded of finite rank
Denote by $\pi$ the projection $\mathcal X\rightarrow X$. Then, the $z$-adic filtration on $\pi^*\mathcal H[z^{-1}]$ induces a filtration on $i_{\tau=z}^*{}^\tau\! V_\alpha{}^\tau\!\widehat\mathcal H$, given by
$$F_ri_{\tau=z}^*{}^\tau\! V_\alpha{}^\tau\!\widehat\mathcal H:=\bigoplus_{s\leq r}\left(\bigoplus_{k\,:\,s\geq\nu_\alpha(k)}\mathcal O_{X}\bar{Q}_k\right)z^s.$$
Then, $\operatorname{Gr}^F\left(i_{\tau=z}^*{}^\tau\! U_\alpha{}^\tau\!\widehat\mathcal H\right)$ is the Rees module associated to a new good filtration $F^{\operatorname{irr}}_{\alpha+\bullet}$ on $\mathcal H$, for some $k=0,\ldots,n-1$, which is the irregular Hodge filtration. More concretely, $F^{\operatorname{irr}}_\bullet\mathcal H$ is given by
$$F^{\operatorname{irr}}_{\alpha+j}\mathcal H=\bigoplus_{k\,:\,j\geq\nu_\alpha(k)}\mathcal O_{X}\bar{Q}_k.$$
Therefore, its jumping numbers are $-\gamma+j-1-n\alpha_j$ for $j=1,\ldots,n$. Since the irregular Hodge filtration is defined up to an overall real shift, we can normalize the jumping numbers to $j-n\alpha_j$ and the irregular Hodge numbers will be their multiplicities.
\end{proof}
\bibliographystyle{amsalpha}
\def$'${$'$}
\providecommand{\bysame}{\leavevmode\hbox to3em{\hrulefill}\thinspace}
\providecommand{\MR}{\relax\ifhmode\unskip\space\fi MR }
\providecommand{\MRhref}[2]{%
\href{http://www.ams.org/mathscinet-getitem?mr=#1}{#2}
}
\providecommand{\href}[2]{#2}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,914 |
Karl Felix von Seyffer (* 25. Januar 1762 in Bitzfeld, Württemberg; † 17. September 1822 in Bogenhausen) war ein deutscher Astronom.
Leben
Seyffer studierte und promovierte an der württembergischen Landesuniversität in Tübingen. Danach lehrte und forschte er als außerordentlicher Professor an der Universität Göttingen. Zu dieser Zeit entstanden diverse Aufsätze, unter anderen zur Polhöhe von Göttingen und zu Mondregenbögen. Im Januar 1792 hielt sich Seyffer in Paris auf und besuchte dort den Klub der Jakobiner. Günther bezeichnet als Seyffers bedeutendste Arbeit die 1794 zu seiner Göttinger Zeit entstandene Bestimmung der Länge von Göttingen, Gotha, Danzig, Berlin und Harefield in Middlessex aus der Sonnenfinsterniß vom 5. September 1793 Seyffer war einer der Teilnehmer des von Franz Xaver von Zach und Marie-Jeanne de Lalande initiierten Ersten europäischen Astronomenkongresses.
1804 gab Seyffer seine Stellung in Göttingen auf und schloss sich 1805 Napoleon Bonaparte als Ingénieur-Géographe in dessen Hauptquartier an. Dort kam er in Kontakt mit der Regierung des neu gegründeten Königreichs Bayern. Diese nahm Seyffer in ihre Dienste. Im Lauf der Jahre war er Hofrat, Mitglied im statistisch-topographischen Büro des Ministeriums für auswärtige Angelegenheiten und später Leiter der Sternwarte Bogenhausen. 1804 wurde Seyffer ordentliches Mitglied der Bayerischen Akademie der Wissenschaften. Auf Seyffer geht die bayrische Steuerkatastrierung zurück, die seinerzeit in Deutschland richtungsweisend war.
Am 17. September 1822 starb Seyffer 60-jährig in Bogenhausen.
Literatur
Weblinks
www.deutsche-biographie.de
Einzelnachweise
Astronom (18. Jahrhundert)
Astronom (19. Jahrhundert)
Hochschullehrer (Georg-August-Universität Göttingen)
Mitglied der Ehrenlegion (Ritter)
Mitglied der Bayerischen Akademie der Wissenschaften
Deutscher
Geboren 1762
Gestorben 1822
Mann | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,029 |
Q: Decrease the website loading time in cypress When I run my test in Cypress, it takes about 15 - 18 sec to start loading the page. Is there no way to solve this issue to decrease the time? Seems like Cypress itself requires such time to configure something, because to load the webpage itself takes no more than 2 sec.
To start loading the website takes ~16 sec
context('Actions', () => {
beforeEach(() => {
cy.visit(Cypress.env('url'))
})
Cypress version: 8.2.0
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,789 |
Media Kit (quick guide)
Marti Leimbach
Writer of contemporary fiction for adults and young adults
Dragonfly Girl
Dragonfly Girl is young adult suspense novel about a troubled high school girl with a gift for science who discovers a "cure" for death and ends up embroiled in an international rivalry.
Wait…a cure for death? As in, the dead come back to life? Yes, but we aren't talking zombies (sorry…I like a good zombie story as much as anyone). And we're not talking about those who've been buried for centuries. Not the dead dead.
But say a person was dead a few hours ago or even a few days ago…yes, there's hope! And the process, which as I wrote the book began to feel more and more real to me, is called "post-death recovery".
You'd think that discovering a cure for death would be a good thing, but it doesn't work out that way for Kira, at least not at first. She's in trouble from the moment she arrives on the page, with school problems, money problems, family problems, and a big lie that sends her hurdling toward danger.
Dragonfly Girl is published by Katherine Tegen Books/Harper Collins USA
Advance Praise for Dragonfly Girl:
…This is a compelling YA debut from the internationally bestselling Leimbach. All the characters have depth, especially Kira, whose growth will entice readers to invest in her struggles and cheer for her successes. Leimbach also handles the science well, explaining what is happening without letting it slow down the action, focusing more on the characters' emotions than the scientific procedures. The book lends itself to upcoming volumes, which should be eagerly anticipated. Kira's race isn't specified, and there is a range of racial and ethnic diversity among secondary characters. VERDICT: A thrilling debut with a heroine to root for and an excellent story that will keep surprising readers.
Dragonfly Girl is unlike any book I've ever read. The plot is taut and devilishly cunning, the science behind the story is brilliantly researched, and the writing pulls you in and doesn't let go until the very last page.You'll find yourself aching for the heroine's hardships at first, before suddenly being whisked off to a heart-thumping adventure that will leave you breathless. THIS BOOK SLAPS!
—Jesse Q. Sutanto, author of DIAL A FOR AUNTIES
… fast pace and high stakes are engaging … An exciting adventure about a girl in STEM.
Dragonfly Girl is a uniquely smart book. Readers will be challenged and delighted, as I was, by its originality. Invest some time in Dragonfly Girl and let author, Marti Leimbach, take you on a surprising and thrilling ride.
—Michael Grant, bestselling author of The Gone series
I loved Dragonfly Girl. Can there be a better way to nudge young people toward the sciences than to introduce them to Kira Adams…? Marti Leimbach has written an intriguing and thrilling novel that could very well entice young people to take a closer look at careers in science…
—Todd Strasser, bestselling author of The Wave and Fallout
Marti Leimbach is known for her bestsellers, Dying Young, made into a film starring Julia Roberts, and Daniel Isn't Talking. Her interest in neurodiversity and the future of science influenced her latest work, the YA action/thriller, Dragonfly Girl.
Post Archives Select Month April 2021 March 2021 February 2021 November 2020
© 2020 - Marti Leimbach - All Rights Reserved. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,662 |
Risk factors for groin injury in sport: an updated systematic review
Jackie L Whittaker1,
Claire Small2,
Lorrie Maffey3,4,
Carolyn A Emery5,6
1Faculty of Kinesiology, Sport Injury Prevention Research Centre, University of Calgary, Calgary, Alberta, Canada
2Pure Sports Medicine, London, UK
3Faculty of Medicine, Division of Sport Medicine, University of British Columbia, Vancouver, British Columbia, Canada
4School of Rehabilitation Science, McMaster University, Canada
5Faculty of Kinesiology, Sport Injury Prevention Research Centre, University of Calgary, Calgary, Canada
6Department of Pediatrics and Department of Community Health Sciences, Alberta Children's Hospital Research Institute for Child and Maternal Health, Cummings School of Medicine, University of Calgary, Calgary, Canada
Correspondence to Dr Jackie L Whittaker, Sport Injury Prevention Research Centre, Faculty of Kinesiology, University of Calgary, 2500 University Dr NW, Calgary, Alberta, Canada T2N 1N4; jwhittak{at}ucalgary.ca
Background The identification of risk factors for groin injury in sport is important to develop and implement injury prevention strategies.
Objective To identify and evaluate the evidence examining risk factors for groin injury in sport.
Material and methods Nine electronic databases were systematically searched to June 2014. Studies selected met the following criteria: original data; analytic design; investigated a risk factor(s); included outcomes for groin injury sustained during sport participation. The Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) guidelines were followed and two independent authors assessed the quality and level of evidence with the Downs and Black (DB) criteria and Oxford Centre of Evidence-Based Medicine model, respectively.
Results Of 2521 potentially relevant studies, 29 were included and scored. Heterogeneity in methodology and injury definition precluded meta-analyses. The most common risk factors investigated included age, hip range of motion, hip adductor strength and height. The median DB score across studies was 11/33 (range 6–20). The majority of studies represented level 2 evidence (cohort studies) however few considered the inter-relationships between risk factors. There is level 1 and 2 evidence that previous groin injury, higher-level of play, reduced hip adductor (absolute and relative to the hip abductors) strength and lower levels of sport-specific training are associated with increased risk of groin injury in sport.
Conclusions We recommended that investigators focus on developing and evaluating preparticipation screening and groin injury prevention programmes through high-quality randomised controlled trials targeting athletes at greater risk of injury.
http://dx.doi.org/10.1136/bjsports-2014-094287
Groin injuries are common in many sports that involve rapid acceleration and deceleration, sudden changes in direction and kicking such as soccer,1–12 rugby,13 Australian rules football,14 ice hockey,15 Gaelic football and cricket.15 ,16 In addition to frequent occurrence, prospective collection of injury data over consecutive soccer seasons has demonstrated that those with a previous groin injury are at a 2.4 (hazard ratio; 95% CI 1.2 to 4.6) times greater risk of groin injury than payers with no previous history.10 This vicious cycle of injury and re-injury may result not only in reduced performance and missed training/competition but chronicity, the end of an athletic career and future mobility disability.
According to van Mechelen,17 the prevention of sport injuries occurs through a four-step process beginning with establishing the extent of the specific injury through a validated injury surveillance system. This is followed by identifying injury risk factors and causal mechanisms through prospective analysis of specific injury patterns, development and introduction of preventative strategies and evaluation of these strategies by determining their impact on injury incidence. Throughout this process it is important to acknowledge that a sport injury is unlikely to result from a single risk factor but rather as a consequence of complex interactions of multiple risk factors and inciting events.18 Thus, studies aimed at identifying risk factors for groin injuries in sport should utilise a prospective design and ensure an adequate sample size to facilitate biostatistical methods that consider the interrelationships between various risk factors.19
Consensus regarding the risk factors for groin injury is lacking and this may be due, in part, to methodological limitations and heterogeneity of previous studies. Our 2007 systematic review of risk factors for groin strain injury in sport reported a deficiency in prospective studies.20 Based on the studies available at that time (n=11; 2 cross-sectional and 9 prospective), there was support for an association of previous injury and greater hip adductor to abductor strength ratio, sport specificity of training and amount of preseason sport-specific training as individual risk factors in groin strain injury. Although this review did not include a formal assessment of the quality or level of evidence of the included studies, it reported significant concerns regarding the internal validity of the included studies. Further, it recommended that any future studies examining risk factors for groin strain injury in sport employ consistent injury definitions, use validated and reliable injury reporting systems to quantify outcome measures and consider the inter-relationships between risk factors by controlling for potential confounding variables (eg, player exposure and previous injury).
As identification of risk factors and their causal mechanisms is a precursor to the development of effective prevention strategies, the lack of consensus related to risk factors for groin injury in sport has likely hindered the process of developing and evaluating groin injury prevention strategies in sport. The objective of this review was to update this previous systematic review and summarise the evidence related to risk factors for groin injury in sport, including critical appraisal of the literature.
This review was conducted according to the Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) guidelines.21
Data sources and search
Relevant studies were identified by searching nine online databases, selected based on their relevance to the research topics, from inception to June 2014. These databases included: MEDLINE (1966-present), CINAHL (Cumulative Index to Nursing and Allied Health Literature; 1982–present), Cochrane database for Systematic and Complete Reviews (1975–present), Cochrane Controlled Trials Registry (1975–present), Cochrane Injuries Group Trials Register, Sport Discus (1980–present), EMBASE (Excerpta medical databases; 1974–present), PubMed (public Medline) and SCOPUS. A combination of medical subject headings (MeSH) and text words were used to execute each search. Table 1 outlines the search terms used by injury, anatomical region or tissue type and risk concept along with the combinations of search terms that formed each search strategy. The only limits set were that studies be published in a peer-reviewed journal. The Cochrane database for Systematic and Complete Reviews was included to identify any systematic reviews and/or meta-analyses such that their reference lists could be manually searched alongside those of all selected studies to identify relevant articles not identified by the search strategies. Manuscripts were organised using the reference management software package, EndNotes V.7.1 (Thomson Reuters, 2013). The number of references obtained from each search strategy for each database was recorded and a running total constructed. After accounting for duplication, the titles and corresponding abstracts of all returned records were reviewed by (JLW) to identify potentially relevant studies. Finally, the full text of all potentially relevant studies was reviewed to determine final study selection by (JLW, CAE).
Search strategy and results of the systematic literature search, with total number of unique articles per database
Studies were included if they investigated the association between any potential injury risk factor (defined as any factor that may increase the potential for injury) or injury prevention strategy with groin injury (defined as any or all of the following; groin or hip adductor injury or muscle strain, tenderness on palpation of the hip adductor or flexor muscles, adductor bone-tendon junction or pubic symphysis and/or pain on resisted hip adduction). Additional inclusion criteria included: primary research of original data, analytic design (eg, experimental, cohort, case–control or cross-sectional), an outcome measure of groin injury sustained during sport participation, an objective exposure measure of one or more potential risk factor or injury prevention strategy for groin injury in sport and study participants who were involved in any sport that involved rapid acceleration and deceleration, sudden changes in direction and kicking. The definition of groin injury was modified slightly (omitted lower abdominal muscles) from the original systematic review to be consistent with clinical entity of adductor-related pain proposed by Holmich et al22 and, as a greater number of studies focusing on the hip adductors and adductor bone-tendon junction were available than at the time of the original review.
Studies were excluded if the injury outcome was only described in general terms such as thigh or hip injury, were not written in English or involved animal models or cadavers. Further, conference proceedings/abstracts, review articles (systematic and narrative), case series or case studies, editorials, commentaries and opinion-based papers were excluded.
Data extraction and study rating process
Data extracted from each study included; study design, study location and population (sport, level, age, sample size), injury outcome (definition), injury estimates (incidence proportion, incidence rate, prevalence), measures of risk (difference in means, correlations, OR, incidence rate ratios; IRR and risk ratio; RR), risk factors and results (significant and non-significant). If available, injury estimates (injury rates) were used to calculate point estimates of IRR (IR exposed/injury rate in unexposed). Two authors (lead author and one of three coauthors) independently assessed the quality and level of evidence of each study. Quality of evidence was evaluated based on criteria for internal validity (study design, quality of reporting, presence of selection and misclassification bias, potential confounding) and external validity (generalisability) using the Downs and Black (DB) quality assessment tool which assigns an individual score calculated out of 33 total points for each study (10 points for reporting, 3 points for external validity, 7 points for bias, 3 points for confounding and 1 for power: see online supplementary appendix 1).23 The level of evidence represented by each study was categorised based on the Oxford Centre of Evidence Based Medicine (OCEBM) model (see online supplementary appendix 2).24 As per study exclusion criteria, levels 1a, 2a, 3a (systematic reviews), 4 (case series) and 5 (opinion-based papers) were not included. Discrepancies in DB scoring or OCEBM categorisation were resolved first by consensus between the two reviewers who rated the study and if required, by the senior author (CAE).
Extracted data, quality and level of evidence were summarised for each study. The quantity, quality and level of evidence for the most commonly investigated modifiable and non-modifiable risk factors for groin injury in sport were collated.
Identification of studies
An overview of the study identification process is provided in figure 1. The initial search yielded 7760 articles (including eight identified through reference list search), 5239 duplicates were removed leaving 2512 potentially relevant articles. Following the removal of studies not meeting inclusion criteria based on abstract review (eg, injury and injury risk were not investigated, population or dance form did not match criteria) this was narrowed to 70. Subsequent to further manuscript evaluation by the two independent reviewers (JLW and CAE), 41 were excluded leaving 29 studies deemed appropriate for inclusion to the systematic review. Electronic or hard copies of two potentially relevant articles were not available for review and as they had not met similar inclusion criteria for the previous review, published in 2007, they were excluded.25 ,26 One study27 included in the previous systematic review was excluded as it did not provide an independent estimate of groin injury (eg, combined low back, groin and hamstring injuries), while another study included in the previous review,15 that included abdominal muscle strain in the injury definition, was included as 83% of the reported injuries were related to the adductor muscles. Owing to inconsistent methodology and injury definition as well as the heterogeneity of the risk factors examined meta-analysis was precluded (see online supplementary table S1).
Study identification Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) flow sheet.
Characteristics of the 29 included studies are summarised in online supplementary table S1. These consisted of 2 intervention studies (1 randomised controlled trial, 1 quasi-experimental), 21 cohort (19 prospective, 1 historical, 1 pilot), 5 case–control and 1 cross-sectional study representing approximately 14 different countries. The median number of participants per study was 219 (range 18–2299) and the combined total number of athletes investigated across studies was 12 131 (9925 males and 2206 females). Twenty-eight of the studies are believed to have included male athletes (11 of these did not specify the sex of their participants however based on the sport investigated it is likely the participants were male) spanning the ages of 12–38 years, while five studies included female athletes (age range 15–41 years). Among the 23 follow-up studies 13 had a follow-up time greater than one season (range 9 weeks—9 seasons), 7 had at least 50 injury cases (range 4–672) and 9 utilised a multivariate statistical approach to identify risk factors for groin injury in sport. Of the 19 studies published since 2007, 1 was a randomised controlled trial, 14 were cohort (12 prospective, 1 historical and 1 pilot) and 4 were case–control. Six of these 19 studies utilised multivariate statistical approaches and 5 had at least 50 injury cases.
Injury estimates
Descriptions of injury estimates (incidence proportion, incidence rate, prevalence), effect estimates (IRR, RR, OR) and significant and non-significant groin injury risk factors are presented in online supplementary table S1.
Quality and level of evidence
The highest level of evidence demonstrated by all reviewed studies was level 1b (Individual randomised controlled trial). The majority (21/28) of studies were classified as level 2b which corresponds to cohort studies.
The median methodological quality for all 29 studies, based on the DB criteria, was 11/33 (range 6–20) with an initial moderate between rater agreement of 65.5% (κ=0.62).43 The aim of the DB criteria is to assess scientific study methodological quality (inclusive of randomised and non-randomised intervention as well as observational studies). Owing to the majority of included studies being observational in nature, seven items (4, 8, 14, 19, 23, 24 and 27; totalling 10 points) on the DB checklist were not applicable. Therefore, 27 of the 29 articles did not have the opportunity to achieve a full score due to their study design. Areas in which the included studies were consistently limited included: incomplete description of how the sample was representative of the population of interest (eg, insufficient description of participant characteristics such as sex, history of previous groin injury, training exposure), limited description of the characteristics of those lost to follow-up, use of invalid or unreliable measures, insufficient reporting of how participants lost to follow-up and differing length of follow-up were accounted for in statistical analyses, inadequate sample size and lack of adjustment for potential modification and confounding by factors such as exposure and previous injury. Further, several of the case–control studies that report a matched design did not account for matching in their analyses (eg, independent t tests vs paired t tests).
The quantity, quality and level of evidence for the most commonly investigated modifiable and non-modifiable risk factors for groin injury in sport are summarised in table 2. The most common risk factors investigated included age, hip range of motion, hip adductor strength, height and weight. There is level 1 and 2 evidence that previous groin injury, higher level of play, reduced hip adductor strength (isolated and relative to hip abductor strength) and lower levels of sport-specific training are associated with increased risk of groin injury in sport. Further, there is consistent evidence to suggest that older age, higher weight or body mass index (BMI), height, reduced hip range of motion (ROM) and performance on fitness tests such as jump height, leg power (squat), 40 m sprint, sidestepping, kicking and VO2max estimated from a shuttle run are not associated with groin injury in sport.
Summary of significant and non-significant groin injury risk factors by quantity, quality and level of evidence
To our knowledge, this is the first systematic review examining risk factors for groin injury in sport that considers both a formal evaluation of study quality and level of evidence. Overall the quality and level of evidence investigating risk factors for groin injury in sport has improved in the past 7 years since our systematic review in 2007.20 Specifically, there are a greater number of prospective studies with larger sample sizes employing multivariate statistical techniques.
Key findings—risk factors
Consistency across the literature support previous groin injury, higher level of play, reduced hip adductor strength (absolute and relative to the hip abductors) and lower levels of sport-specific training as risk factors for groin injury in sport. To date, many authors have speculated on the mechanisms underlying these risk factors. The general consensus regarding the mechanism by which previous injury is a risk factor is inadequate rehabilitation following the initial injury and/or inherent physiological risk in certain individuals that puts them at greater risk of both the initial and subsequent injuries.2 ,10 ,15 ,31 The risk associated with higher level of play may result from a higher intensity in training and game play as well as a greater number of training hours.32 Decreased levels of hip adductor strength (both absolute and in comparison to the hip abductors) may result in decreased muscle capacity, imbalances between the synergistic functions of hip adductor and abductor muscles, and increased risk of muscle injury during movements involving side-to-side cutting, striding, quick acceleration/deceleration and sudden direction changes.9 ,15 Sport-specific training (specifically, pre-season) may address muscle weakness and imbalance as well as promote function specific recruitment resulting in more effective utilisation and less muscle fatigue.20 Consequently reduced sport-specific training may place an athlete at higher injury risk when faced with an increase in training load as the playing season begins.
Although there have been valuable contributions made to the evidence base related to identifying risk factors for groin injury in sport in the past 7 years the conclusions of this systematic review and that of the previous20 are surprisingly similar. Specifically:
previous groin injury,
reduced relative hip adductor strength and
reduced sport-specific training
were all identified as risk factors for groin injury in sport previously. Previous groin injury, and reduced hip adductor strength have also been identified as risk factors for groin/hip injury in field-based sports in a recent systematic review of seven studies.44
In addition, Ryan et al44 reported that older age, higher BMI and reduced hip abductor ROM are risk factors for groin/hip injury in field-based sport. The discrepancies between these findings and those of the current review are likely due to the limited scope of sports considered and the inclusion of studies investigating both hip and groin injuries in the field-based sport review. Of the 29 studies included in the current review, 12 investigated older age as a risk factor for groin injury in sport (see online supplementary table S1). Of these, all but two studies (including one randomised controlled trial (RCT), eight cohort) found no association between older age (both as a dichotomous and continuous variable) and groin injury in sport (see table 2). Similarly, five of six included studies investigating BMI and six of nine investigating hip ROM found no association between the exposure variables and groin injury.
What can we learn from other injuries?
Looking beyond the groin injury literature, the current findings are relatively consistent with a recent systematic review and meta-analysis (including 34 studies) of risk factors for hamstring injury in sport45 which identified previous hamstring injury, quadriceps peak torque and older age as the exposure variables most consistently associated with hamstring muscle strain-type injury. The discrepancy in findings regarding increasing age as a risk factor for groin and hamstring injury may be related to the relatively narrow age range (mean age ≤25.8 years with SDs ranging between 0.8 and 4.6 years) represented in the 12 studies that have investigated age as a risk factor for groin injury. Further, the conclusion that increasing age is a risk factor for hamstring injury45 is potentially influenced by the findings of one study by Arnason et al2 Accordingly additional consideration of the prospective relationship across between age and injury risk across a wider age span for both muscle groups is recommended.
Meta-analyses were not possible due to inconsistent methodology and heterogeneity of the definition of groin injury in the included studies. Further, despite a comprehensive search strategy and rigorous approach to study selection it is important to acknowledge the possibility of omitting a relevant study and inclusion of only English language manuscripts.
As the conclusions and recommendations contained within this review are based on a synthesis and evaluation of existing literature they are limited by its inadequacies. In several instances (eg, game play, fitness tests) there was a lack of consistent high-quality evidence to support nominating a particular exposure variable as a risk factor due to inadequate reporting of concepts essential to establishing internal and external validity. The biggest threats to internal validity were related to the possibility of selection bias and potential confounding. Specifically, due to the lack of reporting of participant characteristics it was often difficult to determine if the athletes selected for a study differed systematically from those in the source population (selection bias). Equally important was the consistent omission of the characteristics of those lost to follow-up, which made it impossible to determine if those lost to follow-up were systematically different from those retained in the study. The inability to assess for selection bias not only questions the internal validity of several studies, it impacts the degree to which the findings of these studies can be generalised to the larger athletic population from which the sample was drawn (external validity).
As stated earlier, it is highly unlikely that a groin injury is a result of a single risk factor, but rather the consequence of complex interactions between multiple risk factors and inciting events.18 Multivariate biostatistical techniques can be used to explore these complex interactions given an adequate sample size. Bahr and Holme19 estimated that 50 injury cases are needed to detect a moderate to strong association between a risk factor and sport injury. Of the 29 studies included in this review only nine employed these techniques, of which only three had 50 or more injury cases and were able to assess these interactions.9 ,15 ,31 As a result, the association between the potential risk factor and groin injury reported in the studies that did not employ these techniques may be biased as they failed to consider any potential confounder (eg,. extraneous variables that may have distorted the relationship between the exposure variable and groin injury).
The last point of consideration is that studies to date may not have considered all possible risk factors for groin injury in sport. For example, a recent systematic review and position statement released by the American Medical Society for Sports Medicine highlights that although there is a lack of clinical data a high ratio of workload-to-recovery time may lead to overuse injuries and burnout in youth sport.46 To the best of our knowledge the relationship between measures of over training or physiological fatigue and groin injury and sport have yet to be investigated.
Both prospective cohort and intervention study designs are important for identifying potential risk factors for injury in sport.19 While prospective cohort studies are critical for establishing temporality between a risk factor and subsequent injury, RCTs provide the strongest evidence for the causal nature of a risk factor (eg, hip abductor and adductor strength, decreased levels of sport-specific training) and the effectiveness of modifying that factor on injury outcomes. Based on the additional prospective studies undertaken in the past 7 years (involving larger samples and employing multivariate statistical techniques), consistency of the finding of the current review with those of the previous review20 and the challenges and high cost of undertaking high quality prospective cohort studies, it is recommended that investigators shift their focus from prospective cohort to high quality RCTs. Specifically, future research should include RCTs that target athletes at greater risk of groin injury during sport (eg, high levels of play, previous injury) with prevention programmes that include interventions targeting the hip abductor and adductor muscles in conjunction with off and preseason sport specific training.
To date two separate intervention studies aimed at addressing modifiable risk factors (eg, dynamic balance, muscle strength and agility), for sport-related lower extremity and groin injuries have been undertaken.32 ,47 Engebretsen et al47 investigated the effectiveness of an injury prevention programme on high-risk (eg, previous injury and/or reduced function) soccer players, while Holmich et al32 selected a cluster (soccer team) design to facilitate implementation. Unfortunately both studies lacked sufficient statistical power to demonstrate a significant effect of the proposed intervention on the occurrence of sport-related groin injuries and Engebretsen et al47 report that player compliance to the training programmes was poor with only 19.4% of the groin injury high-risk group carrying out the minimum recommended training volume. Other reasons for null findings in these studies may be that the intervention did not sufficiently address the risk factors present. For example, there is a body of evidence suggesting that persistence of neuromuscular changes post-injury may have detrimental long-term consequences that contribute to re-injury through increased joint load, decreased movement, and decreased loading variability.48–53 Consequently, prevention programmes focused on purely building strength without restoring coordinated motor control (eg, eliminating protective cocontraction) may not prove as effective. Regardless of the lack of effect detected in these two landmark intervention studies, valuable lessons can be learned from both, the least of which is the importance of developing an implementation strategy and then tracking and accounting for adherence to the prevention programmes in the analysis.
The quality of studies investigating risk factors for groin injury has improved in the past 7 years.
There is relatively consistent level 1 and 2 evidence to suggest that previous groin injury, higher level of play, reduced hip abductor and adductor strength and lower levels of sport-specific training are associated with increased risk of groin injury in sport.
Further, there is consistent level 2 evidence suggesting that higher weight, BMI or height, reduced hip ROM and performance on fitness test such as jump height, leg power (squat), 40 metre sprint, sidestepping, kicking and VO2max estimated from a shuttle run are not associated with groin injury in sport.
Based on the work performed in the field in the past 7 years and the challenges and high cost of undertaking high-quality prospective cohort studies aimed at identifying risk factors for groin injury in sport it is recommended that investigators turn their focus to high-quality randomised controlled trials targeting athletes at greater risk of injury (those at a high level of play with a previous injury) with prevention programmes targeting the hip abductor and adductor muscles in conjunction with off and preseason sport-specific training.
What are the new findings
There has been an improvement in the quality (eg, larger sample size, employing multivariate statistical techniques) and level of evidence of studies investigating risk factors for groin injury in sport in the past 7 years.
There is level 1 and 2 evidence that previous groin injury, higher level of play, reduced hip adductor strength and lower levels of sport-specific training are associated with an increased risk of groin injury in sport.
Based on the work performed in the field, it is recommended that investigators turn their focus to high-quality randomised controlled trials targeting athletes at greater risk of groin injury in sport with prevention programmes targeting the hip abductor and adductor muscles in conjunction with off and preseason sport-specific training.
The authors would like to acknowledge the assistance of the University of Calgary, Faculty of Kinesiology librarian Alex Hayden as well as research assistants Lisa Loos, Leticia Janzen and Rhys Johnson.
Werner J,
Hagglund M,
Walden M, et al
. UEFA injury study: a prospective study of hip and groin injuries in professional football over seven consecutive seasons. Br J Sports Med 2009;43:1036–40. doi:10.1136/bjsm.2009.066944
Arnason A,
Sigurdsson SB,
Gudmundsson A, et al
. Risk factors for injuries in football. Am J Sports Med 2004;32(1 Suppl):5S–16S. doi:10.1177/0363546503258912
Crow JF,
Pearce AJ,
Veale JP, et al
. Hip adductor muscle strength is reduced preceding and during the onset of groin pain in elite junior Australian football players. J Sci Med Sport 2010;13:202–4. doi:10.1016/j.jsams.2009.03.007
Ekstrand J,
Walden M
. Epidemiology of muscle injuries in professional football (soccer). Am J Sports Med 2011;39:1226–32. doi:10.1177/0363546510395879
Anderson DD,
Chubinskaya S,
Guilak F, et al
. Post-traumatic osteoarthritis: improved understanding and opportunities for early intervention. J Orthop Res 2011;29:802–9. doi:10.1002/jor.21359
Ibrahim A,
Murrell GA,
Knapman P
. Adductor strain and hip range of movement in male professional soccer players. J Orthop Surg 2007;15:46–9.
Witvrouw E,
Danneels L,
Asselman P, et al
. Muscle flexibility as a risk factor for developing muscle injuries in male professional soccer players. A prospective study. Am J Sports Med 2003;31:41–6.
Eirale C,
Tol JL,
Whiteley R, et al
. Different injury pattern in goalkeepers compared to field players: a three-year epidemiological study of professional football. J Sci Med Sport 2014;17:34–8. doi:10.1016/j.jsams.2013.05.004
Engebretsen AH,
Myklebust G,
Holme I, et al
. Intrinsic risk factors for groin injuries among male soccer players: a prospective cohort study. Am J Sports Med 2010;38:2051–7. doi:10.1177/0363546510375544
Walden M,
Ekstrand J
. Previous injury as a risk factor for injury in elite football: a prospective study over two consecutive seasons. Br J Sports Med 2006;40:767–72. doi:10.1136/bjsm.2006.026609
. Injuries among male and female elite football players. Scand J Med Sci Sports 2009;19:819–27. doi:10.1111/j.1600-0838.2008.00861.x
Paajanen H,
Ristolainen L,
Turunen H, et al
. Prevalence and etiological factors of sport-related groin injuries in top-level soccer compared to non-contact sports. Arch Orthop Trauma Surg 2011;131:261–6. doi:10.1007/s00402-010-1169-1
O'Connor D
. Groin injuries in professional rugby league players: a prospective study. J Sports Sci 2004;22:629–36. doi:10.1080/02640410310001655804
Orchard J,
Wood T,
Seward H, et al
. Comparison of injuries in elite senior and junior Australian football. J Sci Med Sport 1998;1:83–8. doi:10.1016/S1440-2440(98)80016-9
Emery CA,
Meeuwisse WH
. Risk factors for groin injuries in hockey. Med Sci Sports Exerc 2001;33:1423–33. doi:10.1097/00005768-200109000-00002
Tyler TF,
Nicholas SJ,
Campbell RJ, et al
. The association of hip strength and flexibility with the incidence of adductor muscle strains in professional ice hockey players. Am J Sports Med 2001;29:124–8.
van Mechelen W,
Hlobil H,
Kemper HC
. Incidence, severity, aetiology and prevention of sports injuries. A review of concepts. Sports Med 1992;14:82–99. doi:10.2165/00007256-199214020-00002
Meeuwisse WH,
Tyreman H,
Hagel B, et al
. A dynamic model of etiology in sport injury: the recursive nature of risk and causation. Clin J Sport Med 2007;17:215–19. doi:10.1097/JSM.0b013e3180592a48
Bahr R,
Holme I
. Risk factors for sports injuries—a methodological approach. Br J Sports Med 2003;37:384–92. doi:10.1136/bjsm.37.5.384
Maffey L,
Emery C
. What are the risk factors for groin strain injury in sport? A systematic review of the literature. Sports Med 2007;37:881–94. doi:10.2165/00007256-200737100-00004
Liberati A,
Altman DG,
Tetzlaff J, et al
. The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate health care interventions: explanation and elaboration. PLoS Med 2009;6:1–28. doi:10.1371/journal.pmed.1000100
Holmich P
. Long-standing groin pain in sportspeople falls into three primary patterns, a "clinical entity" approach: a prospective study of 207 patients. Br J Sports Med 2007;41:247–52. doi:10.1136/bjsm.2006.033373
Downs S,
Black N
. The feasibility of creating a checklist for the assessment of the methodolical quality both of randomised and non-randomised studies of health care interventions. J Epidemiol Community Health 1998;52:377–84. doi:10.1136/jech.52.6.377
Howick J,
Phillips B,
Ball C, et al
. Oxford centre for evidence-based medicine: levels of evidence secondary Oxford centre for evidence-based medicine: levels of evidence 2009. http://www.cebm.net/oxford-centre-evidence-based-medicine-levels-evidence-march-2009/
Gillquist J
. The avoidability of soccer injuries. Int J Sports Med 1983;4:124–8. doi:10.1055/s-2008-1026025
Williams JGP
. Limitation of hip joint movement as a factor in traumatic osteitis pubis. Br J Sports Med 1978;12:129–33. doi:10.1136/bjsm.12.3.129
Cusi MF,
Juska-Butel CJ,
Garlick D, et al
. Lumbopelvic stability and injury profile in rugby Union players. NZ J Sports Med 2001;29:14–18.
Chalmers S,
Magarey ME,
Esterman A, et al
. The relationship between pre-season fitness testing and injury in elite junior Australian football players. J Sci Med Sport 2013;16:307–11. doi:10.1016/j.jsams.2012.09.005
Cowan SM,
Schache AG,
Brukner P, et al
. Delayed onset of transversus abdominus in long-standing groin pain. Med Sci Sports Exerc 2004;36:2040–5. doi:10.1249/01.MSS.0000147587.81762.44
Grote K,
Lincoln TL,
Gamble JG
. Hip adductor injury in competitive swimmers. Am J Sports Med 2004;32:104–8. doi:10.1177/0363546503258905
. Risk factors for lower extremity muscle injury in professional soccer: the UEFA Injury Study. Am J Sports Med 2013;41:327–35. doi:10.1177/0363546512470634
Holmich P,
Larsen K,
Krogsgaard K, et al
. Exercise program for prevention of groin pain in football players: a cluster-randomized trial. Scand J Med Sci Sports 2010;20:814–21. doi:10.1111/j.1600-0838.2009.00998.x
Jansen J,
Weir A,
Denis R, et al
. Resting thickness of transversus abdominis is decreased in athletes with longstanding adduction-related groin pain. Man Ther 2010;15:200–5. doi:10.1016/j.math.2009.11.001
Le Gall F,
Carling C,
Reilly T
. Biological maturity and injury in elite youth football. Scand J Med Sci Sports 2007;17:564–72.
Malliaras P,
Hogan A,
Nawrocki A, et al
. Hip flexibility and strength measures: reliability and association with athletic groin pain. Br J Sports Med 2009;43:739–44. doi:10.1136/bjsm.2008.055749
Morrissey D,
Graham J,
Screen H, et al
. Coronal plane hip muscle activation in football code athletes with chronic adductor groin strain injury during standing hip flexion. Man Ther 2012;17:145–9. doi:10.1016/j.math.2011.12.003
Nevin F,
Delahunt E
. Adductor squeeze test values and hip joint range of motion in Gaelic football athletes with longstanding groin pain. J Sci Med Sport 2014;17:155–9. doi:10.1016/j.jsams.2013.04.008
Farhart P,
Kountouris A, et al
. Pace bowlers in cricket with history of lumbar stress fracture have increased risk of lower limb muscle strains, particularly calf strains. J Sports Med 2010;1:177–82. doi:10.2147/OAJSM.S10623
Schick DM,
. Injury rates and profiles in female ice hockey players. Am J Sports Med 2003;31:47–52.
Steffen K,
Andersen TE, et al
. Self-reported injury history and lower limb function as risk factors for injuries in female youth soccer. Am J Sports Med 2008;36:700–8. doi:10.1177/0363546507311598
. The effectiveness of a preseason exercise program to prevent adductor muscle strains in professional ice hockey players. Am J Sports Med 2002;30:680–3.
Verrall GM,
Slavotinek JP,
Barnes PG, et al
. Hip joint range of motion restriction precedes athletic chronic groin injury. J Sci Med Sport 2007;10:463–6. doi:10.1016/j.jsams.2006.11.006
Viera AJ,
Garrett JM
. Understanding interobserver agreement: the kappa statistic. Fam Med 2005;37:360–3.
Ryan J,
DeBurca N,
Mc Creesh K
. Risk factors for groin/hip injuries in field-based sports: a systematic review. Br J Sports Med 2014;48:1089–96. doi:10.1136/bjsports-2013-092263
Freckleton G,
Pizzari T
. Risk factors for hamstring muscle strain injury in sport: a systematic review and meta-analysis. Br J Sports Med 2013;47:351–8. doi:10.1136/bjsports-2011-090664
DiFiori JP,
Benjamin HJ,
Brenner JS, et al
. Overuse injuries and burnout in youth sports: a position statement from the American Medical Society for Sports Medicine. Br J Sports Med 2014;48:287–8. doi:10.1136/bjsports-2013-093299
. Prevention of injuries among male soccer players: a prospective, randomized intervention study targeting players with previous injuries or reduced function. Am J Sports Med 2008;36:1052–60. doi:10.1177/0363546508314432
Glatthorn JF,
Berendts AM,
Bizzini M, et al
. Neuromuscular function after arthroscopic partial meniscectomy. Clin Orthop Relat Res 2010;468:1336–43. doi:10.1007/s11999-009-1172-4
Delahunt E,
Prendiville A,
Sweeney L, et al
. Hip and knee joint kinematics during a diagonal jump landing in anterior cruciate ligament reconstructed females. J Electromyogr Kinesiol 2012;22:598–606. doi:10.1016/j.jelekin.2012.02.009
Pietrosimone BG,
McLeod MM,
Lepley AS
. A theoretical framework for understanding neuromuscular response to lower extremity joint injury. Sports Health 2012;4:31–5. doi:10.1177/1941738111428251
Hall L,
Tsao H,
MacDonald D, et al
. Immediate effects of co-contraction training on otor control of the trunk muscles in people with recurrent low back pain. J Electromyogra Kinesiol 2009;19:763–73. doi:10.1016/j.jelekin.2007.09.008
Hodges PW,
Hoorn V,
Wrigley TV
. The relationship between muscle activation and rate of progression of cartilage loss in knee osteoarthritis. International Federation of Manipulative Physical Therapists Congress. Quebec City, Canada, 2012.
Tucker K
. Moving differently in pain: a new theory to explain the adaptation to pain. Pain 2011;152(3 Suppl):S90–8. doi:10.1016/j.pain.2010.10.020
Data supplement 1 - Online Appendix 1
Twitter Follow Jackie Whittaker at @jwhittak_physio
Contributors JLW and CAE were responsible for the conception and design of the study. JLW and CAE independently reviewed the literature. JLW extracted data from the included studies, while all four authors were involved in rating the literature. JLW was the primary author in preparing the manuscript however all authors contributed to the interpretation of the findings, critical revision of the manuscript and reviewed the document prior to submission.
Funding The Sport Injury Prevention Research Centres is supported by an International Olympic Committee Research Centre Award. JLW is funded through an Alberta Innovates Health Solutions Postdoctoral Clinician Fellowship. CAE holds a Professorship in Pediatric Rehabilitation Alberta Children's Hospital Foundation.
Provenance and peer review This paper was commissioned by the 1st World Conference on Groin Pain in Athletes, Doha, Qatar, November 2014; externally peer reviewed. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,119 |
Dr. Martens is een merk schoeisel, kleding en accessoires. Het schoeisel is ontwikkeld door dr. Klaus Märtens uit Duitsland. De laarzen en schoenen waren aanvankelijk populair bij politieagenten, postbodes en fabrieksarbeiders, later werden ze ook het favoriete schoeisel van skinheads, punks en grungers.
Het bedrijf staat sinds januari 2021 genoteerd aan de aandelenbeurs van Londen en is opgenomen in de FTSE 250-index.
Geschiedenis
Märtens was legerarts gedurende de Tweede Wereldoorlog. Tijdens een verlof ging hij skiën, waarbij hij gewond raakte aan zijn enkel. De gewone legerlaars zat hem daardoor ongemakkelijk, daarom ontwierp hij aangepast schoeisel voor zichzelf. Dit stond model voor de Dr. Martens laarzen: een veterlaars met een grove zool.
In 1947 startte Klaus Märtens in de buurt van München met de productie van zolen uit afgedankt rubber van de Duitse Luftwaffe. Later ging hij schoenen produceren. De zolen werden gemaakt uit epauletten en het leder voor de schoenen werd uit de lederen broeken van het officierenuniform gehaald.
In de jaren 50 waren de schoenen van Dr. Martens dankzij hun comfortabele zolen zeer populair bij dames boven de 40, goed voor 80% van de verkoopcijfers van het merk.
In 1959 kocht de Britse schoenenfabrikant R. Griggs Group Ltd. de patentrechten voor de productie van de schoenen in Groot-Brittannië.
Op 1 april 1960 rolde het eerste paar van model 1460, het populairste model van Dr. Martens, van de band. De neuskap van dit model was verstevigd met een stalen plaat, wat deze veterlaarzen de naam 'boxerhandschoenen voor voeten' bezorgde.
In de jaren 60 maakte de Britse politieke skinheadbeweging het model 1460 tot een deel van zijn imago.
Vanaf de jaren 70 werden Dr. Martens schoenen als een vast stijlonderdeel ook overgenomen door andere stromingen binnen de Britse jeugdcultuur, zoals punkers, goths, etc.
Tegen het einde van de 20ste eeuw had Dr. Martens al meer dan 3000 soorten van het model 1460 gefabriceerd.
In 2003 stond Dr. Martens door dalende verkoop op de rand van faillissement.
In mei 2018 heeft Dr. Martens zijn levenslange garantie stopgezet voor alle schoenen die na die datum werden verkocht.
In 2018 werden 10 miljoen paar Dr. Martens schoenen geproduceerd, waarvan slecht 1% in Groot-Brittannië. De 1460 is het meest gevraagde model gebleven.
In 2019 u maakte The Guardian zich in een publicatie ongerust over een dalende kwaliteit van de Dr. Martens-schoen. Het bedrijf reageerde dat er niets veranderd is sinds de productie naar Azië werd overgebracht.
Bronvermelding
Martens, Dr. | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,993 |
Ashiana Public School, Hamirpur prepare students for all challanges and obstacles that come in the way of success as well as to be a social person also. The courses of study as well as norms of achievement in every field are aimed at preparing our students for educational qualifications acceptable throughout the world.
We provide education from Nursery to 5th Medium in all the Subjects With education we arrange many types of co-curricular activities for students like sports, dance, music, painting competitions and many more time to time. In our campus we have well equipped labs like Home science, computer, physics, chemistry, biology, along with a well stocked library and an art and craft room, To provide advance. The school has ample space for playing different games like hockey, football, volleyball, basket ball, badminton, kho-kho etc. As it is said "A healthy mind rests in a healthy body" - students are initiated to take part in games. Competitions are held periodically on class basis and at inter-house level.
An Athletic Meet is also organised every year. Many students win medals up to state and national levels. We have a team of masters in their fields of education, passionate teachers with focus on innovation in education, who guide the students to get success and their aims and goals. Infact as it is said "A good teacher is like a candle - it consumes itself to light the way for others."
The school is like a family, in a family children are treated with love and devotion by their parents similarly in school teachers take care of the students where they are educated in a safe enviorment, with discipline and respect. The regular medical check-up of every student is ensured. The parents are expected to follow the advice given by the medical officer. First aid is given to the students free of cost, as and when needed, to treat ordinary physical disorder or temporary ailments during school hours. In case of any emergency during school hours, children are taken to the hospital and parents are informed as soon as possible. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,077 |
Q: Google Authorship on a multi-author blog? I hav been having some difficulties getting authorship set up for a multi-author blog. Everything appears to be set up correctly, but I am wondering if having multiple rel="author" tags on the home page is preventing the Google+ Profile of the main author from appearing in search results.
By default, the wordpress theme I am using uses 'the_author_posts_link()' when linking to other blog posts on the home page. and internal pages.(this automatically adds 'rel="author"' to the link).
Although, there is only 1 author profile who is actually linking to his Google+ Profile could have so many rel="author" tags be preventing his blog posts from displaying his Google+ Profile photo in the search results?
On the specific posts of the author who I am attempting to have Google authorship for, his link looks like this:
<a target="_blank" rel="author me" href="http://plus.google.com/xxxxxxxxxxx" title="Google+"></a>
this link appears in the author box at the end of the authors' post.
When testing a url of a post by the said author in the rich-snippets-tool, everything looks great. However, it doesn't appear that way in the search results. I have tried several configurations of this, including using plugins and having the author link in the .
Any advice or suggestions are much appreciated.
thanks.
A: I think it might take some time for the google to update this information to the search index.
As far i've seen the older posts on my blog (multi user) show the author information in a google search. The latest posts don't really get updated with that information.
A post from Feb 2013
Posts from a few days ago
A: FYI, Google has ended the authorship and image in SERPs program. Read https://support.google.com/webmasters/answer/6083347?hl=en
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,835 |
Produced by David Edwards, Anne Storer, and the Online
Distributed Proofreading Team at http://www.pgdp.net (This
file was produced from images generously made available
by The Internet Archive)
Transcriber's Note:
Text within {xx} following ^ = text inserted above the line.
[Illustration: The Purple Cow!]
Published by William Doxey, at the Sign of the Lark, San Francisco.
Copyright.
The Lark Book I., Nos. 1-12, with Table of Contents and Press Comments;
bound in canvas, with a cover design (The Piping Faun) by Bruce Porter,
painted in three colors. Price, 3.00, post-paid.
[Illustration: _THE LARK_
_Book 1 Nos. 1-12_]
_NOTES ON THE BIRTH OF THE LARK_
_Boston Herald._--"The pictures and rhymes in _The Lark_ rank with
the most remarkable things done for children since the days of Mother
Goose."
_Boston Budget._--"_The Lark_ is a reaction against the decadent spirit.
It is blithe, happy, full of the joy of life and the Greek within us--a
herald of the dawn of the new century."
_Boston Commonwealth._--"Everything in _The Lark_ is clever--some, we
may be permitted to add, cleverer than the rest."
_New York Critic._--"The faddists have produced some extraordinary
things in the way of literature, but nothing more freakish has made its
appearance in the last half-century than _The Lark_."
_New York Tribune._--"It is perhaps one-fourth a monthly periodical and
three-fourths an escapade. _The Lark_ ought really to be called 'The
Goose.'"
_New York Herald._--"The current number of _The Lark_ is, if possible,
more curious, more quaint, more preposterously humorous, and more
original than its predecessors. It is entirely unlike any other
publication."
_Richmond Times._--"We do not understand upon what the editor of
_The Lark_ bases anticipation of interest and consequent demand."
_Philadelphia Times._--"The young men who publish _The Lark_ have ideas
of their own. _The Lark_ is smart and funny in a way quite its own, and
it is also capable of serious flights and of musical notes clear enough
to be heard across the continent."
_Cincinnati Commercial Gazette._--"The worst thing about it being that
it is all too brief."
_Jersey City Chronicle._--"Every line in it is well worth perusal."
_St. Paul Globe._--"_The Lark_ partakes of the prevalent temper of life
on the Pacific Coast, where the don't-care mood of the West takes an
especially sunny and cheerful turn, and life looks a bigger joke than
elsewhere in the Union."
_St. Louis Mirror._--"_The Lark_ continues to be odd and ridiculous. Its
humor is quite unlike any other humor ever seen in this country. There
are good men with good pens working on _The Lark_."
_Kansas City Star._--"_The Lark_ seems to have attained a distinction
hitherto considered impossible in the unconventional. It seems really
original. It succeeds in holding in captivity the unexpected."
_Los Angeles: The Land of Sunshine._--"It is unlike anything nearer to
hand than 'Alice in Wonderland.'"
#Lark Posters.#--The full set of Eight Posters for THE LARK will be sent
post-paid for $2.00. The Lark Posters are printed from wooden blocks,
all but the first two having been cut by the artist.
May, 1895 _The Piping Faun_ Bruce Porter
Aug., 1895 _Mother and Child_ Florence Lundborg
Nov., 1895 _Mt. Tamalpais_ Florence Lundborg
Feb., 1896 _Robin Hood_ Florence Lundborg
May, 1896 _The Oread_ Florence Lundborg
Aug., 1896 _Pan Pipes_ Florence Lundborg
Nov., 1896 _Redwood_ Florence Lundborg
Feb., 1897 _Sunrise_ Florence Lundborg
_Published by_ WM. DOXEY, _at the Sign of the Lark, San Francisco._
CONTENTS
DEDICATION.
1. A LEGEND, Rare and Superfine,
Cribbed, some will say, from FRANKENSTEIN,
(It _is_ a little in that line).
2. MY FEET; a Memoir, with a Phase
Resembling some Equestrian Ways.
3. TH' INVISIBLE BRIDGE; a sort of Fable,--
Please understand, if you're able.
4. THE RUNAWAY TRAIN; a weird Creation
Of Fancy and Imagination,
Meant for the Rising Generation.
5. On CITY FLORA, semi-culled
By one whose Fame was somewhat dulled.
6. ASTONISHMENT; depicting how
Peculiar is the Verdant Bough.
7. The PURPLE COW'S projected Feast;
Reflections on a Mythic Beast
That's quite Remarkable, at least.
8. MY HOUSE, and how I make MY BED;
A Nocturne for a Sleepy-Head.
9. On DIGITAL EXTREMITIES;
A Poem (and a gem it is!)
10. THE GOOP; constructed on a Plan
Beyond the Intellect of Man.
11. PARISIAN NECTAR for the Gods;
A little thick--but what's the odds?
12. THE FLYING HOUSE; a Narrative
Of Sanity comparative,
And nothing much declarative.
(_Permission of S. F. Examiner._)
13. The Story of the GIANT HORSE;
'T is quite improbable, of course.
14. _WHAT_ SMITH _TRIED TO_ BELIEVE; a Study
That will appeal to anybuddy.
15. The TOWEL AND THE DOOR,--ah well!
I'll not attempt the Tale to tell.
16. The TOWEL AND THE DOOR again!
The Story's told--is it in vain?
17. The FOOTLESS FEAT of Mrs. Box
_Posteaque, fiat Nox!_
18. And now, allow the PURPLE COW
To make her Bow.
TO THE
READERS OF "_THE LARK_"
WHO HAVE LAUGHED
THEY KNEW NOT WHY,
THESE INARTISTIC ABERRATIONS
ARE GRATEFULLY DEDICATED.
GELETT BURGESS
_THE PECULIAR HISTORY OF THE CHEWING-GUM MAN._
O Willie, an' Wallie, an' Huldy Ann,
They went an' built a big CHEWIN'-GUM MAN:
It was none o' your teenty little dots,
With pinhole eyes an' pencil-spots;
But this was a terribul big one--well,
'T was a'most as high as the Palace Hotel!
_It took 'em a year to chew the gum!!_
And Willie he done it all, 'cept some
That Huldy got her ma to chew,
By the time the head was ready to do.
* * * * *
Well, Willie he chewed it for days 'n' days;
They brung it to him in gret big drays;
An' fast as he got it good an' soft,
Then Wallie he come and carried it oft.
Then he'd roll it into a gret big ball,
_An' he made a-more'n a MILLION in all!_
Then Huldy Ann she spanked 'em flat
An' pinched an' poked, an' the like o' that,
Till she got it inter a gret big hunk--
My! didn't Huldy have the spunk!
And then she sliced one end half-way
To make the laigs ('cause they never stay
When you stick 'em on in a seprit piece--
Seems like the ends was made o' grease);
And she slit an arm right up each side,--
I couldn't a done it if I'd a tried!
O' course, her brothers they helped her, though,
An' rolled the arms an' laigs out, so
They all was smooth with roundin' bends
An' _chopped_ the fingers inter the ends!
An' when their mother had chewn the head,
She went an' _stuck_ it on, instead!
An' then, when the man was almost done,
They had an awful lots o' fun.
A-walkin' down his stummick was best
To make the buttons onter his vest!
They struck big cartwheels in him for eyes;
His eyes was both tremendous size;
His nose was a barrel--an' then beneath
They used a ladder, to make his teeth!
An' when he was layin' acrost the street
Along come their daddy, as white 's a sheet,--
He was skeert half outer his wits, I guess,
An' he didn't know whatter make o' the mess,--
But Huldy she up an' begun to coax
To have him down town, to skeer the folks!
So her dad he grabbed him offen the street,
An' Willie an' Wallie they took his feet,
An' they dragged him clean down to the Cogswell fountain,
An' stood him up as big as a mountain!
You'd orter seen him a-standin' there,
A-straddlin' Market street in the air!
Well, he stood up straight for a week 'n' a half
An' the folks, Gee! didn't they yell 'n' laff:
The boys clum up his laigs quite bold--
The gum was so soft they got good hold;
The cars run under him day an' night,
An' the people come miles to see the sight!
Well, after he'd stayed as stiff 's a post,
With his head on top o' the roofts almost,
The sun come outer the fog one day
An'--well, I guess you can see the way
That gret big feller begun to melt;--
_Imagine how Willie and Wallie felt!_
For first he cocked his head out some,
An' when the heat got inter the gum
He slowly waved his arms ahead
An' slanted forred, just like he was dead!
[Illustration]
An' all day long he leaned an' bent
Till all expected he would have went
An' pitched right over. They roped the street
To keep the crowd away from his feet.
I tell yer he was a sight; my soul!
Twicet as high as a telegraft pole,
Wavin' his arms an' slumpin' his feet
An' a-starin' away down Market street.
Then, what did I tell yer--that blame old head
Their mother had made a-seprit, instead,--
It fell right off an' squashed a horse!
('T was so soft, it didn't _kill_ him, o' course.)
When his hands got so they touched the ground
A hundred policemen they come around;
They stuck a cable-car to his feet,
An' one to his head, a goin' up street,
An' then they pulled him opposite ways,
An' they pulled him for days 'n' days 'n' days,
An' they drored him out so slim an' small
That he reached a _mile 'n' a half_, in all.
An' that was the end o' the CHEWIN'-GUM MAN
For Willie, an' Wallie, an' Huldy Ann.
They come along with an ax next day,
An' chopped him up, and guv him away.
[Illustration]
[Illustration]
My Feet they haul me 'round the House;
They hoist me up the Stairs;
I only have to steer them and
They ride me everywheres.
[Illustration]
I'd never dare to walk across
A Bridge I could not see,
For quite afraid of falling off
I fear that I should be!
_ADULT'S DEPARTMENT:_
Oh, Willie and Wallie and Pinkie Jane!
They run away with a Railroad Train!
'T was Wallie got up the ridiculous plan,--
'T was most as good as the Chewin'-Gum Man!
Wallie is terribul funny--My!
He can make up a face that would make you die,
An' when Pinkie Jane come down to the city
He tried to show off, for she's awful pretty.
So they all went over across the Bay,
To have a picnic, and spend the day.
At Sixteenth Street they got off the cars
A-grinnin' an' giggling so,--My Stars!
A Enormus Crowd begun to collect,
But nobuddy knew just what to expect.
Then up the track come a little spot,
An' nearer and nearer and NEARER it got,
And Willie and Wallie and Pinkie Jane
Stood right in the road of the Overland Train!!!
The folks on the platform begun to yell,
"_Look out!--get off!!_" an' the engine bell
[Illustration]
_THE RUNAWAY TRAIN_:
Was ringin' like mad,--but them children stood
As calm as if they was made of wood!
And a great big fat man yelled,--"_Oh Golly!
For Heaven's sakes, just look at Wallie!_"
As the train came thunderin' down the rail,
The wimmin all turned terribul pale.
But Wallie he stood there, stiff 's a soldier,
An' then (you remember what I told yer)
He made up a horribul face,--and whack!
He SCARED THE ENGINE RIGHT OFF'N THE TRACK!
An' the train jumped forreds an' squirmed around,
A-wrigglin' an' jigglin' over the ground;
And all the people they had to git,
For the blame old engine it had a fit!
But when the train got onto the track,
Them children they clum right onto its back,
And they tickled it so that all to once
It gave 'em a lot of shivers an' grunts,
And it humped itself way up in the air,
And p'raps it didn't give them a scare!
[Illustration]
_AN IMPOSSIBLE EPIC_:
Then it puffed an' puffed, a-faster an' faster,
While Wallie sat there like an old school-master,
A-drivin' that train till, I tell you what!
You no idea what a nerve he's got!
Willie he held on to Wallie, an' Jane
Held onto Willie with might and main.
Then they hitched along, like an old inch-worm,
With now a spazzum, and then a squirm;
But Willie and Wallie and Pinkie Jane,
They soon got sick o' that Railroad train!
But when they crawled to the last end car
To jump on the ground, where it wasn't far,
They got a heap worse off, instead,
For that nasty train, it stood on its head!
An' they all yelled, "Telegraft Huldy Ann,
And make her come as quick as she can.
We can't get off. Oh, hurry up, please!
What would we do if the thing should sneeze?"
[Illustration]
_SEQUEL TO THE CHEWING-GUM MAN_
I tell yer them children was in a fix
While that mad engine was doin' his tricks.
But the messenger-boy found Huldy Ann,
An' she said, "I'm glad that I ain't a man!
I'll show 'em how!" an' she crossed the Bay,
An' she see in a wink where the trouble lay.
An' she said, "You go, an' you telegraft back
For a load o' candy to block the track!"
An' when they sent it, she piled it high
With chocolate caramels, good ones,--My!
Peppermint drops and cocoanut cream,
Till it looked too good for a Christmas dream!
And the sun it melted and finished the job
Into one great elegant sticky gob!
So the train run into it lickety-split,
An' the cow-catcher stuck, when the engine hit,--
An' the tail o' the train flew up and threw
Them children into that caramel goo!
They fell clear in,--way over their head,
But Ann eat 'em out, an' sent 'em to bed!
[Illustration]
[Illustration]
There is a Theory some deny,
That Lamp Posts once were three foot high,
And a Little Boy was terrible strong,
And he stretched 'em out to 'leven foot long!
[Illustration]
I picked some Leaves from off a Tree,
And then I nearly Fainted:
For somehow it Astonished me
To find they'd All been Painted!
[Illustration]
I never saw a PURPLE COW, I never HOPE to see one;
But I can tell you, anyhow, I'd rather SEE than BE one!
[Illustration]
My House is made of Graham Bread,
Except the ceiling 's made of White;
Of Angel Cake I make my Bed;
I eat my Pillow every night!
[Illustration]
I'd rather have Fingers than Toes;
I'd rather have Ears than a Nose;
And as for my Hair,
I'm glad it's all there,
I'll be awfully sad when it goes!
[Illustration]
Now you are what I call a GOOP!
A Co-tangent harmonious Loop
You appear to be facing due South
But O what have you done with your Mouth?
[Illustration]
Many People seem to Think
Plaster o' Paris good to Drink:
Though conducive unto Quiet
I prefer another Diet!
[Illustration]
THE:FLYING:HOUSE
Written and Illustrated by GELETT:BURGESS
O Willie an' Wallie, you better believe,
They had a circus on Christmas Eve
With Huldy Ann an' Pinkie Jane--
The folks imagined they'd went insane!
Them twins had an awfully narrow shave--
They nearly was killt, for they wouldn't behave!
Huldy's a winner! She hatched the scheme
On the day before Christmas; an' that there team--
That Willie an' Wallie--they worked like mad--
You've no idea what a time they had!
'Twas the day before Christmas, at half-past three,
When Huldy she up an' she says, says she:
"You Willie an' Wallie, you go in the yard
An' get that windmill--it won't be hard--
An' bring it an' put it on top of the house,
An' don't make no more noise than a mouse!
'For I know something I won't tell,
Nine little <DW65>s in a peanut shell!'"
Well, the twins they knew when she said that,
Huldy wa' n't talkin' much through her hat.
So they worked an' they tugged for more 'n an hour,
'Till they got that windmill off'n the tower;
An' they hauled it up to the roof with ropes,
Way on the ridgepole, 'tween the <DW72>s.
[Illustration]
[Illustration]
They was almost dead, it tired 'em so,
An' Will druv a splinter into his toe!
An' all this time both Pinkie Jane
An' Huldy was workin' with might an' main,
A-shuttin' the doors, an' the windows too,
An' stoppin' up cracks where the leaks come through.
An' when it was tight, she slipped inside
An' turned the gas on good an' wide!
An' she screamed, "Look out that you don't get smothered:
Climb up on the roof where I won't be bothered!"
When the house filled up with the gas inside,
It trembled an' jiggled from side to side;
An' when the gas filled it good an' full
The ole foundations began to pull;
Then Huldy she pushed it a little mite,
An' the house riz up in the air all right!
An' it riz an' riz like a ole balloon.
An' Ann got aboard of it none too soon;
For it flew away off up into the sky
With her holdin' on by her hands--Oh my!
But she clum on top, an' you'd oughter have seen
Them workin' that wheel like a flyin' machine!
Well, after they'd flew an hour or so
They came to a mountain all covered with snow,
An' there on the top they happened to see
A enermous great big Christmas tree!
Then Huldy steered 'em over the top,
An' they let down an anchor to make 'em stop;
An' Willie an' Wallie they yelled with glee,
An' jumped right into that Christmas tree!
They let down a ladder for them two girls
That didn't darst jump for spoilin' their curls!
They was toys an' games an' wagons an' dolls,
All trimmed with tinsel an' fol-de-rols!
For Santa Claus had just drove away,
An' Wallie he said that he seen the sleigh!
Well, when they'd eat all the candy they could,
They loaded their house with things up good.
(But they hurried for fear that the old man'd come back
An' catch 'em an' give 'em a larrupin' whack!)
Then they got on the roof, an' they cut the string
An' away they flew like everything!
[Illustration]
The twins worked the wheel an' Huldy steered,
An' Pinkie clung tight--she was awfully skeered:
They got back home at half-past six,
But, oh! they got into a nawful fix!
For just as they sunk the house gave a lurch
An' they landed right on top of a church!
An' they punched a hole through the roof with the steeple,
To the great amazement of all of the people!
An' the toys fell out of that house in the air,
An' all the children in the town was there.
So every one got a present again
'Cept Willie an' Wallie an' Huldy an' Jane--
An' it served 'em right, don't you think? because
They'd stolen the presents from Santa Clause.
[Illustration]
[Illustration]
Once there was a GIANT HORSE,
That walked through all the Town,
A-stepping into all the Roofs,
And Smashing Houses down!
[Illustration]
WHAT:SMITH:TRIED:TO:BELIEVE _refused by_ ST NICHOLAS, BIBELOT,
NEW:REVIEW, POLYNESIAN:MONITOR _and_ SAN FRANCISCO:CLIMAX
Well, I come home late that night, near one o'clock, I reckon, and I
undressed in the dark as per usual. When I gut into bed I thot it felt
as tho sumbuddy hed bin there, and when I kicked out my leg sure enough
there was sumbuddy there. Well, I thot Rats, what's the difference; I'll
go to sleep, it's only a man. But I kinder could'nt sleep, so I got up
and lit a cigaroot, and I saw the feller that was in bed with me wos
dead. Well, I thot Rats, what's the difference, he wont git over to my
side of the bed anyway; so I turned over and went to sleep. Well, I
fired my cigaroot in ther paper-basket and went to sleep. Well, after
a while I thot I smealed smoke, and it wasn't cigaroot smoke, but the
basket was all afire, and burning like a editor's soul after death.
Well, I thot Rats, what's the difference. Well, it looked so bright and
comfortable I thot I'd get up and read. By this time one corner of the
room was goin' like 4 o'clock, and it was nice and warm. After I'd read
about ten minits, it got so hot I cuddent stand it, and I got up and
went into ther next room. Well, I thot Rats, what's the difference.
Well, in about a hour there was a big crowd outside of the house, and
they was all yellin' Fire to beat the band. I looked out er winder.
Jump, says the fireman, and I jumped. Then I walked off, and a feller
says, says he, "You blame fool, you've bruk yer leg." Well, I thot Rats,
what's the difference?
[Illustration]
The Towel hangs upon the Wall,
And, somehow, I don't care at all!
The Door is open;--I must say
I rather fancy it that Way!
[Illustration]
,llaW eht nopu sgnah lewoT ehT
!lla ta erac t'nod I, wohemos,dnA
yas tsum I--;nepo si rooD ehT
!yaW taht ti ycnaf rehtar I
_THE SOLES OF THE UNFORTUNATES._
Likkery had but one leg[A] when I married him.[B] I did not realize what
this meant {it meant 41 right-foot shoes [for he was extravagant (and I
was economical[C]) to a degree] in his dressing closet} until he died.
{I could not bear to throw
{them away.
{
{The clerks asserted that all
{their one-legged right-footed
I could not get rid of them {customers wore
{large sizes.[D]
{
{There were not weddings
{enough to throw them all
{after the carriages.
Chapter II.
[Sidenote: Mr. Silk _WAS_ a two-legged gentleman.]
My second marriage WOULD have been happy, but my husband met with a
distressing accident, which necessitated an amputation ^{of his right
leg} of his wrong leg. So the collection increased.
In spite of all my precautions, Mr. Silk's shoes would often be left
pointing toward the bed.[E] How I suffered! At last Mr. Silk died. The
day after the funeral, I made a procession of all the shoes--
ORDER:
1. Patent leathers
2. Brogans
3. Bluchers (small)
4. Bluchers (large)
5. Tan shoes
6. Slippers (carpet)
7. Congresses
8. Riding boots
9. Pumps
Sixty-two right-foot shoes, ^{toe to heel,} they reached from my
bedroom[F] to the stairs.
I was in despair when a small-footed man named Box proposed to me. I
looked at his feet and accepted him. (I was sure the shoes would fit.)
* * * * *
As soon as he was asleep I approached his prostrate form (my axe was
sharp {I ground it myself} and my mind was set).
Sixty-two soles inspired me.[G] I struck the blow!--Then the HORROR of
my deed seized me. The rest is too awful!
NOTE: I had cut off the wrong foot!
[A] Left leg.
[B] Fool that I was.
[C] For he could get a pair at the same price as a single shoe.
[D] Likkery wore No. 3's.
[E] It is a common superstition among children that this encourages bad
dreams.
[F] Bay-window.
[G] I was determined they should at last be worn out.
[Illustration]
Ah, yes, I wrote the "Purple Cow"--
I'm Sorry, now, I wrote it;
But I can tell you Anyhow
I'll Kill you if you Quote it!
The Lark Book II., Nos. 13-24, with Table of Contents and EPILARK; bound
in canvas, with cover design (Pan Pipes) by Florence Lundborg, painted
in three colors. Price, 3.00, post-paid.
[Illustration: Book II--Nos. 13-24]
_NOTES ON THE PASSING OF THE LARK_
_Literary Review._--"Its ways were ways of pleasantness, and all its
paths were peace. It had no enemies and all its friends were true ones.
We see it go with a real regret and a feeling that we could have better
spared a better paper."--CAROLYN WELLS.
_New York Times._--"Regret moderately deep and thoroughly sincere will
be felt all over the country, at the announcement that _The Lark_ has
ceased publication. A considerable number of people could see no humor
and less meaning in its songs, but thousands of others had keener eyes
and ears, and looked and listened with delight."
_Cincinnati Commercial Tribune._--"_The Lark_ is dead, and the _Epilark_
has come and gone, leaving behind them only a haunting echo of joyous
song and a love of living delicious to contemplate."
_St. Paul Daily Globe._--"But the mood in which we turn the Japanese
pages of the last _Lark_ is anything but flippant. It is something to
have known youth and gayety, enthusiasm and a bravery which flies in the
face of day, and now--something to have lost them. _The Lark_ has lived
and now dies well, and, to some at least, the time of its irregular
appearance will no longer be a red-letter day."
_The Philosopher._--"And now _The Lark_ announces its end. It was the
freshest, purest breath of air that ever blew across the atmosphere of
letters."
_London Times._--"So unique in literature and illustration, we are sorry
to note that its publication is to be suspended. The bound volumes for
the two years it has been running deserve a place in the libraries of
all lovers of the odd and advanced in literature."
_Paragraphs._--"No more shall its cool notes delight the tree-tops, and
no longer may we follow in the footsteps of Vivette. It is a pity, of
course; but what can you expect? Larks must be fed, and--no one thinks
of feeding them."
_Trenton Tribune._--"Its clever foolery shows how big a void was created
when _The Lark_ decided to sing no more. _The Lark_ was the one new
thing in junior magazinedom that did not outlive its welcome."
_St. Louis Mirror._--"It smacked of Robert Louis Stevenson. It was
'Alice in Wonderland' in picture. It was art through a crazy
looking-glass. It was the realism of nonsense. The whole country laughed
at the strange pictures with the brilliantly unintelligible verses. But
much of it was not understood of the people who need diagrams. _The
Lark_ was always too high in the blue for the many; but for those who
might mount with him or to him--for those the magazinelet was published.
Those enjoyed it; and now they regret it--for _The Lark_ is no more. It
was so original that its death is its only unoriginality."
#The Lark Almanac for 1899:#
Being a collection of vagaries from THE LARK, with original designs by
Porter Garnett; uniform in size with "The Purple Cow." Price, 50c.
_Published by_ WM. DOXEY, _at the Sign of the Lark, San Francisco_
"Who'll be the Clerk!"
"I!" said _THE LARK_.
End of the Project Gutenberg EBook of The Purple Cow!, by Gelett Burgess
*** | {
"redpajama_set_name": "RedPajamaBook"
} | 4,656 |
I sent my 23 january of documents, but it was still not active account..
I sent my documents to my e-mail address validation-ie@soyoustart.com.
Do I need to send to another email address?
I sent my information to you in email but my membership has not been activated. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,227 |
Q: Class with navigation property and with or without foreign key Let's say I have the following classes, auto generated by Entity Framework, that have an association:
public class Parent()
{
public int ParentID { get; set; } // PK
public int ChildID { get; set; } // FK
public string Description { get; set; }
public Child Child { get; set; } // Navigation property
}
public class Child()
{
public int ChildID { get; set; } // PK
public Parent Parent { get; set; } // Navigation property
}
As you can see, the Parent class contains a foreign key property to the Child class.
Now, let's say I want to retrieve some data from my database with LINQ. What I would do is create a custom class (model) so that I don't have to work with the auto generated classes (I can easily add more properties, methods,...).
public class ChildModel()
{
public int ChildID { get; set; }
// More properties/methods
}
When creating the ParentModel class, I have two ways of creating this class:
A class with both the property ChildID and a navigation property Child.
public class ParentModel()
{
public int ParentID { get; set; }
public int ChildID { get; set; }
public ChildModel Child { get; set; }
}
Or a class with only a navigation property Child and no ChildID property.
public class ParentModel()
{
public int ParentID { get; set; }
public ChildModel Child { get; set; }
}
With the second method, I always have to create an extra class when I only need the ChildID, with the second method I don't have to. But when I do create the ChildModel, I have to initialize both ChildIDs so that I don't run into any problems later.
What would be the best way to create my model classes? With or without the foreign key? Are there any advantages/disadvantages when using one of the two methods described above?
A: Using both childId and Child property seems to be the worst option because of potential mistakes / inconsistencies.
Having only the Navigation property seems best option for several reasons:
*
*If the relationship is optional you have a clear indication that there is no child by setting the property to null. In case you have only childId, you need to set it to some magic number like -1 or 0, which is less elegant I suppose, or make it int? type which isn't a better solution either.
*With Navigation property you can implement several features like automatic lazy loading.
*Your objects stay abstract to the actual storage and relationship implementation.
A: Microsoft recommends using both, although your example looks like you have the foreign key on the wrong class. I would have expected the Child class to be dependant on the Parent. The parent class doesn't need the foreign key because it's not dependant on its children.
To quote Microsoft:
In addition to navigation properties, we recommend that you include foreign key properties on the types that represent dependent objects.
https://msdn.microsoft.com/en-nz/data/jj679962.aspx
public class ParentModel()
{
public int ParentID { get; set; }
//navigation property
public ChildModel Child { get; set; }
}
public class ChildModel()
{
public int ChildID { get; set; }
// More properties/methods
//foreign key
public int ParentID { get; set; }
//navigation property
public ParentModel Parent { get; set; }
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,489 |
{"url":"http:\/\/sourceforge.net\/p\/kile\/mailman\/message\/4522347\/","text":"## [Kile-devel] Inserting labels in \\ref command\n\n [Kile-devel] Inserting labels in \\ref command From: Hooman Javidnia - 2003-07-31 05:35:03 Attachments: Message as HTML Hi there, Is there any way to insert one of the previously defined labels to a \\ref command? I remember in WinEdt when you write a \\ref command, a window pops up and shows all the defined labels and you can select from the list. Is there any similar functionality in Kile? Best, Hooman \n\n [Kile-devel] Inserting labels in \\ref command From: Hooman Javidnia - 2003-07-31 05:35:03 Attachments: Message as HTML Hi there, Is there any way to insert one of the previously defined labels to a \\ref command? I remember in WinEdt when you write a \\ref command, a window pops up and shows all the defined labels and you can select from the list. Is there any similar functionality in Kile? Best, Hooman \n Re: [Kile-devel] Inserting labels in \\ref command From: Jeroen Wijnhout - 2003-07-31 06:37:44 On Thursday 31 July 2003 07:15, Hooman Javidnia wrote: > Hi there, > Is there any way to insert one of the previously defined labels to a > \\ref command? I remember in WinEdt when you write a \\ref command, a > window pops up and shows all the defined labels and you can select from > the list. Is there any similar functionality in Kile? > Best, > Hooman Yes, select \\ref or \\pageref in the toolbar (a drop - down box, the first entry is label) or in the LaTeX menu. best, Jeroen \n [Kile-devel] other questions! From: Hooman Javidnia - 2003-07-31 07:01:01 Every time I run pdflatex and want to view the PDF output, the setting of the viewer is reset. Isn't there anyway to define a zoom level and stick to it? Another problem is the forward and backward search capability. Every time I run pdflatex, the viewer goes to the beginning of the file. The same holds true with latex, too. Third problem is related to Quick Build. Whenever I try to use it, the first page of the document appears in the viewer and the sand clock works, but I can't navigate to other pages. I don't know if it is bug, or there is something wrong in my settings. Again thanks for the great software! \n [Kile-devel] Re: other questions! From: Jeroen Wijnhout - 2003-07-31 08:28:43 On Thursday 31 July 2003 09:01, Hooman Javidnia wrote: > Every time I run pdflatex and want to view the PDF output, the setting > of the viewer is reset. Isn't there anyway to define a zoom level and > stick to it? No, not yet. > Another problem is the forward and backward search capability. Every > time I run pdflatex, the viewer goes to the beginning of the file. The > same holds true with latex, too. Forward and inverse search is only supported when you use a DVI viewer. Please use KDVI to view the output if you want to use forward and inverse search. > Third problem is related to Quick Build. Whenever I try to use it, the > first page of the document appears in the viewer and the sand clock > works, but I can't navigate to other pages. I don't know if it is bug, > or there is something wrong in my settings. This appears to be a kghostview bug, since I've encountered it while using kghostview separately many times. I can't reliably reproduce it, can you? best, Jeroen","date":"2015-08-31 13:47:53","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.942072331905365, \"perplexity\": 2098.4986326260955}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-35\/segments\/1440644066017.21\/warc\/CC-MAIN-20150827025426-00139-ip-10-171-96-226.ec2.internal.warc.gz\"}"} | null | null |
About American Recycling
American Recycling | Paper Recycling | Metal Recycling | Plastic Recycling | Recycling Systems Serving Central California's Paper, Metal, and Plastic Recycling Needs.
Paper Making and Recycling
– March 9, 2011Posted in: Paper
Over the centuries, paper has been made from a wide variety of materials such as cotton, wheat straw, sugar cane waste, flax, bamboo, wood, linen rags, and hemp. Regardless of the source, you need fiber to make paper. Today fiber comes mainly from two sources — wood and recycled paper products.
Paper mills differ in their processes based on the source of fiber used and the end product produced. There are three basic types of mills:
Pulp mills
Recycled paper processing mills
Mills that use both recycled and virgin fiber
Pulp mills make pulp, a mixture of cellulose fibers and water used as the basis of all paper products. Pulp is made in several ways, depending on the type of paper being produced. Wood chips, which come from logs or from residues from sawmills, furniture manufacturers and other sources, can be chemically or mechanically separated into individual wood fibers in a process called pulping.
In chemical pulping, the most common pulping process in the United States, the wood chips are "cooked" in a digester at an elevated pressure with an appropriate solution of chemicals to dissolve the lignin (the "glue" that binds the fibers in the wood) and allow the cellulose fiber bundles in the wood to separate into individual cellulose fibers. Since chemical processing is gentle on the cellulose fiber, chemical pulps tend to have longer fibers and make strong paper such as printing and writing papers and paperboard.
In mechanical pulping, chemicals are not used to remove the lignin in the wood chips. Instead, wood chips are pressed against a grinder that physically separates the fibers. Mechanical pulps have shorter fiber lengths and produce papers which do not require as much strength — such as newsprint.
After the fibers have been separated, the mill washes and decontaminates the pulp. To produce a white paper product, the mill must bleach the pulp to remove color associated with remaining residual lignin. Typically, the bleaching chemicals (such as chlorine dioxide, oxygen, or hydrogen peroxide) are injected into the pulp and the resulting mixture is washed with water.
The bleached or unbleached wood pulp — which at this point is in a very dilute slurry — is then pumped onto rolling wire screen mats that vibrate slightly to allow water to drain out of the pulp and to help the fibers interlock into sheets. By varying the amount of pulp pumped onto the rolling mats, the speed of the mat, and the speed of the vibrations, paper with different qualities and properties can be achieved. The sheets then pass through a long series of rollers that press out any remaining moisture, followed by steam-heated drums that dry the paper. Finally, a process called calendaring polishes the sheets and smoothes out wrinkles. Large sheets of paper are wound onto rolls and can then be cut to produce a variety of paper products.
Recycled paper processing mills use paper as their feedstock. The recovered paper is combined with water in a large vessel called a pulper that acts like a blender to separate fibers in the paper sheets from each other. The resultant slurry then passes through screens and other separation processes to remove contaminants such as ink, clays, dirt, plastic and metals. The amount of contaminants that are acceptable in the pulp depends upon the type of paper being produced. Mechanical separation equipment includes coarse and fine screens, centrifugal cleaners, and dispersion or kneading units that break apart ink particles. Deinking processes use special systems aided by soaps or surfactants to wash or float ink and other particles away from the fiber.
Recovered fiber can be used to produce new paper products made entirely of recovered fiber (i.e. 100 percent recycled content) or from a blend of recovered and virgin fiber. Fiber cannot, however, be recycled endlessly. It is generally accepted that a fiber can be used five to seven times before it becomes too short (as a result of repulping and other handling) to be useable in new paper products. Recovered paper with long cellulose fibers (such as office paper) has the greatest flexibility for recycling as it can be used to produce new paper products that use either long or short fibers. Recovered paper with short cellulose fibers (such as newspaper) can only be recycled into other products that use short cellulose fibers. For this reason, recovered paper with long fibers is generally of higher value than recovered paper with short fiber.
Some mills use both recycled and virgin fiber to make paper. These mills are typically set up to process virgin wood into pulp and incorporate recovered fiber by buying bales of recycled pulp which are added to the wood pulp. Customer demand, environmental awareness, and economics are some of the reasons mills add recovered fiber to their products.
Source: US EPA
Recycling paper instead of making it from new material generates 74 percent less air pollution and uses 50 percent less water.
Please call us for a free waste stream analysis at (209) 537-4410.
Paper Facts
One ton of corrugated recycled saves 9 million BTUs of energy, 2872 lbs CO2 equiv. in greenhouse gasses, 8904 gallons of wastewater, and 1304 lbs of solid waste.*
a record-high 57.4 percent of the paper consumed in the U.S. was recovered for recycling in 2008.
more than 80 percent of OCC (old corrugated containers) was recovered for recycling in 2008.
*Environmental impact estimates were made using the Environmental Defense Fund Paper Calculator. For more information visit http://www.papercalculator.org.
Paper Resources
Environmental Defense Fund Paper Calculator
EPA Paper Recycling Information
American Forest & Paper Association
We offer free waste stream consultations to help determine the best equipment at the lowest price for our customers. In many cases, the systems we install will pay for themselves with increased revenue, decreased labor, and automated functions. If you have Modesto recycling or Ceres recycling we want to hear from you. Please call us for a free waste stream analysis at (209)537-4410
Copyright American Recycling. All Rights Reserved. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,957 |
{"url":"http:\/\/math.stackexchange.com\/questions\/177\/will-this-procedure-generate-random-points-uniformly-distributed-within-a-given","text":"# Will this procedure generate random points uniformly distributed within a given circle? Proof?\n\nConsider the task of generating random points uniformly distributed within a circle of a given radius $r$ that is centered at the origin. Assume that we are given a random number generator $R$ that generates a floating point number uniformly distributed in the range $[0, 1)$.\n\nConsider the following procedure:\n\n1. Generate a random point $p = (x, y)$ within a square of side $2r$ centered at the origin. This can be easily achieved by:\n\na. Using the random number generator $R$ to generate two random numbers $x$ and $y$, where $x, y \\in [0, 1)$, and then transforming $x$ and $y$ to the range $[0, r)$ (by multiplying each by $r$).\n\nb. Flipping a fair coin to decide whether to reflect $p$ around the $x$-axis.\n\nc. Flipping another fair coin to decide whether to reflect $p$ around the $y$-axis.\n\n2. Now, if $p$ happens to fall outside the given circle, discard $p$ and generate another point. Repeat the procedure until $p$ falls within the circle.\n\nIs the previous procedure correct? That is, are the random points generated by it uniformly distributed within the given circle? How can one formally [dis]prove it?\n\nBackground Info\n\nThe task was actually given in Ruby Quiz - Random Points within a Circle (#234). If you're interested, you can check my solution in which I've implemented the procedure described above. I would like to know whether the procedure is mathematically correct or not, but I couldn't figure out how to formally [dis]prove it.\n\nNote that the actual task was to generate random points uniformly distributed within a circle of a given radius and position, but I intentionally left that out in the question because the generated points can be easily translated to their correct positions relative to the given center.\n\n-\n@jacob surely you mean -pi and +pi or 0 and 2pi? And that was exactly what I was thinking :) You have to jump through hoops to do this in Cartesian co-ords, while it is trivial in polar co-ordinates. \u2013\u00a0 workmad3 Jul 20 '10 at 23:18\n@workmad3 yeah, -pi and +pi. But I deleted it as my suggestion wasn't uniform and I couldn't work out how to make it uniform. \u2013\u00a0 Jacob Jul 21 '10 at 17:42\nI wasn't sure how to get uniformity either, which is why I was looking at suggesting polar co-ords in a comment rather than a complete answer :) \u2013\u00a0 workmad3 Jul 21 '10 at 22:00\nOf course, in step 1 you can simply set $x=2r\\cdot R-r$, $x=2r\\cdot R-r$ instead of generating the signs separately. \u2013\u00a0 Hagen von Eitzen Sep 8 '12 at 7:13\n\nYes this will work; it's called rejection sampling.\n\nEven better is to generate a point in polar coordinates though: pick \u03b8 from [0, 2\u03c0) and r2 from [0, R2] (ie. multiply R by the square-root of a random number in [0, 1] - without the square-root it is non-uniform).\n\n-\n+1 for nailing down \"rejection sampling.\" I don't think that I would've been able to find the term myself. Still, I can't figure out how to establish, from the rejection sampling procedure, that the uniform distribution of the generated points follows from the uniform distribution of the random number generator. \u2013\u00a0 Yaser Sulaiman Jul 21 '10 at 18:17\n@Yaser: Every non-rejected point trivially has equal probability of being chosen; that is the definition of uniform. The only thing we lose is a guarantee of how long a number will take to generate. \u2013\u00a0 BlueRaja - Danny Pflughoeft Nov 10 '11 at 22:34\n@BlueRaja-DannyPflughoeft Nice answer. Deserves +50 bounty and an upvote from my side. Will reward tomorrow. \u2013\u00a0 Ahaan S. Rungta Dec 23 '13 at 12:23\n\nI'm not saying that your method is the simplest one to obtain uniformly distributed sample points in the disk $D$ of radius $r>0$, but it is certainly correct.\n\nLet $Q:=[{-r},r]^2$ and assume that the points generated in step 1. of your procedure are uniformly distributed in $Q$. For any set $A\\subset Q$ denote by $|A|$ the area of $A$ and by $P(A)$ the probability that a sample point $p$ falls on the set $A$. Then one has the well known formula about switching conditionals: $$P(A\\,|\\,D)={P(A)\\>P(D\\,|\\,A)\\over P(D)}\\ .$$ Now when $A\\subset D$ then $P(D\\,|\\,A)=1$, and by assumption $$P(A)={|A|\\over|Q|},\\quad P(D)={|D|\\over|Q|}\\ .$$ It follows that $$P(A\\,|\\,D)={|A|\\over|D|}\\qquad\\forall \\> A\\subset D\\ ,$$ as it should be.\n\n-\n\nI'm going to use $P(a,b)$ for probability of x = a, and y = b.\n\n$P(a,b) = P[x = |a|]P[y = |b|] * 1\/4$ for any a, b inside the square.\n\nTherefore you are picking a coordinate uniformly inside the square.\n\nNow the problem reduced to the following:\n\nPick a element uniformly in a set A, then discard ones that are not B (B is a subset of A). Is it the same as pick a element uniformly in the set $A \\cap B = B$?\n\nI think this is true, I don't know if the following is a formal proof(haven't done probability in a while). please point out my mistakes.\n\nP(B) is the event that a element in B is picked. P(A) is the event that a element in A is picked.\n\nPick a x uniformly, we have b \\in B is P(x=b|B), it's obviously uniform.\n\nThe conditional probability P(B|A) = P(A \\cap B)\/P(A) = P(B)\/P(A) = P(B)\n\nP(A) = 1, w\/e you pick are in A.\n\nP(x=b| (B|A)) = P(x=b|B), which is uniform.","date":"2015-01-31 09:07:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8885197639465332, \"perplexity\": 266.22382619872263}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-06\/segments\/1422118108509.48\/warc\/CC-MAIN-20150124164828-00230-ip-10-180-212-252.ec2.internal.warc.gz\"}"} | null | null |
Pastor Lewie was born and raised in Pennsylvania before deciding to move out West to work on a ranch. Growing up in a family of faith, he eventually accepted Christ as his Savior. Graduate of Montana Bible College in Bozeman, MT. He is husband to Kaydee Kelley and father of 7 children. Pastor Lewie has been at Malta Community Church since 2014. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,933 |
package com.miicaa.detail;
import java.util.ArrayList;
import android.os.Bundle;
import android.os.Handler;
import android.os.Looper;
import android.view.LayoutInflater;
import android.view.View;
import android.view.View.OnClickListener;
import android.view.ViewGroup;
import android.widget.ImageView;
import android.widget.TextView;
import com.miicaa.detail.DetailProgressFragment.PrgressDoPeople;
import com.miicaa.home.R.layout;
import com.miicaa.home.data.business.matter.MatterInfo;
import com.miicaa.home.data.net.ResponseData;
import org.androidannotations.api.BackgroundExecutor;
import org.androidannotations.api.view.HasViews;
import org.androidannotations.api.view.OnViewChangedListener;
import org.androidannotations.api.view.OnViewChangedNotifier;
public final class DetailProgressFragment_
extends DetailProgressFragment
implements HasViews, OnViewChangedListener
{
private final OnViewChangedNotifier onViewChangedNotifier_ = new OnViewChangedNotifier();
private View contentView_;
public final static String OPERATE_GROUP_ARG = "operateGroup";
public final static String DATA_ID_ARG = "dataId";
public final static String M_INFO_ARG = "mInfo";
private Handler handler_ = new Handler(Looper.getMainLooper());
@Override
public void onCreate(Bundle savedInstanceState) {
OnViewChangedNotifier previousNotifier = OnViewChangedNotifier.replaceNotifier(onViewChangedNotifier_);
init_(savedInstanceState);
super.onCreate(savedInstanceState);
OnViewChangedNotifier.replaceNotifier(previousNotifier);
}
public View findViewById(int id) {
if (contentView_ == null) {
return null;
}
return contentView_.findViewById(id);
}
@Override
public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState) {
contentView_ = super.onCreateView(inflater, container, savedInstanceState);
if (contentView_ == null) {
contentView_ = inflater.inflate(layout.matter_do_progress, container, false);
}
return contentView_;
}
private void init_(Bundle savedInstanceState) {
OnViewChangedNotifier.registerOnViewChangedListener(this);
injectFragmentArguments_();
afterInject();
}
@Override
public void onViewCreated(View view, Bundle savedInstanceState) {
super.onViewCreated(view, savedInstanceState);
onViewChangedNotifier_.notifyViewChanged(this);
}
public static DetailProgressFragment_.FragmentBuilder_ builder() {
return new DetailProgressFragment_.FragmentBuilder_();
}
@Override
public void onViewChanged(HasViews hasViews) {
nodo = ((ImageView) hasViews.findViewById(com.miicaa.home.R.id.nodoLayout));
doingView = ((TextView) hasViews.findViewById(com.miicaa.home.R.id.matterDoing));
gridview = ((MyGridView) hasViews.findViewById(com.miicaa.home.R.id.grid));
done = ((ImageView) hasViews.findViewById(com.miicaa.home.R.id.doneLayout));
headName = ((TextView) hasViews.findViewById(com.miicaa.home.R.id.head_name));
headImg = ((ImageView) hasViews.findViewById(com.miicaa.home.R.id.head_img));
completeView = ((TextView) hasViews.findViewById(com.miicaa.home.R.id.matterComplete));
listview = ((DetailProgressListView) hasViews.findViewById(com.miicaa.home.R.id.progressList));
todo = ((ImageView) hasViews.findViewById(com.miicaa.home.R.id.todoLayout));
noDoView = ((TextView) hasViews.findViewById(com.miicaa.home.R.id.matterNodo));
{
View view = hasViews.findViewById(com.miicaa.home.R.id.matterDoing);
if (view!= null) {
view.setOnClickListener(new OnClickListener() {
@Override
public void onClick(View view) {
DetailProgressFragment_.this.todoClick();
}
}
);
}
}
{
View view = hasViews.findViewById(com.miicaa.home.R.id.matterNodo);
if (view!= null) {
view.setOnClickListener(new OnClickListener() {
@Override
public void onClick(View view) {
DetailProgressFragment_.this.nodoClick();
}
}
);
}
}
{
View view = hasViews.findViewById(com.miicaa.home.R.id.matterComplete);
if (view!= null) {
view.setOnClickListener(new OnClickListener() {
@Override
public void onClick(View view) {
DetailProgressFragment_.this.doneClick();
}
}
);
}
}
init();
}
private void injectFragmentArguments_() {
Bundle args_ = getArguments();
if (args_!= null) {
if (args_.containsKey(OPERATE_GROUP_ARG)) {
operateGroup = args_.getString(OPERATE_GROUP_ARG);
}
if (args_.containsKey(DATA_ID_ARG)) {
dataId = args_.getString(DATA_ID_ARG);
}
if (args_.containsKey(M_INFO_ARG)) {
mInfo = ((MatterInfo) args_.getSerializable(M_INFO_ARG));
}
}
}
@Override
public void resetShow() {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.resetShow();
}
}
);
}
@Override
public void showPeople(final int position, final View v) {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.showPeople(position, v);
}
}
);
}
@Override
public void noshowPeople(final int position, final View v) {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.noshowPeople(position, v);
}
}
);
}
@Override
public void toRemind() {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.toRemind();
}
}
);
}
@Override
public void refreshGrid(final ArrayList<PrgressDoPeople> infos) {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.refreshGrid(infos);
}
}
);
}
@Override
public void doneList() {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.doneList();
}
}
);
}
@Override
public void numToDo(final ProgressTongjiInfo info) {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.numToDo(info);
}
}
);
}
@Override
public void showGrid(final ImageView v) {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.showGrid(v);
}
}
);
}
@Override
public void setProgressCountListener(final OnTabCountListener tabListener) {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.setProgressCountListener(tabListener);
}
}
);
}
@Override
public void refreshlist(final ArrayList<ProgressListInfo> infos) {
handler_.post(new Runnable() {
@Override
public void run() {
DetailProgressFragment_.super.refreshlist(infos);
}
}
);
}
@Override
public void todoList() {
BackgroundExecutor.execute(new BackgroundExecutor.Task("", 0, "") {
@Override
public void execute() {
try {
DetailProgressFragment_.super.todoList();
} catch (Throwable e) {
Thread.getDefaultUncaughtExceptionHandler().uncaughtException(Thread.currentThread(), e);
}
}
}
);
}
@Override
public void jsonToCache(final ResponseData data) {
BackgroundExecutor.execute(new BackgroundExecutor.Task("", 0, "") {
@Override
public void execute() {
try {
DetailProgressFragment_.super.jsonToCache(data);
} catch (Throwable e) {
Thread.getDefaultUncaughtExceptionHandler().uncaughtException(Thread.currentThread(), e);
}
}
}
);
}
@Override
public void nodoList() {
BackgroundExecutor.execute(new BackgroundExecutor.Task("", 0, "") {
@Override
public void execute() {
try {
DetailProgressFragment_.super.nodoList();
} catch (Throwable e) {
Thread.getDefaultUncaughtExceptionHandler().uncaughtException(Thread.currentThread(), e);
}
}
}
);
}
public static class FragmentBuilder_ {
private Bundle args_;
private FragmentBuilder_() {
args_ = new Bundle();
}
public DetailProgressFragment build() {
DetailProgressFragment_ fragment_ = new DetailProgressFragment_();
fragment_.setArguments(args_);
return fragment_;
}
public DetailProgressFragment_.FragmentBuilder_ operateGroup(String operateGroup) {
args_.putString(OPERATE_GROUP_ARG, operateGroup);
return this;
}
public DetailProgressFragment_.FragmentBuilder_ dataId(String dataId) {
args_.putString(DATA_ID_ARG, dataId);
return this;
}
public DetailProgressFragment_.FragmentBuilder_ mInfo(MatterInfo mInfo) {
args_.putSerializable(M_INFO_ARG, mInfo);
return this;
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,384 |
{"url":"https:\/\/geniebook.com\/tuition\/secondary-1\/maths\/percentage","text":"Study S1 Mathematics Maths - Percentage - Geniebook\n\n# Percentage\n\nIn this chapter, we will be discussing the below-mentioned topics in detail:\n\n\u2022 Fractions, Ratio, Decimals and Percentage\n\u2022 Convert a non-integer percentage to fraction\/ decimal and vice versa\n\u2022 Percentages greater than $$100\\%$$ or less than $$1\\%$$\n\u2022 Percentage of quantities\n\u2022 Percentage of a quantity\n\u2022 Express one quantity as a percentage of another quantity\n\u2022 Compare two quantities by percentage\n\u2022 Percentage change\n\n## Fractions, Ratio, Decimals and Percentage\n\nLet\u2019s understand this with the help of some examples:\n\n#### Decimals\n\n\\begin{align} \\frac{2}{5} \\end{align} $$2:5$$ \\begin{align} \\frac{2}{5} \\times 100 = 40\\% \\end{align} \\begin{align*} 40\\% &= \\frac{40}{100}\\\\ \\\\ &= 0.4 \\end{align*}\n\\begin{align} 25\\% &= \\frac{25}{100}\\\\\\\\ &= \\frac{1}{4} \\end{align} $$1:4$$ $$25\\%$$ $$0.25$$\n\\begin{align} \\frac{90}{100} = \\frac{9}{10} \\end{align} $$9:10$$ \\begin{align} 0.9 \\times 100\\% = 90\\% \\end{align} $$0.9$$\n\n## Percentages Greater Than $$100\\%$$ or Less Than $$1\\%$$\n\nLet\u2019s understand this with the help of some examples:\n\nQuestion 1:\n\nWithout using a calculator, express each of the following percentages as a fraction.\n\n1. $$105\\%$$\n2. $$0.04\\%$$\n\nSolution:\n\n1.\n\n\\begin{align*} 105\\% &= \\frac{105}{100}\\\\ &= \\frac{21}{20}\\\\ &= \\frac{11}{20} \\end{align*}\n\n1.\n\n\\begin{align*} 0.04\\% &= \\frac{0.04 \u00d7 100}{100 \u00d7 100}\\\\ &= \\frac{4}{10000}\\\\ &= \\frac{1}{2500} \\end{align*}\n\nQuestion 2:\n\nWithout using a calculator, express each of the following percentages as a decimal.\n\n1. $$274\\%$$\n2. $$0.38\\%$$\n\nSolution:\n\n1.\n\n\\begin{align*} 274\\% &= \\frac{274}{100}\\\\ \\\\ &= 2.74 \\\\ \\\\ \\end{align*}\n\n1.\n\n\\begin{align*} 0.38\\% &= \\frac{0.38}{100}\\\\ \\\\ &= 0.0038\\\\ \\end{align*}\n\n## Percentage Of A Quantity\n\nLet\u2019s understand this with the help of some examples:\n\nQuestion 3:\n\nA box contains $$60$$ balls, of which $$16$$ are red.\n\n1. If $$40\\%$$ of the balls are green, find the number of green balls.\n2. The rest of the balls in the box are yellow.\n\nIf $$70\\%$$ of the yellow balls are removed, find the number of yellow balls left.\n\nSolution:\n\n1. Number of green balls\\begin{align} = \\frac{40}{100} \\times 60\\\\ \\end{align}\n\n$$\\qquad\\qquad\\qquad\\qquad\\qquad= 24 \\;balls$$\n\nOR\n\nNumber of green balls $$= 0.4 \u00d7 60$$\n\n$$\\qquad\\qquad\\qquad\\qquad\\quad\\;\\;= 24 \\;balls$$\n\n1. Number of yellow balls at first\\begin{align*} &= 60 \\;\u2013 16 \\;\u2013 24 \\end{align*}\n\n$$\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad= 20$$\n\nNumber of yellow balls remaining $$= \\frac{30}{100} \u00d7 20$$\n\n$$\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad= 6 \\;balls$$\n\nOR\n\nNumber of yellow balls remaining $$= 0.3 \u00d7 20$$\n\n$$\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\quad= 6 \\;balls$$\n\n## Comparing two quantities by percentage\n\nLet\u2019s understand this with the help of some examples:\n\nQuestion 4:\n\nShop $$A$$ sold $$225$$ out of $$1000$$ vinyl records in January. Shop $$B$$ sold $$400$$ out of $$1500$$ vinyl records in the same month. Which shop had a higher proportion of sales in January?\n\nSolution:\n\nPercentage of sales by Shop\\begin{align} A=\\frac{225}{1000} \\times 100 \\end{align}\n\n\\begin{align} \\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad=22.5\\% \\end{align}\n\nPercentage of sales by Shop\\begin{align} B= \\frac{400}{1500} \\times 100 \\end{align}\n\n\\begin{align} \\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad= 26 \\frac{2}{3}\\% \\end{align}\n\nShop $$B$$ had a higher proportion of sales in January.\n\nContinue Learning\nBasic Geometry Linear Equations\nNumber Patterns Percentage\nPrime Numbers Ratio, Rate And Speed\nFunctions & Linear Graphs 1 Integers, Rational Numbers And Real Numbers\nBasic Algebra And Algebraic Manipulation 1 Approximation And Estimation\nResources - Academic Topics\nPrimary\nPrimary 1\nPrimary 2\nPrimary 3\nPrimary 4\nPrimary 5\nPrimary 6\nSecondary\nSecondary 1\nEnglish\nMaths\nBasic Geometry\nLinear Equations\nNumber Patterns\nPercentage\nPrime Numbers\nRatio, Rate And Speed\nFunctions & Linear Graphs 1\nIntegers, Rational Numbers And Real Numbers\nBasic Algebra And Algebraic Manipulation 1\nApproximation And Estimation\nScience\nSecondary 2\nSecondary 3\nSecondary 4","date":"2023-02-01 22:04:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 10, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 1.0000098943710327, \"perplexity\": 7393.677440190616}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764499953.47\/warc\/CC-MAIN-20230201211725-20230202001725-00319.warc.gz\"}"} | null | null |
Q: Laravel 9 edit route with {id} parameter returns Not Found (404) despite being defined Below is an example of the route definition in my routes/web.php file.
<?php
use Illuminate\Support\Facades\Route;
use App\Http\Controllers\WidgetController;
Route::controller(WidgetController::class)->name('widgets.')->prefix('widgets')->group(function () {
Route::get('{id}/{slug}', 'show')->name('show');
Route::get('create', 'create')->name('create')->middleware('auth');
Route::post('store', 'store')->name('store')->middleware('auth');
Route::get('{id}/edit', 'edit')->name('edit')->middleware('auth');
Route::post('update', 'update')->name('update')->middleware('auth');
});
All the routes listed work fine except for one.
Route::get('{id}/edit', 'edit')->name('edit')->middleware('auth');
For whatever reason, it works completely fine when it's written like this:
Route::get('{id}', 'edit')->name('edit')->middleware('auth');
or this:
Route::get('{id}//edit', 'edit')->name('edit')->middleware('auth');
With "Route::resource", the default would be the first "edit" route. However, I get a 404 when defining it like that. My associated controller method is written like this:
public function edit($id)
{
// Rest of code here
}
Could it be that Laravel is mistaking "edit" as a second parameter? But that doesn't really make much sense considering it's the default for the resource method.
A: Try putting
Route::get('{id}/edit', 'edit')->nam
Above
Route::get('{id}/{slug}'
Since {slug} could be anything it's more then likely getting executed first. I would suggest putting that last.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,789 |
\section*{Appendix}
\section{Procedural Clutch Generation}
\label{ap:procedural_clutch}
ES clutches are defined by the following variables: a \emph{starting point}, a \emph{surface direction}, and a \emph{length and width}. The \emph{starting point} is defined using barycentric coordinates $(u_e, v_e)$ on a particular element $e$ of the garment mesh. The \emph{surface direction} is a vector in barycentric space $(\overrightarrow{u_e}, \overrightarrow{v_e})$ from the starting point to another barycentric coordinate on the same element $e$.
We start by tracing out a piece-wise linear path of the desired length in the direction of $(\overrightarrow{u_e}, \overrightarrow{v_e})$ until an edge is encountered, whereby the vector is converted to Euclidean space $\in\mathbb{R}^{3n}$ and rotated to lie on the surface of the next triangle $e_i$. This is repeated until the length of the vector is exhausted. Two endpoints are produced, one at the starting point, and one at the last barycentric coordinate of where the path finishes.
From this path, a mesh is triangulated by creating center vertices at edge intersections and projecting side vertices to the left and right of the path based on $\overrightarrow{e_n} \times \overrightarrow{p_{xyz}}$, the cross product of the element normal and the path direction in world space respectively. This is scaled by the $width$ parameter. The resulting mesh has rest vertices $\mathbf{q}=(\mathbf{q}_1,\ldots,\mathbf{q}_m)\in\mathbb{R}^{3n}$ and $\bar{\mathbf{q}}=(\bar{\mathbf{q}}_1,\ldots,\bar{\mathbf{q}}_m)\in\mathbb{R}^{3n}$ when deformed.
We give special treatment to the side vertices of the two endpoints by walking them in an orthogonal direction to the main path using the same walking algorithm outlined above.
The endpoints $q^c$ of the clutch mesh (3 at each end) are connected to the garment mesh using simple quadratic penalty functions, which allows for firm attachment. The full path walking and meshing algorithm is fast enough to work in real-time, allowing for rapid user placement and re-positioning of ES clutches.
{\vfill\pagebreak}
\section{Garment-on-Body Model}
\label{ap:sim_model}
As our garment model, we use a compressible neo-Hookean material model \cite{bonet_wood_2008} adapted with a relaxed energy under wrinkling as in \cite{vechev2022cdkg}. This allows the garment to wrinkle under compression without producing geometric artifacts. This results in the garment energy $E_\mathrm{garment}(\mathbf{x}, d)$, which is a function of the garment design $d$, and the deformed nodal positions $\mathbf{x}$. We similarly convert the discrete body mesh to a continuous implicit signed distance field \cite{oztireli2009feature}, resulting in the energy $E_\mathrm{body}(v, \mathbf{x})$, which pushes back on the garment vertices $\mathbf{x}$ away from the body. This allows the garment to smoothly slide on top of the body and to lift-off from its surface. To attach the garment to the body in specific areas, we introduce a simple coupling potential, $E_\mathrm{attach} = \frac{1}{2}k(x^c-x^v_c)^T(x^c-x^v_c)$, attracting elements of the garment mesh $x^c$ to corresponding elements $v_c$ on the body mesh. As the garment mesh is initialized from the SMPL mesh, for more accurate simulation, we subdivide the garment mesh until it has 16x the resolution of the base SMPL template mesh.
\section{On-Body Topology Optimization}
\label{ap:onbody_tpo}
To design passive reinforcement structures, Vechev et al. use a bi-directional evolutionary structural optimization (BESO) algorithm \cite{huang2007convergent, huang2009bi} to solve the constrained optimization problem with a single objective,
\begin{equation}
\label{eq:BESOObjective}
\begin{split}
\mathbf{d}^* = \arg\max_{\mathbf{d}} \quad E_\mathrm{garment}(x^*, \mathbf{d}) \\
\textrm{s.t.} \quad \sum_e{A^e} d^e=A^*\ ,\quad \mathbf{f}(x^*)= \mathbf{0} .
\end{split}
\end{equation}
The goal of this formulation is to find an optimal per-element material assignment $\mathbf{d}^*$ that maximizes the energy of the garment in its equilibrium state $\mathbf{x}^*$ while satisfying constraints on force equilibrium, $\mathbf{f}(x^*)= \mathbf{0}$, and material budget, $\sum_e{A_e} d_e=A^*$. The strain energy of the garment is defined per element as
\begin{equation}
\label{eq:GarmentEnergy}
E_{\mathrm{garment}} = \sum_e t^e A^eW_\mathrm{garment}^e(x^*, d^e)\ ,
\end{equation}
where $W_\mathrm{garment}^e$ is the elemental strain energy density, and $t^e, A^e$ are the thickness and area of the element respectively.
\section{Example Applications}
We show four applications enabled by the ability of active kinesthetic garments to selectively and dynamically engage clutches with a single design.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/applications.png}
\caption{Applications in (a) Workplace Training, (b) Posture Correction, (c) Resistance Training, and (d) VR Gaming.}
\label{fig:applications} \vspace{-.25cm}
\end{figure}
\paragraph*{Workplace Training}
When picking up a virtual box, we activate all ES clutches on the shirt to provide stability to the upper-body, preventing the arms from going through the box, and preventing the user from overly bending their back. More complex motion control could also provide further training and guidance in combination with a complex control loop (i.e. using body pose as an input).
\paragraph*{Posture Correction}
Bad posture is a very common problem when sitting at a desk, and many posture correcting shirts already exist to help this issue. However, only active kinesthetic garments can periodically allow the user to go into a slouching posture on demand, in addition to keeping other limbs completely unrestricted (i.e. elbow).
\paragraph*{Resistance Training}
Multiple clutches can be selectively activated to resist a target motion, the upper clutch in the case of arm extension, and the lower clutch in the case of arm flexion. The opposing clutch is meanwhile disabled, to prevent full arm-locking. This shows how a single garment can be re-configured at run-time for resisting multiple motions, potentially encompassing a user's entire workout.
\paragraph*{VR Gaming}
VR immersion can be increased significantly by providing physical forces when users make contact with the world. In this game, a user practices hitting tennis balls out of the air, and only the upper back clutch is activated on contact, noting that the elbow clutch remains off and does not prevent natural elbow bending during such sports movements.
\section{Discussion and Future Work}
Our user study results indicate that automatically-designed active kinesthetic garments were able to have a significant impact on user motion, whereas the manually designed counterparts could not meet this threshold, indicating the need for automated methods to assist designers in such tasks.
\paragraph{Emergent Structural Properties}
We found in our evaluation three emergent structural properties: 1) no connecting material is isolated from the main structure (no disparate island) 2) all active components are at junctures of connecting material, and 3) overlapping, yet distinct load paths are created for each specific motion. When comparing designs using our dual-objective directly to the single compliance minimization objective in \cite{vechev2022cdkg} (b), we find that these same properties do not emerge (See Fig. \ref{fig:structural_properties}). Each property plays an important role --- for example, if clutches are not at junctures, then their activation will have no effect on the user. Similarly, unbalanced load paths and islands of disconnected material may degrade performance for particular motions and comfort respectively. Users on the other hand performed well in terms of connecting clutches, but struggled to balance load paths, leading to very poor performance in particular motions.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/structural_properties.png}
\caption{Emergent structural properties for the multi-motion shirt designed with dual-objective minimization (a) vs single compliance minimization from \cite{vechev2022cdkg} (b).}
\label{fig:structural_properties} \vspace{-.25cm}
\end{figure}
\paragraph{Limitations}
The main work of the designer in our tool is in the manual placement of ES clutches. As the number of active components and motions grows, the requirement for manual clutch placement may become more and more challenging. Our method can be extended to optimize for ES clutch placement, thereby freeing designers from this task, potentially increasing the relative efficiency of the design. Our method is also limited to a simple mode of activation, where clutches are either all active or inactive. However, clutch activations can be controlled individually and continuously through voltage input that affect the degree of resistance. Accounting for these degrees of freedom during design could further improve efficiency and allow for more targeted resistance to selected motions.
While our active kinesthetic garments are fully wearable and mobile, they do not have any sensing capabilities. Integrating sensing could be done via capacitive sensors, which could be optimized based on the same strain-maximization principle used for connecting clutches.
Our study was limited to only six male participants and the type of feedback collected was mainly quantitative. Our method could be used to create garments for female users and even \emph{personalized} garments by simply changing the $\beta$ and gender parameters in the SMPL/STAR models. Richer VR interaction opportunities can be explored in the future by moving beyond simple button presses and object intersections, for example, by integrating body-pose sensing into the control loop.
\section{Conclusion}
We presented a computational approach for automatic design of active kinesthetic garments that block user-specified body motion on demand. As our core technical contribution, we cast the design of reinforcing structures that connect and anchor individual clutches as an on-body topology optimization problem and introduced a novel objective term that encourages maximum resistance of the garment when clutches are active while minimizing interference with body motion when they are inactive. Our experiments indicate that our designs are highly effective and consistently and significantly outperform user-created designs.
The structure optimization techniques developed here have the potential to be useful in the routing and placement of other types of active components such as actuators and sensors. By laying out a theoretical and algorithmic basis for this central problem, we hope that our work will serve as a step toward computational design of highly integrated multi-modal wearable interfaces in the future.
\section{Evaluation}
We conduct a multi-faceted evaluation of our method showing results for different types of motions and garments in simulation, a mechanical force study, and a VR pointing task.
\subsection{Automatic Designs}
We show a range of designs produced by our method for a variety of motions and garment types. For all experiments, we use a common rest pose with the body in an A-pose, and sample from a set of motions that include \emph{Arms Forward, Arms Raise, Arm Flexion, Arm Extension, Bend Forwards} (see Fig.\ref{fig-single-motions}). Three garments are designed using our tool to cover a variety of body sites: a short-sleeve shirt, an arm-sleeve, and a long-sleeve shirt. All clutches are placed manually on the garments, typically over high strain energy areas of the garments (see Fig. \ref{fig-system}a).
We set the following standard BESO parameters for all experiments: evolutionary rate $ER = 1.5\%$, maximum material added per iteration $AR = 1.5\%$, material interpolation $p=1.6$. Similarly, we set the material budget to $A^*= 15\%$ for all examples except for arm flexion and extension, where we use $A^*$ = 20\%. As our primary metric, we use the \emph{relative energy density}
\begin{equation}
\rho(\gamma,\mathbf{d}) = \frac{E_\mathrm{garment}(x^*(\gamma,\mathbf{d}),\mathbf{d})\cdot A_\mathrm{dense}}
{E_\mathrm{garment}(x^*(\gamma,\mathbf{1}),\mathbf{1})\cdot A_\mathrm{opt}} \ ,
\end{equation}
i.e., the ratio between energy density for the optimized and fully dense designs.
As the optimization progresses, we expect to see a widening gap in this metric between active and inactive clutch states (see Fig. \ref{fig-evolutionary-progress} for a visualization).
\paragraph*{Single-Motion Designs}
We begin by showing results for the single motion cases of our method. We target Arm Flexion with a single (8cm) clutch on the elbow, and Arm Extension also with a single (8cm) clutch on the inside of the forearm. We show two separate results in Fig. \ref{fig-single-motions} a, and b. Relative to the fully dense design, we see that energy density \emph{increases} to 1.14 for flexion, and 1.74 for extension when clutches are active. When clutches are inactive, relative energy density \emph{decreases} to 0.34 and 0.54, respectively.
Next, we target single motions on the upper body using three clutches of 15cm length. Fig. \ref{fig-single-motions} shows results for Arms Forward, Arms Raise, and Bend Forwards, with increases in relative energy density of 2.13, 1.51, and 2.47 respectively. For deactivated clutches, we observe that relative energy density decreases to 0.48, 0.66, and 0.73 for each design.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/single_motion}
\caption{Single-Motion designs for (a) Arm Flexion, (b) Arm Extension, (c) Arms Forwards, (d) Arms Raise, and (e) Bend Forwards. Color coding indicates energy density. }
\label{fig-single-motions} \vspace{-.25cm}
\end{figure}
\paragraph*{Multi-Motion Designs}
The ability to resist multiple motions with a single design is an important step towards programmable active kinesthetic garments. We used our method to create three such designs, starting with an arm sleeve design (Fig. \ref{fig-multi-motion-sleeve}) that combines Flexion and Extension. It uses the same 20\% material budget as in the single motion designs, but now this material must be distributed to balance performance for two distinct motions. The optimized design achieves relative energy densities of 0.88 and 1.27 for Flexion and Extension, respectively, which is 77\% and 73\% of the corresponding single-motion designs. For perspective, when evaluating the single-motion designs for Flexion/Extension on the Extension/Flexion motion, the relative efficiency is only 2\%/5\%. These results are not unexpected as Flexion and Extension are orthogonal motions such that designs optimized for only one of them are ineffective for the other one.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/multiple_motions_sleeve_arm.png}
\caption{Multi-motion design for simultaneously optimized for (a) Arm Flexion and (b) Arm Extension. This design effectively integrates the single motion designs of Fig. \ref{fig-single-motions} into an intertwined structure (c). }
\label{fig-multi-motion-sleeve} \vspace{-.25cm}
\end{figure}
Our second design is a shirt that combines three upper body motions as shown in Fig. \ref{fig-multi-motion-shirt}.
Many of the features observed in the single-motion versions can be seen here, with clutches linking disconnected reinforcements. It is worth noting that each of these motions leads to a distinct load path (light green/yellow) running through at least one of the clutches. We also compare the performance of the multi-motion design to the single-motion versions. As can be seen in Table. \ref{tbl:shirt-designs-comparison}, the multi-motion design is within 83\%, 72\%, and 65\% as efficient as the single-motion designs, and yet using the same material budget. The performance of the single-motion designs on motions for which they were not optimized is, again, significantly lower.
Additionally, for each motion we show the progress plots of the evolutionary optimization in Fig. \ref{fig-evolutionary-progress}. As our automatic design method removes material, we see a clear separation in relative energy density for active and inactive states for all three motions. In the \emph{inactive} mode, the relative energy densities of the garment for each motion are \emph{decreased} by 0.62, 0.72, and 0.5, showing that our method is able to consistently achieve its minimization objective.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/multiple_motions_shirt.png}
\caption{Active kinesthetic shirt designed for the three motions: (a) Arms Forwards, (b) Arms Raise, and (c) Bend Forwards. Strain energy density is shown in color-coding with increasing intensity from \textit{dark blue} to \textit{red}.}
\label{fig-multi-motion-shirt} \vspace{-.25cm}
\end{figure}
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/multiple_motions_shirt_plots.png}
\caption{Progress of the evolutionary optimization algorithm for the Shirt Design for (a) Arms Forwards, (b) Arms Raise, and (c) Bend Forwards. }
\label{fig-evolutionary-progress} \vspace{-.25cm}
\end{figure}
\begin{table}[h]
\begin{tabular}{ p{2.75cm} p{1.0cm} p{1.0cm} p{1.0cm} p{1.0cm} }
\hline
\multirow{2}{*}{ Evaluated On} & \multicolumn{4}{c}{Optimized For } \\
& Forwards & Raise & Bend & All \\ \hline
\rule{0pt}{3ex}Arms Forwards & 2.13 & 0.46 & 0.34 & 1.77 \\
Arms Raise & 0.62 & 1.51 & 0.14 & 1.08\\
Bend Forwards & 0.35 & 0.81 & 2.47 & 1.60\\ \hline
\end{tabular}
\caption{Comparison of garments optimized for a single motion against a garment optimized for all three motions. A higher number corresponds to an increase in relative energy density when clutches are active.}
\label{tbl:shirt-designs-comparison}
\end{table}
Our final example investigates the scalability of our method to more complex scenarios involving five clutches and five motions. The performance of this design exhibits relative energy density increases of 1.41, 0.85, 1.62, 0.64, and 1.16 for the motions Arms Forwards, Arms Raise, Bend Forwards, Arm Flexion, and Arm Extension, respectively. These numbers are comparable to the results obtained for our other multi-motion garments, especially as the allotted per-motion coverage has decreased overall. In general, the more motions a given design supports with the \emph{same} material coverage target (i.e. 15\%), the material available per motion will decrease and thus be less energy-dense in the ON state. In this case, the material coverage target can be increased, or the designer can sample from an earlier progression step with higher coverage.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/multiple_motions_shirt_long.png}
\caption{Active kinesthetic long-sleeve shirt with five clutches designed for five motions as indicated.}
\label{fig-multi-motion-long-sleeves} \vspace{-.25cm}
\end{figure}
\subsection{Comparison to Manual Designs}
We conducted a pilot study to provide a manual baseline for our automatically generated designs. A central question in this context is whether users converge towards particular designs and if those designs exhibit features found in automatically generated ones. We recruited six participants (5M, 1F), two of whom were experts in structural optimization techniques (P2, P3). Using our interactive tool, we asked users to 'draw' stiff material on garment meshes, connecting a set of already placed clutches. Participants were asked to distribute material in such a way as to maximally resist the set of specified motions when clutches are activated. Each participant created two designs, a 2-clutch, 2-motion arm sleeve, covering no more than 20\% of the available area, and a 3-clutch 3-motion shirt with a coverage budget of 15\%. Each of these designs corresponds to an automatically generated designs shown in the previous section. The secondary goal of minimizing energy when the clutch is inactive was not assigned.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/manual_designs.png}
\caption{Manually-designed garments for 2-motion arm sleeve (top), and 3-motion shirt (bottom) for participants P1 (left) to P6 (right) with clutches shown in green. Note the large variance among the designs, particularly in the shirt case. The sleeve from P1 and the shirt from P2 were chosen for fabrication. * Denotes expert designed garments.}
\label{fig-manual-designed-garments} \vspace{-.25cm}
\end{figure}
The manually-created results shown in Fig. \ref{fig-manual-designed-garments} exhibit large variety in their designs.
While most examples can be expected to perform reasonably, none of them resembled the automatically generated designs. Compared to the fully dense version, manually-created designs were only 0.48x and 0.27x as energy-dense for the arm sleeve and shirt, respectively. Automatic designs, on the other hand, showed a 1.1x and 1.48x higher energy density. We can see that in the case of designing for a larger number of motions, the effectiveness of user designs drops drastically, while automatically generated designs can maintain a relatively high energy density. Looking at only designs from expert users, we see relative average energy densities of 0.54 for the sleeve, and 0.34 for the shirt, still much lower than our automatic designs. Non-expert designs on the other hand had average relative energy densities of 0.44 for the sleeve and 0.23 for the shirt, showing a much larger drop in performance for the more complex shirt design. Thus, automatic design methods can be especially useful for such users. Table \ref{tbl:manual-designs} summarizes these findings.
\begin{table}[h]
\begin{tabular}{ p{2.0cm} p{0.5cm} p{0.5cm} p{0.5cm} p{0.5cm} p{0.5cm} p{0.5cm} p{0.5cm} }
\hline
Garment / \\Motion & Auto & P1 & P2$^*$ & P3$^*$ & P4 & P5 & P6 \\ \hline
\rule{0pt}{3ex}Sleeve / Flex & \textbf{0.88} & 0.50 & 0.53 & 0.54 & 0.67 & 0.26 & 0.58 \\
Sleeve / Ext & \textbf{1.28} & 0.37 & 0.66 & 0.44 & .55 & 0.21 & 0.45 \\
Shirt / Forward & \textbf{1.77} & 0.11 & 0.45 & 0.14 & .19 & 0.08 & 0.14 \\
Shirt / Raise & \textbf{1.08} & 0.10 & 0.37 & 0.07 & .14 & 0.02 & 0.19 \\
Shirt / Bend & \textbf{1.60} & 0.38 & 0.75 & 0.27 & .64 & 0.32 & 0.47 \\
\hline
\end{tabular}
\caption{Performance summary of manually-created designs. We report the energy density of the garment relative to the fully dense design. Note that the automatic design has the highest energy densities across all motions. * Denotes designs by expert users.}
\label{tbl:manual-designs}
\end{table}
\subsection{Physical Validation}
We seek to quantify the resistive force of our automatically designed garments under the motions for which they were optimized, and compare them against Manual-Design counterparts. We selected two designs for fabrication - the multi-motion arm sleeve and multi-motion short-sleeve shirt. We fabricated both, the designs produced by our automatic method and the corresponding manually-designed garments. For the shirt, we selected the clearly highest performing garment, which was from P2, while for the sleeve, we selected the design from P1. This sleeve design represents a common (line) design seen in literature \cite{Ramachandran2021, ramachandran2021arm, Diller2016}, while having similar performance as other designs.
In order to best isolate the impact of the connecting structure, we replace clutches with flexible plastic strips that connect to a force sensor as shown in Fig. \ref{fig:force_graph}. For the Arms Forward motion, we mount the force sensor in the upper back, while for the Arms Raise and Bend Forward motions, we mount it on the bottom left clutch location. The target motion is then slowly performed by the experimenter wearing the garment (three trials per motion), while the force is measured using a 10kg DYLY-108 force sensor with an HX711 load cell amplifier (see the Video Figure for visual demonstration).
The results shown in Fig. \ref{fig:force_graph} indicate that, relative to the manual design, the designs generated by our method were on average two times and up to four times more efficient in terms of force output. These measurements confirm our observations made on simulation results in which, as for the experimental case, the largest difference in relative energy density was observed for the Arms Raise motion.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/Force_graph.png}
\caption{Physical force measurements. Left: experimental setup with force with clutch replaced by a stand-in equipped with a force sensor. Right: maximum force (N) readings when blocking different movements as labeled for the manually-designed (blue) and automatically generated (green) shirt and sleeve garments.}
\label{fig:force_graph} \vspace{-.25cm}
\end{figure}
\subsection{User Evaluation}
\label{sec:eval-user}
To quantitatively evaluate the ability of our active kinesthetic garments to efficiently block motion, we conduct a user study based on a VR pointing task in which participants were asked to reach targets from a predefined set of locations within their reach.
The hypothesis that we seek to test is that, when wearing our optimized designs, users generally need more time to reach targets when clutches are active compared to when they are inactive. A secondary hypothesis is that our automatically generated designs lead to higher blocking efficiency than a user-generated baseline.
\paragraph*{Procedure and Setup}
Six healthy adult subjects ($M$=28.1; $SD$=4.14;) were recruited. Since we only fabricated one size of our designs, participants were all male and similar in size to the template STAR mesh. All participants wore noise cancelling headphones. The procedure and tasks were described and an introduction to the garments and the active components was given. After donning the garments (shirt and sleeve), clutches were attached and adjusted according to participant size to achieve sufficient pre-tension. The left hand of participants was rested on a tripod such for stability.
Participants were then introduced to the VR setting and asked to practice touching the spherical targets with and without clutch activation until they felt comfortable proceeding. The study was implemented in Unity 2021 using a Meta Quest 2 relying on the built-in hand-tracking functionality.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/user_study_setup}
\caption{User study setup. Participant wearing Auto-Designed garment and reaching for target (left), and their corresponding motion in the virtual environment (right).}
\label{fig:study_setup} \vspace{-.25cm}
\end{figure}
\paragraph*{Study Design}
We use a within-subject design with two independent variables: \emph{Feedback Type \{via Auto-Designed, via Manual-Designed, Visual Only\}} and \emph{ Target Placement: \{Forward, Raise, Bend, Flex, Ext\}}. Each target is placed to elicit a specific motion from the user, and is color-coded to 4 to participants which target they should touch (see Fig.\ref{fig:study_setup}). As a dependent variable, we measure \emph{Time}, which starts automatically when the participant's hand leaves the starting position (white sphere), and ends as soon as they touch it again. The main task was to touch a given target in one continuous ballistic back-and-forth motion at a natural speed. For each target placement, three trials were collected for a total of 30 trials, one half with clutches active, the other half with clutches deactivated (Visual). The order of clutch activation was randomized and participants were not told if the clutch was on or off. The order of the feedback type was also randomized. At the end of the study, participants were free to comment on their experience using each garment design.
\paragraph*{Results}
The mean time to reach targets were 1.68s ($\sigma=0.77)$ for the Auto-Designed condition, 1.32s ($\sigma=0.43)$ for Manual-Designed, and 1.33s ($\sigma=0.43)$ for Visual. A longer reach time indicates more impact on the participant's ability to reach the target. The full results are visualized in Figure \ref{fig:study_results}. A two-way repeated-measures ANOVA resulted in a significant effect on feedback type ($F(2, 5) = 29.82,\ p<.001$), target placement ($F(4, 5) = 34.45, \ p<.001$) and interaction ($F(8, 5) = 5.72, \ p=.004$). We conducted a Holm-corrected post-hoc test and found significant differences for feedback type. Our Automatic Design method significantly impacted participant movement time compared to both Manual Design feedback ($p<.001$) and Visual feedback ($p<.001$). We found no significant difference between Manual Design feedback and Visual feedback. When looking at times across target placements, our Automatic Design method significantly impacted participant movement time for the Bend and Raise motions when comparing to both Visual and Manual Design baselines (both $p<.001$).
From these results, we see a trend that the automatically designed garments performed better in terms of limiting user motion, particularly when the motions involved larger movements in the upper body.
We observe that our Auto-Designed garments performed substantially better in larger motions than the Manual-Design counterparts, results which are in-line with both simulated and force-characterization data.
The exception is the Forward motion, where we observed a less substantial impact, possibly due to the fact that participants could twist their body to reach that target. The low performance of the Flex and Ext methods could be due to the fact that we use smaller ES clutches for these motions, and the force was too small compared to the force produced by larger motions (see Fig. \ref{fig:force_graph}), and thus, below a critical threshold that would have an impact on user motion. Thus, our first hypothesis was confirmed for two of the three larger upper body motions.
What is surprising is that the performance of the Manual-Design baseline was nearly indistinguishable from the Visual baseline, even for larger motions. In relation to this, two participants commented that they had trouble perceiving any resisting effects of the Manual-Design.This shows that, even with the same active components, our optimization-based approach for designing connecting structures can indeed make the difference between a system having clear or negligible impact on user motion.
\begin{figure}[h]
\center
\includegraphics[width=1.0\columnwidth]{figures/study_results.png}
\caption{User study results showing the average trial time for each feedback type and target location. }
\label{fig:study_results} \vspace{-0.25cm}
\end{figure}
\section{Introduction}
Kinesthetic garments are an efficient and non-obtrusive way of providing force feedback for human body motion. By augmenting stretchable fabric with strategically designed reinforcements, they offer targeted resistance to motions along specific directions \cite{vechev2022cdkg}.
They are part of an emerging trend of soft robotic garments \cite{sanchez2021textile} that have the potential to assist human wearers in various ways such as during locomotion \cite{kim2019reducing, lee2018autonomous}, rehabilitation \cite{al2016wrist}, and increasing immersion in mixed reality \cite{gunther2019pneumact, rognon2018flyjacket, al2017frozen}. However, relying only on \textit{passive} mechanical structure for feedback prevents their use in such applications because they require \emph{active} feedback.
In this work, we propose a computational approach for designing \textit{active kinesthetic garments} that can resist user-defined motions \textit{on demand}.
To implement such adaptive resistance, we rely on electrostatic clutches \cite{hinchet2019highforce}, i.e., pre-fabricated components that provide extremely high stiffness contrast between their active and inactive states.
Designing active kinesthetic garments then amounts to determining clutch placements, typically placed over high-strain areas, and finding a passive structure that connects and anchors the active components. Crucially, this layout should result in the garment providing maximal resistance when clutches are active, but minimally interfere with motion otherwise. Designing effective connecting structures requires the understanding of the interaction between stretchable garments in multiple states sliding over a deforming body in multiple poses, a very difficult and unintuitive task.
To address this challenge, we formalize the design of active kinesthetic garments as an on-body topology optimization problem whose objective function explicitly balances the opposing goals for active and inactive states.
By maximizing the difference in elastic energy between active and inactive states, our formulation encourages layouts in which clutches link disconnected parts of the passive structure. In this way, clutches leverage the passive structure to establish strong, load-carrying paths when active while maintaining freedom of movement otherwise.
We implement our formulation within a standard evolutionary optimization algorithm, and produce a set of active kinesthetic garment designs that each target multiple motions spanning different body sites. Our results indicate that designs produced with our approach are highly effective and outperform manually-designed alternatives by significant margins. To further substantiate this analysis, we manufacture a subset of our designs for experimental evaluation. Both mechanical testing and a VR pointing task indicate clear advantages for the designs created with our method. To summarize, we make the following contributions:
\begin{itemize}
\item A \emph{computational design pipeline} for the automatic creation of active kinesthetic garments that includes a novel objective function that considers active components and multiple motions.
\item A set of \emph{fabricated active kinesthetic garments} built on compliant material integrating ES clutches as kinesthetic feedback components.
\item A comprehensive \emph{evaluation} showing the effectiveness of our method in simulation, in a physical validation, and in a VR user study against manually-designed and visual baselines.
\end{itemize}
\section{Computational Design Pipeline}
Our method supports designers in the task of creating \textit{active} kinesthetic garments that can resist any motion from a predefined set of movements. The design goals of our pipeline are to enable kinesthetic garments that maximize the feedback felt by users when ES Clutches are active, while minimizing interference with their motion when inactive. Our pipeline consists of three main phases: 1) input --- where designers specify motions, garment designs, and clutch placements; 2) automatic design --- where our method automatically links clutches with stiff material to satisfy the above design goals; and 3) a fabrication phase. The full computational pipeline is illustrated in Fig \ref{fig-system}.
\subsection{Input}
Our pipeline requires three components as input: a set of body motion, a base garment, and a predefined number of ES clutches.
\paragraph*{Motions} are specified using the STAR/SMPL parametric human body model \cite{osman2020star, loper2015smpl} which produces a surface mesh $v$ with N = 6890 vertices $\in\mathbb{R}^{3n}$ based on a $72$ pose $\mv{\theta}$ parameters.
To create target poses, we sample from the AMASS dataset \cite{mahmood2019amass} and make individual adjustments to the $\mv{\theta}$ as needed. We define a motion as a single rest pose $\bar{\mathbf{v}}$ and an accompanying deformed pose $\mathbf{v}$. A \emph{set} of motions is defined with $\mathbf{v}=(\mathbf{v}_1,\ldots,\mathbf{v}_i)$ deformed poses, and a common rest pose $\bar{\mathbf{v}}$.
\paragraph*{Garments and Connecting Structures} are modeled as 2D mesh surfaces embedded on the body, initialized with the same rest and deformed nodal positions as the underlying body mesh. A garment in its rest state is defined through nodal positions $\bar{\mathbf{x}}=(\bar{\mathbf{x}}_1,\ldots,\bar{\mathbf{x}}_n)\in\mathbb{R}^{3}$ and $\mathbf{x}=(\mathbf{x}_1,\ldots,\mathbf{x}_n)\in\mathbb{R}^{3n}$ when deformed. The connecting structure of the garment is modeled using a bi-material distribution where each triangle element $e$ of the garment mesh is assigned a specific material property. This property is set through the design variable $d^e \in [{0, 1}]$ for each element $e$, where $0$ and $1$ correspond to \textit{cloth} and \textit{reinforced cloth} respectively.
\paragraph*{Active Components}
In our formulation, ES clutches are modeled as rectangular surface meshes that are attached to the garment at a predefined set of vertices. A key requirement for optimal ES clutch operation is that they are initialized in a \emph{taut} state, that is, all slack must be removed from the system before forces are felt at the endpoints. We create a low-dimensional parametrization of ES clutches that is defined by the following variables: a \emph{starting point}, a \emph{surface direction}, and a \emph{length and width}.
From this, we procedurally generate a spline, and extrude a mesh (see Appendix \ref{ap:procedural_clutch}) with rest vertices $\mathbf{q}=(\mathbf{q}_1,\ldots,\mathbf{q}_m)\in\mathbb{R}^{3n}$ and $\bar{\mathbf{q}}=(\bar{\mathbf{q}}_1,\ldots,\bar{\mathbf{q}}_m)\in\mathbb{R}^{3n}$ when deformed. The endpoints $q^c$ of the clutch mesh (three at each end) are connected to the garment mesh using simple quadratic penalty functions, which allows for firm attachment.
\subsection{Automatic Design}
Finding a passive mechanical structure that optimally connects electrostatic clutches placed by the user is a key challenge in the design of active kinesthetic garments. Recent work by Vechev et al. \cite{vechev2022cdkg} demonstrated a method for on-body topology optimization using a single compliance-minimization objective (summarized in Appendix \ref{ap:onbody_tpo}).
Such an objective cannot be applied in our setting, as it has no notion of component states, and the single objective does not sufficiently capture the high-level goal of minimizing motion interference when components are inactive. Therefore, we propose to extend this formulation from passive reinforcements to our setting of active kinesthetic garments by \textit{(1)} distinguishing between active and inactive clutch states by extending the simulation model with stateful components, \textit{(2)} reconciling the different design goals for active and inactive states through a new state-dependant dual-objective, and \textit{(3)} accounting for multiple motions.
\paragraph*{Active Component Model and Simulation}
ES Clutch stiffness varies according to their state, thus, we model their behaviour using a bi-modal material. We implement this as a neo-Hookean material that resists compression and changes modes depending on the activation vector $\gamma = [\gamma_0, \gamma_1,..., \gamma_n], \quad \gamma_n \in [{0, 1}]$. Each $\gamma_i$ determines the state of clutch $i$, with $0$ and $1$ corresponding to inactive and active states, respectively. The Young's modulus of the clutch material is then set to $Y_\mathrm{clutch}^i=\gamma_iY_\mathrm{stiff}+(1-\gamma_i)Y_\mathrm{cloth}$. The elastic energy stored in the clutches during deformation is defined as $E_\mathrm{clutches}(q, \gamma)$. We define penalty terms $E_\mathrm{body}(v, \mathbf{q})$ preventing clutches from entering the body, and an additional term $E_\mathrm{attach} = \frac{1}{2}k(q^c-x^x_c)^T(q^c-x^x_c)$ that attaches the six endpoint vertices to their respective locations $x_c$ on the garment.
Throughout all examples, we set constant values for Young's Modulus to $Y_\mathrm{cloth} = 0.5\textrm{MPa}$, $Y_\mathrm{reinforced\_cloth} = 0.5\textrm{GPa}$, and $Y_\mathrm{stiff} = 3.0\textrm{GPa}$. We use a Poisson's ratio of 0.33 for all materials.
We combine our active component model, with the garment-on-body model described in \cite{vechev2022cdkg}. The terms $E_\mathrm{garment}(\mathbf{x}, d)$, $E_\mathrm{body}(v, \mathbf{x})$, and $E_\mathrm{attach}$ are summarized in Appendix \ref{ap:sim_model}. With the model and energies defined above, we perform a quasi-static simulation by solving an unconstrained optimization problem,
\begin{equation}
\label{eq:CoupledSystemEnergy}
\begin{split}
\mathbf{x}^*, \mathbf{q}^* = \arg\min_{\mathbf{x}, \mathbf{q}} \quad E_\mathrm{garment}(\mathbf{x}, d) + E_\mathrm{body}(v, \mathbf{x}) + E_\mathrm{attach}(\mathbf{x}) \ + \\
E_\mathrm{clutches}(\mathbf{q}, \gamma) + E_\mathrm{body}(v, \mathbf{q}) + E_\mathrm{attach}(\mathbf{q}) \ ,
\end{split}
\end{equation}
using the GPU-based L-BFGS \cite{liu1989limited} optimizer provided by PyTorch \cite{pytorch}. We take advantage of GPU parallelism by simulating all states (poses) simultaneously. We consider simulations converged once the gradient norm of (\ref{eq:CoupledSystemEnergy}) reaches 1e-7.
\paragraph*{State-Dependant Dual-Objective}
A central goal for the structural optimization step is to find a material layout such that the garment resists the specified motions as strongly as possible when clutches are active, while showing minimal resistance otherwise. Assuming all-elastic materials, we translate this goal into the requirement that the stored energy of the garment should be maximized when clutches are active, and minimized when they are inactive.
Our key insight is to introduce an \emph{energy differential objective} that combines these opposing goals as
\begin{equation}
\label{eq:SingleMotionObjective}
\begin{split}\mathbf{d}^* = \arg\max_{\mathbf{d}} \quad E_\mathrm{garment}(x_{ON}^*(\mathbf{d, q, \gamma}), \mathbf{d}) \\
- E_\mathrm{garment}(x_{OFF}^*(\mathbf{d, q, \gamma}), \mathbf{d}) \\ \textrm{s.t.} \quad \sum_e{A_e} d_e=A^*\ ,\quad \mathbf{f}(x_{ON}^*)= \mathbf{0}, \quad \mathbf{f}(x_{OFF}^*)= \mathbf{0} \end{split} \ ,
\end{equation}
where $\mathbf{q}$ holds the variables of all clutches, and $x_{ON}^*$, $x_{OFF}^*$ are distinct equilibrium states corresponding to all clutches being active ($\gamma_i=1 \forall i$) and inactive ($\gamma_i=0 \forall i$), respectively.
To solve this optimization problem with the BESO algorithm, we must compute the per-element sensitivities, i.e., the partial derivatives of the objective function with respect to per-element material assignment variables $d^e$. Following (\ref{eq:SingleMotionObjective}), we simply have to sum the sensitivity values for the active and inactive states to obtain a single value that is used in the BESO ranking procedure. Everything else follows the procedure described in \cite{vechev2022cdkg} and is summarized in Appendix \ref{ap:onbody_tpo}.
\paragraph*{Multiple Motions}
Whereas the method described in \cite{vechev2022cdkg} computes static reinforcements for a single target motion, we ultimately want to move towards \emph{programmable garments} that can resist many motions by use of their active components.
To this end, we extend (\ref{eq:SingleMotionObjective}) to the multi-motion setting by summing contributions for all poses as
\begin{equation}
\label{eq:MultiMotionObjective}
\begin{split}\mathbf{d}^* = \arg\max_{\mathbf{d}} \quad
\sum_k \hat{E}_\mathrm{garment}^k(x_{k, ON}^*(\mathbf{d, q, \gamma}), \mathbf{d}) \\
- \sum_k \hat{E}_\mathrm{garment}^k(x_{k, OFF}^*(\mathbf{d, q, \gamma}), \mathbf{d}) \\
\textrm{s.t.} \quad \sum_e{A^e} d^e=A^*\ ,\quad \mathbf{f}(x_{k, ON}^*)= \mathbf{0}, \quad \mathbf{f}(x_{k, OFF}^*)= \mathbf{0} \ \forall k \ ,
\end{split}
\end{equation}
where $k$ runs over all input poses.
A problem with this simple approach is that the optimization may receive larger rewards for increasing an already good performance for a given pose instead of improving the worst-performing case.
We address this problem by normalizing the strain energy density for each pose in a pre-processing step
\begin{equation}
\label{eq:NormalizedGarmentEnergy}
\hat{E}_{\mathrm{garment}}^k = \sum_e t^e A^e\hat{W}_\mathrm{garment}^{k,e}(x^*, d^e), \ \hat{W}^{k,e} = \frac{W^{k,e}}{\max_e(W^{k,e})} \ .
\end{equation}
In this way, each pose is given the same importance, irrespective of its initial strain energy, thus encouraging material layouts that more evenly distribute the garment's performance across all input motions.
\subsection{Hardware Details and Fabrication}
In the last step of the pipeline, designs are fabricated.
\paragraph*{ES Clutches} provide resistance to elongation when active \cite{hinchet2019highforce}, while remaining stretchable with low resistance when inactive. They are thin, light and flexible which make them highly compliant and consume very low power when engaged (e.g. one 14cm by 1cm clutch consumes 12 mW at 350V). The ES clutches from \cite{hinchet2019highforce} were modified for better integration by making them stiffer to reduce bending, packaging them in elastic guides to keep them fully self-retractable and safer for on-body use. Each ES clutch is composed of 3 parts: an electrode strip, an insulating strip, and a stretchable textile guide. Strips are made of 125 $\mu$m metalized polyester films from McMaster-Carr. Films are laser cut into long 1cm wide strips of various lengths. Additionally, insulating strips are covered with a 25$\mu$m thick layer of poly (vinylidene fluoride-trifluoroethylene-chlorotrifluoroethylene) from Piezotech-Arkema \cite{hinchet2019highforce}.
\paragraph*{Garments and Attachments}
All designs are exported as meshes and manually processed in Blender. We simplify geometry, and unroll the designs onto flat surfaces using the Paper model plugin (without changing area). As our connecting material, we attached a layer of polyurethane (Siser EasyWeed Stretch) onto 100\% cotton fabric. This material combination enables much higher forces than in \cite{vechev2022cdkg}. As base garments we used stretchable GripGrab UV sleeves and Nike Dri-Fit Pro Compression shirts. The different parts of the connecting structure were cut with a Trotec 300 laser cutter and glued onto base garments following marks taken on an experimenter wearing the garment. Next, pressure buttons are riveted at locations where ES clutches connect. Finally, ES clutches are fixed onto the garments using pressure buttons and connected with thin wires to a custom voltage power supply powered by a USB power bank and controlled by Bluetooth (see Fig. \ref{fig-system}b). The overall modular system can accommodate different sizes of clutches and slight variations in body sizes.
\section{Related Work} We summarize works in the areas of computational methods in garment modeling and augmentation, intersecting with hardware and devices capable of providing body-scale kinesthetic feedback.
\paragraph*{Body-scale Kinesthetic Haptic Feedback Systems}
Early work to provide kinesthetic feedback to the body used motors and hydraulic pistons to actuate heavy bulky haptic platforms. More recently, several wearable body kinesthetic feedback systems have been developed, mostly based on electromagnetic motors \cite{Chen2016, Shen2019} with rods \cite{Schiele2011, Barnaby2019} or cables \cite{Asbeck2014, Fang2020} transmission, and based on pneumatic actuators \cite{gunther2019pneumact, Delazio2018} which are soft and more comfortable at the detriment of a bulkier equipment (pumps, compressors, valves). An alternative way to provide body kinesthetic feedback are passive blocking mechanisms like vacuum jamming \cite{Choi2018} (still requiring pumps) and ES clutches \cite{Diller2016, hinchet2018dextres, Ramachandran2021, ramachandran2021arm}. In particular, ES clutches offer the advantages of being ultra-thin, light, and soft enabling the design of compliant kinesthetic garment designs. Such kinesthetic systems are typically manually designed to specifically fit a limb/joint and block a certain motion. In contrast, we leverage an automatic design method that models and simulates clutches, allowing us to accommodate any set of motions and body areas.
\paragraph*{Topology Optimization}
Topology optimization is a powerful method used in engineering disciplines to most efficiently distribute a finite amount of material, typically to minimize compliance \cite{bendsoe2013topology, zehnder2021ntopo}. The graphics community has also combined compliance minimization with user guided input \cite{martinez2015structure, schumacher2016stenciling}. It has also been demonstrated on elastic materials \cite{Skouras13Computational} as well as structures undergoing large displacements \cite{bruns2001topology}. Closer to our work, topology optimization has moved into the on-body domain where it has been used for personalized cast design \cite{zhang2019customization} and casts designed for thermal comfort \cite{zhang2017thermal}. Most recently, Vechev et al. demonstrated the design of \emph{kinesthetic garments}, which are passively reinforced garments designed to resist a single motion \cite{vechev2022cdkg}. However, this work only formulates a single compliance minimization objective, and thus cannot be used in a setting that leverages active components. We extend this approach in two important ways, first by the addition of a dual objective that considers the active and inactive states of our components. A second important contribution is a formulation that enables optimization for multiple motions.
\paragraph*{Intelligent Garment Augmentation}
The intelligent design of garments is an emerging discipline with important applications for the general population. Computational design approaches to garment design have recently started to consider motion as a fundamental design quantity in so-called 4D garments \cite{liu2021knitting} that minimize friction and pressure via integrated knitting maps. In addition to minimizing friction during motion, Montes et al. also optimize for pressure distributions and body fit by employing a physically based model of skin-tight garments on the body \cite{montes2020computational}. Vechev et al. augment existing skin-tight clothing with passive reinforced materials to resist a single given motion, employing a more flexible model of the garment that allows cloth to slide and lift-off from the body \cite{vechev2022cdkg}. Optimization of component placement has also been used in soft-robotic garments, in combining elastic cords, clutches, and dampers to reduce the force and power required by a person to generate lower body motion \cite{ortiz2017energy}. Evolutionary optimization techniques were employed by Gholami et al. for designing garments with optimally placed fabric sensors \cite{gholami2019lower}. Muthukumarana et al. integrated combinations of active shape-memory based components into garments allowing for actuation on clothing \cite{muthukumarana2021clothtiles}. In our work, we augment garments with active components that generate kinesthetic feedback and design supporting optimization objectives to create efficient structures connecting them.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,422 |
package io.dockstore.webservice;
import static io.dockstore.webservice.Constants.DOCKSTORE_YML_PATH;
import static io.dockstore.webservice.Constants.LAMBDA_FAILURE;
import static io.dockstore.webservice.resources.ResourceConstants.PAGINATION_LIMIT;
import static junit.framework.TestCase.assertNotSame;
import static org.hibernate.validator.internal.util.Contracts.assertNotNull;
import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertFalse;
import static org.junit.Assert.assertTrue;
import static org.junit.Assert.fail;
import io.dockstore.client.cli.BaseIT;
import io.dockstore.client.cli.BasicIT;
import io.dockstore.common.CommonTestUtilities;
import io.dockstore.common.ConfidentialTest;
import io.dockstore.common.DescriptorLanguage;
import io.dockstore.common.SourceControl;
import io.dockstore.webservice.core.BioWorkflow;
import io.dockstore.webservice.core.Service;
import io.dockstore.webservice.core.SourceFile;
import io.dockstore.webservice.core.User;
import io.dockstore.webservice.core.Workflow;
import io.dockstore.webservice.core.WorkflowMode;
import io.dockstore.webservice.jdbi.FileDAO;
import io.dockstore.webservice.jdbi.ServiceDAO;
import io.dockstore.webservice.jdbi.UserDAO;
import io.dockstore.webservice.jdbi.WorkflowDAO;
import io.dropwizard.client.JerseyClientBuilder;
import io.swagger.api.impl.ToolsImplCommon;
import io.swagger.client.ApiClient;
import io.swagger.client.ApiException;
import io.swagger.client.api.Ga4GhApi;
import io.swagger.client.api.UsersApi;
import io.swagger.client.api.WorkflowsApi;
import io.swagger.client.model.StarRequest;
import io.swagger.client.model.Tool;
import java.util.List;
import java.util.Map;
import javax.ws.rs.client.Client;
import javax.ws.rs.core.MultivaluedMap;
import javax.ws.rs.core.Response;
import org.apache.http.HttpStatus;
import org.glassfish.jersey.client.ClientProperties;
import org.hibernate.Session;
import org.hibernate.SessionFactory;
import org.hibernate.Transaction;
import org.hibernate.context.internal.ManagedSessionContext;
import org.junit.Assert;
import org.junit.Before;
import org.junit.Ignore;
import org.junit.Rule;
import org.junit.Test;
import org.junit.contrib.java.lang.system.ExpectedSystemExit;
import org.junit.contrib.java.lang.system.SystemErrRule;
import org.junit.contrib.java.lang.system.SystemOutRule;
import org.junit.experimental.categories.Category;
import org.junit.rules.ExpectedException;
/**
* @author dyuen
*/
@Category(ConfidentialTest.class)
public class ServiceIT extends BaseIT {
private final boolean servicesExposedInTRS = false;
@Rule
public final SystemOutRule systemOutRule = new SystemOutRule().enableLog().muteForSuccessfulTests();
@Rule
public final SystemErrRule systemErrRule = new SystemErrRule().enableLog().muteForSuccessfulTests();
@Rule
public final ExpectedSystemExit systemExit = ExpectedSystemExit.none();
@Rule
public ExpectedException thrown = ExpectedException.none();
private WorkflowDAO workflowDAO;
private ServiceDAO serviceDAO;
private Session session;
private UserDAO userDAO;
private FileDAO fileDAO;
@Before
public void setup() {
DockstoreWebserviceApplication application = SUPPORT.getApplication();
SessionFactory sessionFactory = application.getHibernate().getSessionFactory();
this.workflowDAO = new WorkflowDAO(sessionFactory);
this.serviceDAO = new ServiceDAO(sessionFactory);
this.userDAO = new UserDAO(sessionFactory);
this.fileDAO = new FileDAO(sessionFactory);
// non-confidential test database sequences seem messed up and need to be iterated past, but other tests may depend on ids
testingPostgres.runUpdateStatement("alter sequence enduser_id_seq increment by 50 restart with 100");
testingPostgres.runUpdateStatement("alter sequence token_id_seq increment by 50 restart with 100");
// used to allow us to use tokenDAO outside of the web service
this.session = application.getHibernate().getSessionFactory().openSession();
ManagedSessionContext.bind(session);
}
@Test
public void checkWorkflowAndServiceHierarchy() {
CreateContent createContent = new CreateContent().invoke(false);
long workflowID = createContent.getWorkflowID();
long serviceID = createContent.getServiceID();
long serviceID2 = createContent.getServiceID2();
// might not be right if our test database is larger than PAGINATION_LIMIT
final List<Workflow> allPublished = workflowDAO.findAllPublished(0, Integer.valueOf(PAGINATION_LIMIT), null, null, null);
assertTrue(allPublished.stream().anyMatch(workflow -> workflow.getId() == workflowID && workflow instanceof BioWorkflow));
assertTrue(allPublished.stream().anyMatch(workflow -> workflow.getId() == serviceID && workflow instanceof Service));
assertTrue(allPublished.stream().anyMatch(workflow -> workflow.getId() == serviceID2 && workflow instanceof Service));
final Service byId = serviceDAO.findById(serviceID);
final Service byId1 = serviceDAO.findById(workflowID);
assertTrue(byId != null && byId1 == null);
session.close();
}
@Test
@Ignore("https://github.com/dockstore/dockstore/pull/4720")
public void testTRSOutputOfService() {
new CreateContent().invoke();
final ApiClient webClient = getWebClient(true, false);
Ga4GhApi client = new Ga4GhApi(webClient);
final List<Tool> tools = client.toolsGet(null, null, null, null, null, null, null, null, null, null, null);
assertTrue(tools.stream().filter(tool -> tool.getToolclass().getName().equalsIgnoreCase("workflow")).count() >= 1);
// TODO: change boolean once services are exposed
if (servicesExposedInTRS) {
assertTrue(tools.stream().filter(tool -> tool.getToolclass().getName().equalsIgnoreCase("service")).count() >= 2);
}
}
@Test
public void testProprietaryAPI() {
final CreateContent invoke = new CreateContent().invoke();
final ApiClient webClient = getWebClient(true, false);
WorkflowsApi client = new WorkflowsApi(webClient);
final List<io.swagger.client.model.Workflow> services = client.allPublishedWorkflows(null, null, null, null, null, true, null);
final List<io.swagger.client.model.Workflow> workflows = client.allPublishedWorkflows(null, null, null, null, null, false, null);
assertTrue(workflows.size() >= 2 && workflows.stream()
.noneMatch(workflow -> workflow.getDescriptorType().getValue().equalsIgnoreCase(DescriptorLanguage.SERVICE.toString())));
Client jerseyClient = new JerseyClientBuilder(SUPPORT.getEnvironment()).build("test client");
testXTotalCount(jerseyClient, String.format("http://localhost:%d/workflows/published", SUPPORT.getLocalPort()));
testXTotalCount(jerseyClient, String.format("http://localhost:%d/workflows/published?services=true", SUPPORT.getLocalPort()));
assertTrue(services.size() >= 1 && services.stream()
.allMatch(workflow -> workflow.getDescriptorType().getValue().equalsIgnoreCase(DescriptorLanguage.SERVICE.toString())));
// try some standard things we would like services to be able to do
client.starEntry(invoke.getServiceID(), new StarRequest().star(true));
client.updateLabels(invoke.getServiceID(), "foo,batman,chicken", "");
// did it happen?
final io.swagger.client.model.Workflow workflow = client.getWorkflow(invoke.getServiceID(), "");
assertFalse(workflow.getStarredUsers().isEmpty());
assertTrue(workflow.getLabels().stream().anyMatch(label -> "batman".equals(label.getValue())));
}
/**
* Test X-total-count. It so happens there's two services and two bioworkflows
*
* @param jerseyClient Jersey Client to test endpoint
* @param path Path of endpoint
*/
private void testXTotalCount(Client jerseyClient, String path) {
Response response = jerseyClient.target(path).request().property(ClientProperties.READ_TIMEOUT, 0).get();
assertEquals(HttpStatus.SC_OK, response.getStatus());
MultivaluedMap<String, Object> headers = response.getHeaders();
Object xTotalCount = headers.getFirst("X-total-count");
assertEquals("2", xTotalCount);
}
@Test
public void testGeneralDefaultPathMechanism() {
final CreateContent invoke = new CreateContent().invoke();
final ApiClient webClient = getWebClient(true, false);
WorkflowsApi client = new WorkflowsApi(webClient);
// did it happen?
final io.swagger.client.model.Workflow workflow = client.getWorkflow(invoke.getServiceID(), "");
}
/**
* This tests endpoints that will be triggered by GitHub App webhooks.
* A service is created and a version is added for a release 1.0
*/
@Test
public void testGitHubAppEndpoints() throws Exception {
CommonTestUtilities.cleanStatePrivate2(SUPPORT, false, testingPostgres);
final ApiClient webClient = getWebClient("DockstoreTestUser2", testingPostgres);
WorkflowsApi client = new WorkflowsApi(webClient);
String serviceRepo = "DockstoreTestUser2/test-service";
String installationId = "1179416";
// Add version
client.handleGitHubRelease(serviceRepo, "DockstoreTestUser2", "refs/tags/1.0", installationId);
long workflowCount = testingPostgres.runSelectStatement("select count(*) from service", long.class);
assertEquals(1, workflowCount);
io.swagger.client.model.Workflow service = client.getWorkflowByPath("github.com/" + serviceRepo, SERVICE, "versions");
assertNotNull(service);
assertEquals("Should have a new version", 1, service.getWorkflowVersions().size());
List<SourceFile> sourceFiles = fileDAO.findSourceFilesByVersion(service.getWorkflowVersions().get(0).getId());
assertEquals("Should have 3 source files", 3, sourceFiles.size());
long users = testingPostgres.runSelectStatement("select count(*) from user_entry where entryid = '" + service.getId() + "'", long.class);
assertEquals("Should have 1 user", 1, users);
final long count = testingPostgres.runSelectStatement(
"select count(*) from service where sourcecontrol = 'github.com' and organization = 'DockstoreTestUser2' and repository = 'test-service'",
long.class);
Assert.assertEquals("there should be one matching service", 1, count);
// Test user endpoints
UsersApi usersApi = new UsersApi(webClient);
final long userId = testingPostgres.runSelectStatement("select userid from user_entry where entryid = '" + service.getId() + "'", long.class);
List<io.swagger.client.model.Workflow> services = usersApi.userServices(userId);
List<io.swagger.client.model.Workflow> workflows = usersApi.userWorkflows(userId);
assertEquals("There should be one service", 1, services.size());
assertEquals("There should be no workflows", 0, workflows.size());
// Should not be able to refresh service
try {
client.refresh(services.get(0).getId(), false);
fail("Should not be able refresh a service");
} catch (ApiException ex) {
assertEquals("Should fail since you cannot refresh services.", HttpStatus.SC_BAD_REQUEST, ex.getCode());
}
}
/**
* Ensures that you cannot create a service if the given user is not on Dockstore
*/
@Test
public void createServiceNoUser() throws Exception {
CommonTestUtilities.cleanStatePrivate2(SUPPORT, false, testingPostgres);
final ApiClient webClient = getWebClient("admin@admin.com", testingPostgres);
WorkflowsApi client = new WorkflowsApi(webClient);
String serviceRepo = "DockstoreTestUser2/test-service";
String installationId = "1179416";
// Add service
try {
client.handleGitHubRelease(serviceRepo, "iamnotarealuser", "refs/tags/1.0", installationId);
fail("Should not reach this statement.");
} catch (ApiException ex) {
assertEquals("Should have error code 418", LAMBDA_FAILURE, ex.getCode());
}
final long count = testingPostgres.runSelectStatement(
"select count(*) from service where sourcecontrol = 'github.com' and organization = 'DockstoreTestUser2' and repository = 'test-service'",
long.class);
Assert.assertEquals("there should be no matching service", 0, count);
}
/**
* Ensures that a service and workflow can have the same path
*
* @throws Exception
*/
@Test
public void testServiceWithSamePathAsWorkflow() throws Exception {
CommonTestUtilities.cleanStatePrivate2(SUPPORT, false, testingPostgres);
final ApiClient webClient = getWebClient(BasicIT.USER_2_USERNAME, testingPostgres);
WorkflowsApi client = new WorkflowsApi(webClient);
final String github = SourceControl.GITHUB.toString();
String serviceRepo = "DockstoreTestUser2/test-service";
String installationId = "1179416";
// Add service
client.handleGitHubRelease(serviceRepo, BasicIT.USER_2_USERNAME, "refs/tags/1.0", installationId);
long workflowCount = testingPostgres.runSelectStatement("select count(*) from service", long.class);
assertEquals(1, workflowCount);
// Add workflow with same path as service
final io.swagger.client.model.Workflow workflow = client
.manualRegister("github", serviceRepo, "/Dockstore.cwl", "", "cwl", "/test.json");
assertNotNull(workflow);
// forcibly publish both for testing
testingPostgres.runUpdateStatement("update workflow set ispublished = 't'");
testingPostgres.runUpdateStatement("update service set ispublished = 't'");
// test retrieval
final io.swagger.client.model.Workflow returnedWorkflow = client.getPublishedWorkflowByPath(github + "/" + serviceRepo, BIOWORKFLOW, "", null);
final io.swagger.client.model.Workflow returnedService = client.getPublishedWorkflowByPath(github + "/" + serviceRepo, SERVICE, "", null);
assertNotSame(returnedWorkflow.getId(), returnedService.getId());
// test GA4GH retrieval
Ga4GhApi ga4GhApi = new Ga4GhApi(webClient);
final Tool tool1 = ga4GhApi.toolsIdGet(ToolsImplCommon.WORKFLOW_PREFIX + "/" + github + "/" + serviceRepo);
final Tool tool2 = ga4GhApi.toolsIdGet(ToolsImplCommon.SERVICE_PREFIX + "/" + github + "/" + serviceRepo);
assertNotSame(tool1.getId(), tool2.getId());
}
/**
* This tests that you can't add a version that doesn't exist
*/
@Test
public void updateServiceIncorrectTag() throws Exception {
CommonTestUtilities.cleanStatePrivate2(SUPPORT, false, testingPostgres);
final ApiClient webClient = getWebClient("admin@admin.com", testingPostgres);
WorkflowsApi client = new WorkflowsApi(webClient);
String serviceRepo = "DockstoreTestUser2/test-service";
String installationId = "1179416";
// Add version that doesn't exist
try {
client.handleGitHubRelease(serviceRepo, "admin@admin.com", "refs/tags/1.0-fake", installationId);
fail("Should not reach this statement.");
} catch (ApiException ex) {
assertEquals("Should have error code 418", LAMBDA_FAILURE, ex.getCode());
}
}
/**
* This tests that you can't add a version with an invalid dockstore.yml or no dockstore.yml
*/
@Test
public void updateServiceNoOrInvalidYml() throws Exception {
CommonTestUtilities.cleanStatePrivate2(SUPPORT, false, testingPostgres);
final ApiClient webClient = getWebClient("admin@admin.com", testingPostgres);
WorkflowsApi client = new WorkflowsApi(webClient);
String serviceRepo = "DockstoreTestUser2/test-service";
String installationId = "1179416";
// Add version that has no dockstore.yml
try {
client.handleGitHubRelease(serviceRepo, "admin@admin.com", "refs/tags/no-yml", installationId);
fail("Should not reach this statement.");
} catch (ApiException ex) {
assertEquals("Should have error code 418", LAMBDA_FAILURE, ex.getCode());
}
// Add version that has invalid dockstore.yml
try {
client.handleGitHubRelease(serviceRepo, "admin@admin.com", "refs/tags/invalid-yml", installationId);
fail("Should not reach this statement.");
} catch (ApiException ex) {
assertEquals("Should have error code 418", LAMBDA_FAILURE, ex.getCode());
}
}
/**
* Tests that refresh will only grab the releases
*/
@Test
public void updateServiceSync() throws Exception {
testingPostgres.runUpdateStatement("update enduser set isadmin = 't' where username = 'DockstoreTestUser2';");
CommonTestUtilities.cleanStatePrivate2(SUPPORT, false, testingPostgres);
final ApiClient webClient = getWebClient("DockstoreTestUser2", testingPostgres);
WorkflowsApi client = new WorkflowsApi(webClient);
String serviceRepo = "DockstoreTestUser2/test-service";
String installationId = "1179416";
// Add service
client.handleGitHubRelease(serviceRepo, "DockstoreTestUser2", "refs/tags/1.0", installationId);
long workflowCount = testingPostgres.runSelectStatement("select count(*) from service", long.class);
assertEquals(1, workflowCount);
io.swagger.client.model.Workflow service = client.getWorkflowByPath("github.com/" + serviceRepo, SERVICE, "");
// io.swagger.client.model.Workflow service = services.get(0);
try {
client.refresh(service.getId(), false);
fail("Should fail on refresh and not reach this point");
} catch (ApiException ex) {
assertEquals("Should not be able to refresh a dockstore.yml service.", HttpStatus.SC_BAD_REQUEST, ex.getCode());
}
}
/**
* This tests that you cannot create a service from an in invalid GitHub repository
*/
@Test
public void createServiceNoGitHubRepo() throws Exception {
CommonTestUtilities.cleanStatePrivate2(SUPPORT, false, testingPostgres);
final ApiClient webClient = getWebClient("admin@admin.com", testingPostgres);
WorkflowsApi client = new WorkflowsApi(webClient);
String serviceRepo = "DockstoreTestUser2/test-service-foo-bar-not-real";
String installationId = "1179416";
// Add service
try {
client.handleGitHubRelease(serviceRepo, "admin@admin.com", "refs/tags/1.0", installationId);
fail("Should not reach this statement.");
} catch (ApiException ex) {
assertEquals("Should have error code 418", LAMBDA_FAILURE, ex.getCode());
}
}
private class CreateContent {
private long workflowID;
private long serviceID;
private long serviceID2;
long getWorkflowID() {
return workflowID;
}
long getServiceID() {
return serviceID;
}
long getServiceID2() {
return serviceID2;
}
CreateContent invoke() {
return invoke(true);
}
CreateContent invoke(boolean cleanup) {
final Transaction transaction = session.beginTransaction();
Workflow testWorkflow = new BioWorkflow();
testWorkflow.setDescription("foo workflow");
testWorkflow.setIsPublished(true);
testWorkflow.setSourceControl(SourceControl.GITHUB);
testWorkflow.setDescriptorType(DescriptorLanguage.CWL);
testWorkflow.setOrganization("shield");
testWorkflow.setRepository("shield_repo");
Service testService = new Service();
testService.setDescription("test service");
testService.setIsPublished(true);
testService.setSourceControl(SourceControl.GITHUB);
testService.setDescriptorType(DescriptorLanguage.SERVICE);
testService.setMode(WorkflowMode.DOCKSTORE_YML);
testService.setOrganization("hydra");
testService.setRepository("hydra_repo");
testService.setDefaultWorkflowPath(DOCKSTORE_YML_PATH);
Service test2Service = new Service();
test2Service.setDescription("test service");
test2Service.setIsPublished(true);
test2Service.setSourceControl(SourceControl.GITHUB);
test2Service.setMode(WorkflowMode.DOCKSTORE_YML);
test2Service.setDescriptorType(DescriptorLanguage.SERVICE);
test2Service.setOrganization("hydra");
test2Service.setRepository("hydra_repo2");
test2Service.setDefaultWorkflowPath(DOCKSTORE_YML_PATH);
final Map<DescriptorLanguage.FileType, String> defaultPaths = test2Service.getDefaultPaths();
for (DescriptorLanguage.FileType val : DescriptorLanguage.FileType.values()) {
defaultPaths.put(val, "path for " + val);
}
test2Service.setDefaultPaths(defaultPaths);
// add all users to all things for now
for (User user : userDAO.findAll()) {
testWorkflow.addUser(user);
testService.addUser(user);
test2Service.addUser(user);
}
workflowID = workflowDAO.create(testWorkflow);
serviceID = serviceDAO.create(testService);
serviceID2 = serviceDAO.create(test2Service);
assertTrue(workflowID != 0 && serviceID != 0);
session.flush();
transaction.commit();
if (cleanup) {
session.close();
}
return this;
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,384 |
A Tale of the Meanest Goose You Ever Did Meet.
Once upon a time, there was a mean 'ol goose named Madam Honks a Lot who decided to build a nest.
Every day, she'd gather sticks and place them in a pile next to the shed. All she cared about was gathering sticks. No more days of nibbling on fresh green grass. Gone were the moments of dunking her head in her water bowl when no one was looking.
Sticks became her life. And her life was nothing without more sticks.
Once her nest was complete she promptly sat on her nest and laid two beautiful, shiny goose-sized eggs.
But, in all her stick-gathering Madam Honks a Lot forgot about ONE. BIG. PROBLEM.
She forgot that in order for her to have baby geese, she needed to meet, court, and fall in love with a Sir Honks a Lot. Those beautiful, shiny goose-sized eggs of hers would never hatch.
Fortunately for Madam Honks a Lot, a kind, amazing, and gorgeous woman had a brilliant plan.
The woman decided to place 10 fertilized CHICKEN eggs under Madam Honks a Lot. This was no easy feat, since Madam Honks a Lot thought the woman was trying to steal her goose eggs, or WORSE, her sticks.
For exactly 21 days, Madam Honks a Lot sat on those chicken eggs, but she didn't like it one bit.
On Day 7, she decided gathering more sticks was more fun that sitting on her nest.
On Day 9, she bit the gorgeous woman's hand when the woman was trying to give Madam Honks a Lot a nice watermelon treat!
On Day 10, she tried to hide behind a tree.
But, on Day 11-21, she sat on her nest like a good little goose.
In the middle of the night, probably while the gorgeous woman was sleeping, one of the eggs hatched! And Madam Honks a Lot took one look at that baby chick and pushed him out of the nest. He did not survive.
When the woman discovered this crime, she was shocked! She gave Madam Honks a Lot a very stern talk and promptly scooped up the rest of the eggs and placed them in an incubator to hatch.
Out of all the eggs that were left, only one baby chick hatched.
And even though he didn't have a chicken mother or a mean ol' goose mother, he was the cutest little chick in the history of chicks.
And he grew up to be the best tasting chicken dinner the gorgeous woman had ever eaten.
Just kidding! The chicken lived happily ever after on the farm.
And Madam Honks a Lot continued to be a mean ol' goose. Figures.
This story was part of an Instagram series on Weed 'em & Reap's Instagram account HERE. | {
"redpajama_set_name": "RedPajamaC4"
} | 742 |
{"url":"https:\/\/hkex.gitlab.io\/emagpy\/auto_examples\/nb_quickstart.html","text":"# EMagPy Quickstart\u00b6\n\nIn this tutorial you will learn how to import and processes EMI data with the emagpy API (Application Progamming Interface). The API is a set of classes, function and methods that can be called from the command line or in script and jupyter notebook. EMagPy also has a graphical user interface (GUI) that make use of the API behind the scene. The advantage of the API is that is allows more automated task to be performed and user in interactive environment such as this jupyter notebook.\n\n## Import EMagPy\u00b6\n\nYou can either download emagpy from source from https:\/\/gitlab.com\/hkex\/emagpy or install it using pip install emagpy. Then you can import the main class from the emagpy module: Problem.\n\nimport os\nimport numpy as np\nimport sys\nimport pandas as pd\nsys.path.insert(0,'..\/src\/') # this add the emagpy\/src directory to the PATH\nfrom emagpy import Problem # import the main Problem class from emagpy\n\n\n## Data import\u00b6\n\nAfter importing the module we will import the file coverCrop.csv from the test folder.\n\ntestdir = '..\/src\/examples\/cover-crop\/'\n\nk = Problem() # this create the main object\nk.createSurvey(testdir + 'coverCrop.csv') # this import the data\n\nRemoving 1 NaN from survey\n\n\nThe data are usually imported from a .csv file with the headers being the coil configuration. Below is an example of the coverCrop.csv file.\n\nimport pandas as pd\n\nx y VCP0.32 VCP0.71 VCP1.18 VCP0.32_inph VCP0.71_inph VCP1.18_inph HCP0.32 HCP0.71 HCP1.18 HCP0.32_inph HCP0.71_inph HCP1.18_inph\n0 0 0 34.090222 34.67 38.32 1.79 1.90 2.13 33.53 39.77 45.22 2.13 2.27 2.68\n1 1 0 35.350111 36.69 40.16 1.79 1.87 2.13 39.72 43.81 46.76 2.20 2.30 2.72\n2 2 0 36.680000 35.79 39.21 1.81 1.87 2.14 36.10 40.63 45.16 2.14 2.29 2.71\n3 3 0 41.960556 34.26 37.43 1.76 1.30 2.12 35.64 39.47 41.97 2.18 2.22 2.63\n4 4 0 29.250444 28.91 33.51 1.79 1.92 2.19 32.46 36.36 40.58 2.23 2.24 2.69\n\n## Data visualization\u00b6\n\nYou can use the Problem.show() function to visualize the data as a line graph. Additionnaly if spatial coordinates are in the csv file (columns x an y). A map can also be produced using Problem.showMap().\n\nk.show(vmax=50)\n\nk.showMap(coil='VCP0.71', contour=True, pts=True)\n\n\n## Data inversion\u00b6\n\nTo invert the data we must first define a starting model with a given number of layers and a starting conductivity in mS\/m.\n\nk.setInit(depths0=[0.5, 1], # specify the BOTTOM of each layer (the last layer is infinite)\nconds0=[20, 20, 20],\nfixedConds=[False, False, False])# conductivity in mS\/m\n\n\nThen there are different forward model available: - CS : Cumulative Senstivity (following McNeil 1980). Default and fastest forward model. - CSgn : Which is a fast Gauss-Newton inversion based on CS. Choosing this forward model will automatically make use of the Problem.\u00ecnvertGN() method and ignore the arguments passed to invert() except alpha. - FSlin : Full Solution based on Maxwell\u2019s equations using the LIN (Low Induction Number) approximation to convert the quadrature (Q) to ECa - FSeq : Full Solution based on Maxwell\u2019s equations that doesn\u2019t rely on the LIN but rather compute an apparent value based on optimization (see Andrade et al., 2016). - Q : Full Solution based on Maxwell\u2019s equations where the quadrature (Q) is directly minimize without being converted to ECa. This forward model is prefered for high EC (> 100 mS\/m).\n\nTo solve the optimization problem, two types of solvers are available: - L-BFGS-B (default), TNC, CG, Nelder-Mead minimizes an objective function using scipy.optimize.minimize(). - ROPE, SCEUA, DREAM are MCMC-based method provided by the spotpy package that works well when the depth of each layer is not fixed.\n\nThe inverted section can be seen using showResults() and showSlice() if spatial data are available. The quality of the inversion can be assessed using showMisfit() and showOne2one().\n\n# default minimize() based inversion with CS and L-BFGS-B solver\nk.invert()\nk.showResults()\nk.showMisfit()\nk.showOne2one()\n\n120\/120 inverted\n\nk.showSlice(islice=0, contour=True, vmin=12, vmax=50)\nk.showSlice(islice=2, contour=True, vmin=12, vmax=50)\n\nhelp(k.showSlice) # how to access the help for each method\n\nHelp on method showSlice in module emagpy.Problem:\n\nshowSlice(index=0, islice=0, contour=False, vmin=None, vmax=None, cmap='viridis_r', ax=None, pts=False) method of emagpy.Problem.Problem instance\nShow depth slice of EC (if islice > 0) and depth (if islice < 0).\n\nParameters\n----------\nindex : int, optional\nSurvey index. Default is first.\nislice : int, optional\nLayer index (if islice > 0). Default is first layer. If islice < 0,\nthe depths will be display instead (e.g. islice = -1 will display\nthe depth of the bottom of the first layer).\ncontour : bool, optional\nIf True then there will be contouring.\nvmin : float, optional\nMinimum value for colorscale.\nvmax : float, optional\nMaximum value for colorscale.\ncmap : str, optional\nName of colormap. Default is viridis_r.\nax : Matplotlib.Axes, optional\nIf specified, the graph will be plotted against it.\npts : boolean, optional\nIf True (default) the data points will be plotted over the contour.\n\n\nDownload python script: nb_quickstart.py\n\nDownload Jupyter notebook: nb_quickstart.ipynb\n\nView the notebook in the Jupyter nbviewer\n\nRun this example interactively:","date":"2023-03-30 07:18:18","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.23007354140281677, \"perplexity\": 4979.239325083373}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296949107.48\/warc\/CC-MAIN-20230330070451-20230330100451-00073.warc.gz\"}"} | null | null |
Analog photos of a carnival in Mexico.
I finally got some film developed. One of the rolls included these pictures I took in september when my family, David, and I drove to our neighboring town in Mexico and to their feria. A mexican feria is almost the same concept as an american carnival– lots of lights and rides, games to be played and prices waiting to be won, filled with delicious food, both local and from out of town. You can also listen to bands play or admire cattle. They, however, don't compare when talking about the experience. In my opinion, ferias are more fun and since the moment you walk in, you get an adrenaline thrill.
I know carnivals vary from town to town but something I haven't seen in our local carnival, besides food and candies being entirely mexican, is that ferias have vendors selling multiple things like bedlinen, dinnerware, decorations for the home, jewelry, bags, and other handmade accessories. Did I also mention there are indigenous men throwing themselves from an almost 100 ft pole and flying?
Sorry about the bad quality, but this is what the bedlinen stands look like. The seller is up there with a microphone talking like an auctioneer would. He gathers different products and sells them to you. You cannot go to the feria without hearing these men making deals; it's almost like a tradition, really.
Not my photo. The Voladores de Papantla doing their traditional dance/ritual. There are 5 men; 4 jump and one stays on top playing the flute. It's mesmerizing. Total respect for these men who do it continuously.
grandma went too and she was telling us stories about how she, her friends, and sisters would go to the feria before getting married. she said they would all make deals where they all had get on every ride and no one could say no. she also remembers going to the feria with my grandpa. the first time they went together on a date was my grandfathers first time ever on a ride. oh how I wish I could see how this town looked like in the 60s in person..
we must get a corn every chance we get. family rule!
Photos taken with a Minolta XG7 in Kodak Portra 400 film. I'm still practicing film photography. I thought these weren't going to come out good since I was having trouble with this camera. But no, once I got my hands on these pictures I was happy. I am in love with my minolta and this film. Always room for improvement though. I just wanted to document this day.
I hope you have a nice tuesday.
p.s. – in february david and I went to the carnival. you can check out that post here.
p.s.s. – (just in case you noticed) I had published this post before, but look it down because of some technical problems.
Next postone more day and this week is over. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,803 |
{"url":"https:\/\/xmswiki.com\/wiki\/SMS:ADCIRC_Weirs_and_Island_Barriers","text":"# SMS:ADCIRC Weirs and Island Barriers\n\nAn ADCIRC weir is a boundary type that are assigned to two nodestrings on an ADCIRC mesh. A weir comprises of two nodestrings next to each other with an equal amount of nodes on each nodestrings. In order to add a weir in ADCIRC, there must be two adjacent nodestrings available as shown in figures 1 and 2 below.\n\n Figure 1 \u2013 Parallel nodestrings that can be made into weirs. Figure 2 \u2013 Adjacent nodestrings that can be assigned as weir.\n\nThe number of nodes on each nodestrings must be of an equal amount or a weir cannot be assigned. See figure 3 below. Each node and it's corresponding node on the parallel nodestring will form a node pair.\n\nFigure 3 \u2013 Nodestrings with same number of nodes.\n\n## Weir Options\n\nOnce two nodestrings with same number of nodes exist, they can be assigned as a weir by selecting both weirs and selecting Assign BC. The Nodestring attributes will open. By selecting Weir and then clicking on the Parameters button, the Weir Options dialog will open. The dialog shows the different Node pairs and elevation for each node pair.\n\nExample of the Weir Options dialog.\n\n### Elevation\n\nElevation of each node pair. The elevation for each node pair can be entered manually or can be interpolated from a dataset\n\n### Super\n\nWeir flow coefficients for super critical flow. A typical value for this is 1.0.\n\n### Sub\n\nWeir flow coefficients for sub critical flow. A typical value for this is 1.0.\n\n\u2022 Pipe\n\u2022 Elevation = elevation of the pipe\n\u2022 Diameter = diameter of pipe\n\u2022 Coefficient = f (L\/D)\n${\\displaystyle f\\cdot {\\frac {L}{D}}}$ where\nL is the length of the pipe\nD is the hydraulic diameter of the pipe (for a pipe of circular section, this equals to the internal diameter of the pipe)\nf is a dimensionless coefficient called the Darcy friction factor. It can be found from a Moody diagram or by solving the Colebrook equation.\n\n### Interpolate Elevations Button\n\nClicking on the Interpolate Elevations button opens the XY Series Editor. The XY Series Editor can be used to generate and edit curves defined by a list of x and y coordinates. The curve can be created and edited by directly editing the xy coordinates using a spreadsheet list of the coordinates. An entire list of curves can be generated and edited with the editor and curves can be imported from and exported to text files for future use. It is also possible to paste the xy data directly to the spreadsheet.\n\n## Extract Elevations\n\nExample of the Extract Weir Elevations dialog.\n\nData entered in as a weir or island barrier boundary condition for ADCIRC define the crest elevation between the nodes. This elevation data is independent from the elevation of the nodes on the grid (usually it is assigned from a separate source).\n\nSMS includes tools to incorporate these elevations into a Cartesian grid that will be used in a different model and\/or a coverage. These tools are accessed by selecting the Extract Weir Elevations... command in the Nodestrings menu. This command is not available unless there is an ADCIRC mesh loaded into SMS.\n\n\u2022 The first section includes a toggle box to specify which weirs\/barriers are to be used in the operation. If the toggle is not selected, all weir\/barrier boundary conditions in the simulation are used. If it is toggled, only the weirs\/barriers that are selected (or partially selected) will be used. If a single nodestring from a weir\/barrier is selected, it is treated the same as if both were selected.\n\u2022 The second section maps the specified weirs to arcs. SMS will create one arc for each weir\/barrier, bisecting the area between the nodestrings that make up the boundary condition. The elevation of the nodes\/vertices created on the arc will match the specified crest elevations for the weir\/barrier. This can also determine if these arcs should be added to a new or existing coverage.\n\u2022 The third section modifies the elevation of the cells in one or more Cartesian grids, if they are loaded into SMS, to correspond to the weir\/barrier elevation. Adding the elevations to the grid causes the land surface to actually represent the shape of the weir\/barrier. Caution should be exercised since assigning the crest elevation to the grid can cause steep slopes between the weir\/barrier cells and adjacent cells.\n\nAfter selecting OK in the dialog, SMS will compute elevations at the midpoint of each node pair in the BC. This is done by first interpolating between the node elevations of each pair, and then subtracting the weir\/barrier elevation (which were specified in the weir or island barrier parameters) from that value.\n\nIf the coverage option is used, SMS will create arcs that represent the weirs or barriers on the specified coverage. The computed elevations will be assigned along the arc. If one or more grids are used, SMS will set the elevation values for all grid cells that lie underneath the midpoints to match the computed values.\n\n## Remove Weir\n\nSelecting two nodestrings that have been assigned a weir boundary condition allows using the Remove Weir command in the right-click menu. Using this command will bring up the Remove Weir dialog. This dialog gives the following options for removing the weir:\n\nThe Remove Weir dialog\n\u2022 Pave over \u2013 Removes the nodestrings that had been assigned the weir boundary condition.\n\u2022 Merge nodestrings \u2013 Results in new nodes down the center of where the two nodestrings used to make the weir boundary conditions.\n\u2022 Runumber \u2013 Generally required for model execution. This should be done later if not done with this step.","date":"2021-08-04 10:30:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 1, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.553724467754364, \"perplexity\": 1921.9216255475246}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046154798.45\/warc\/CC-MAIN-20210804080449-20210804110449-00376.warc.gz\"}"} | null | null |
Read the coverage stories of the events and happenings from the world of Pakistani cinema.
"Bin Roye" has its Press Conference in Karachi ; Announces its release date and...
Momin Ali Munshi - May 26, 2015 4
by Momin Ali MunshiAlthough the first two quarters of the year 2015 were/are not particularly encouraging for the Pakistani Cinema as only three films...
LSA 2017: Winners of film awards at the 16th Lux Style Awards 2017
Momin Ali Munshi - April 26, 2017 0
The 16th LUX Style Awards took place in Karachi this past week and we gave you, our readers, live updates from the event on...
Exclusive: Everything you need to know about the 5th HUM Awards!
Wow, time sure does fly! It just seems like a few weeks ago that we were at the 4th Hum Awards, while in just...
Information Minister Marriyum Aurangzeb promises tax exemptions for the film industry at Hum Awards
Zeeshan Mahmood - April 30, 2017 0
Minister of Information and Broadcasting Marriyum Aurangzeb announced the government's plan of incentivizing the film industry of Pakistan at 5th Hum Awards in Lahore...
The music of up-coming film Bachaana launched with a press event in Hardee's Lahore
Momin Ali Munshi - January 28, 2016 0
After the successful trailer launch event which took place in Karachi, upcoming film Bachaana launched its music with a press event in Hardee's Lahore....
Nominations for the 16th Annual Lux Style Awards are out!
Momin Ali Munshi - March 15, 2017 2
It just feels like yesterday when Ali Zafar gave one of the most memorable opening performances ever for an award show, when Sohai Ali Abro danced...
Arth 2 is a complete commercial film with great script at its core, says...
Zeeshan Mahmood - December 29, 2015 0
The press conference of Shaan Shahid's directorial comeback Arth 2 held today at Avari Hotel in Lahore. The conference was attended by the entire...
[Live] ARY Film Awards 2016: Watch out for all the action live from Dubai
Galaxy Lollywood - April 16, 2016 0
The biggest film event of the year is being held tonight in Dubai and Galaxy Lollywood is here to provide you all the action...
Humayun Saeed hosts THE party to celebrate the success of Pakistani Cinema.
Momin Ali Munshi - July 31, 2015 0
Humayun Saeed is surely one of the biggest names of the Pakistan Showbiz Industry and he is one of the few superstars we have....
Song line up of Noor Bukhari's 'Ishq Positive' unveiled
Aayan Mirza - July 17, 2016 0
Noor Bukhari's Ishq Positive has its release nearing up with it's cinema date set to be 22 July 2016, and before that comes a... | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,221 |
Q: java game I have made won't keep score import java.util.Scanner;
public class Game{
int score = 0;
Scanner reader = new Scanner(System.in);
String name;
String enter;
public void Play() {
System.out.print("Enter Player One Name: ");
name = reader.nextLine();//enter player name
Only using one player for now waiting to see if it works with one before adding another
System.out.println("Welcome Players!"+
"To win the game press enter to roll" +
"The first player to score 50 wins!!!"+
"Press enter to start the game!!!");
enter = reader.nextLine(); //This is a dummy code. Just pauses and waits for enter press.
int roll = (int)(Math.random()* 6 + 1);
score += roll; //will add roll value to current score
System.out.println("you rolled a: " + roll + " and are now on "
+ score);
while(score <= 50){
//String enter;
enter = reader.nextLine();
roll = (int)(Math.random()* 6 + 1);
score += roll;
I had thought that this would add the number you rolled to your current score.
if(roll % 7==0){
System.out.println("move forward 2 spaces!!" +
"New score is: " + score );
}else{
System.out.println(score);
}
if(roll % 9==0){
System.out.println("Sorry move back two spaces :("+
"New score is: " + score);
}else{
System.out.println(score);
}
if (roll == 12){
System.out.println("oh no! You lost all points"+
"New score is: " + score + roll);
score = 0;
}else{
System.out.println(score );
}
System.out.println(roll);
}
}
A: roll will always be between one and six, according to this code, and thus none of the if tests will ever be true. Did you mean to test score, perhaps? Or maybe you meant to accumulate rolls in roll by doing roll += (int)(Math.random()* 6 + 1); in your loop?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,039 |
The Pa-hsien Mountain (), or Eight Immortals Mountain, is a mountain in Heping District, Taichung, Taiwan. It is a branch of Mount Yu. Its height is 2,448 metres, which is around 8,000 Taiwanese feet (台尺). The pronunciation of eight thousand (baqian) and eight immortals are similar in Chinese, hence the name.
One of the three major logging stations in Taiwan used to be in the forest. There is an amusement park located on the part of the mountain that is located in Heping District. It is estimated that there are 59 native birds and 5 migratory birds.
See also
Eight Immortals
Penglai Mountain
References
Landforms of Nantou County
Mountains of Taiwan | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,337 |
module FunWith
module Testing
class TestCase < Minitest::Test
puts "----------------------------------------------- #{__FILE__}-----------------------------------------------"
extend TestCaseExtensions
end
end
end | {
"redpajama_set_name": "RedPajamaGithub"
} | 6,434 |
Atka es una ciudad situada en la costa este de la isla Atka, en el área censal de Aleutianas Occidentales en el estado estadounidense de Alaska. Según el censo de 2010 tenía una población de 61 habitantes.
Demografía
Según el censo de 2010, Atka tenía una población en la que el 4,9% eran blancos, 0,0% afroamericanos, 95,1% amerindios, 0,0% asiáticos, 0,0% isleños del Pacífico, el 0,0% de otras razas, y el 0,0% pertenecían a dos o más razas. Del total de la población el 0,0% eran hispanos o latinos de cualquier raza.
Localidades adyacentes
El siguiente diagrama muestra a las localidades más próximas a Atka.
Referencias
Enlaces externos
Localidades del Área censal de Aleutianas Occidentales | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 673 |
Just Listed! Check out this cute condo in Lochwood Landings! From top to bottom this home is gorgeous and move in ready today! Step inside to findan inviting family room with all new wide plank laminate flooring and a cozy fireplace! Adjacent you'll find a dining room that leads into thekitchen. This beautiful kitchen is bright and fresh with all new S/S appliances (included!) and new quartz countertops! Around the corner,you'll find 1 bedroom with new carpet, and an updated bathroom! Also, you'll find many updated fixtures, and all new interior paint throughout! This home truly feels new and fresh with all of its updates! Water, as well as other great HOA amenities, -included in your dues! Near shopping, many parks, a beautiful lake, restaurants and easy access to freeways. Easy access to the mountains! Don't wait; this cute home won't last long! | {
"redpajama_set_name": "RedPajamaC4"
} | 4,617 |
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" name="viewport"
content="width=device-width, initial-scale=1, maximum-scale=1, minimum-scale=1">
<!-- jQuery -->
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.3/jquery.min.js"></script>
<!-- Bootstrap -->
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.5/css/bootstrap.min.css">
<!-- React -->
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.3.2/react.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.3.2/react-dom.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/babel-core/5.8.34/browser.min.js"></script>
<!-- UU5 -->
<!-- <link rel="stylesheet" href="../../lib/uu5/uu5-03.min.css" /> -->
<script type="application/javascript" src="../../lib/uu5g03/uu5g03.min.js"></script>
<title>Example UU5.Forms.Checkbox 05</title>
</head>
<body>
<div id="renderHere"></div>
<script type="text/babel">
var Page = React.createClass({
statics: {
pageHeader: "Příklad UU5.Forms.Checkbox 05",
pageFooter: "Vytvořeno pomocí frameworku <UU5.DocKit.Bricks.LinkUU5/>",
sourceCode: "exampleUU5FormsCheckbox05.html"
},
render() {
return (
<UU5.Layout.Root>
{/*@@viewOn:0*/}
<UU5.Layout.Flc overflow={true}>
<h4>Checkbox Props: value</h4>
<UU5.FormsV3.Checkbox
label='Animal'
value
/>
<br/>
<h4>Checkbox Props: onGlyphicon, offGlyphicon, labelPosition='right'</h4>
<UU5.FormsV3.Checkbox
label='Animal'
onGlyphicon='uu-glyphicon-calendar'
offGlyphicon='uu-glyphicon-cross'
labelPosition='right'
/>
</UU5.Layout.Flc>
{/*@@viewOff:0*/}
</UU5.Layout.Root>
);
}
});
ReactDOM.render(React.createElement(Page, null), document.getElementById('renderHere'));
</script>
</body>
</html>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,427 |
I owe this photograph to some of my very best friends. Thank you to Shane Nelson for showing me this stunning location and a thank you to Andrew Flees for always joining me on epic adventures, you boys are the coolest! This is 'Lake of the Bones' (Shane gets credit for naming the place as well) it is a hidden dream destination in the Sleeping Bear Dunes and has the parks largest Ghost Forest. I hope everyone enjoys the warmth captured in this photograph!
Canon 6D, Nikon 14-24 (@14mm), ISO 100, F/22, two exposures were made to tackle the massive dynamic range, one at 1/5th for shadows one at 1/25 for highlights. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,912 |
Note: There may be some duplication due to cross-posting.
The police have fined a man £90 after he covered his head with his jumper to avoid a police trial of facial recognition technology (FRT). Other people were stopped by police during the trial for trying to hide their faces to avoid the cameras.
On the evening before National Security Advisor John Bolton reiterated that "all options [including, presumably, military intervention] are on the table" regarding the situation in Venezuela, Twitter announced that it had joined the US-backed coup by taking down 2,000 accounts that it said were engaged in a "state-backed influence campaign", according to RT.
Twitter has announced that it took down about 2,000 accounts in Venezuela, most of which it claimed were "engaged in a state-backed influence campaign." This comes amid accusations of a US-led coup attempt.
On September 15, 1970, U.S. President Richard Nixon and National Security Adviser Henry Kissinger authorized the U.S. government to do everything possible to undermine the incoming government of the socialist president of Chile, Salvador Allende. Nixon and Kissinger, according to the notes kept by CIA Director Richard Helms, wanted to "make the economy scream" in Chile; they were "not concerned [about the] risks involved." War was acceptable to them as long as Allende's government was removed from power. The CIA started Project FUBELT, with $10 million as a first installment to begin the covert destabilization of the country.
Europe's General Data Protection Regulation which was implemented last summer has far-reaching privacy rules. Commonly referred as the , this is now the standard which has forced most tech companies to rethink not only data collection practices but also how data is collected or they risk high fines. Where the US lacks a similar regulation to protect privacy of Internet users, many characterize Europe's GDPR as hurting privacy instead of protecting it while others accuse the EU of policing across its own borders. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,279 |
{"url":"https:\/\/physics.stackexchange.com\/questions\/303879\/can-an-accelerated-timelike-trajectory-reach-the-boundary-of-ads-space-in-finite\/304136","text":"# Can an accelerated timelike trajectory reach the boundary of AdS space in finite time?\n\nI understand why in anti-de Sitter (AdS) spacetime, null geodesics can reach spatial infinity in finite coordinate time, while timelike geodesics cannot reach spatial infinity at all, not even in infinite coordinate time (in the sense that any timelike geodesic's radius is bounded). But what about accelerated (i.e. non-geodesic) timelike trajectories? Can they reach spatial infinity in finite coordinate time? Finite proper time? In not, can they come arbitrarily close, unlike timelike geodesics?\n\nIntuitively, it seems to me that the case of accelerated timelike trajectories is intermediate between the case of timelike geodesics and the case of null geodesics, because an accelerated timelike trajectory can \"escape from the origin better than\" any timelike geodesic by accelerating against the AdS gravitational attraction, but it can't \"escape from the origin as well as\" a null geodesic because it can never hit the speed of light. My intuition is that an accelerated timelike trajectory could reach spatial infinity, but only in both infinite proper time and infinite coordinate time.\n\nBut I'm not confident that I'm correct, because I don't have good intuition for the boundary behavior of AdS space. The fact that all timelike geodesics are bounded away from spatial infinity suggests to me that it's \"harder\" to reach spatial infinity in AdS space than in Minkowski space. But on the other hand, the fact that null geodesics can reach spatial infinity in finite coordinate time suggests that it's \"easier\" to reach spatial infinity in AdS space than in Minkowski space. Clearly these intuitions conflict with each other.\n\n\u2022 I have not seen the details on AdS, but are you sure it's timelike geodesics, or instead timelike trajectories? Jan 9, 2017 at 5:56\n\u2022 Related, but does not have the answer to your question. Still, maybe you can use what's there. That's in physics.stackexchange.com\/questions\/116813\/\u2026 Jan 9, 2017 at 6:25\n\u2022 @BobBee ^^ What exactly do you mean by \"it's\"? I'm sure that timelike geodesics are bounded, and my question is whether or not all other timelike trajectories are as well. Jan 9, 2017 at 7:14\n\u2022 I meant you don't need to label them accelerated. You mean any time like trajectories, and I was trying to confirm that's what you wanted. The reference in my other post may help with an approach, but does not answer it directly. Jan 9, 2017 at 18:14\n\u2022 @BobBee Yes, as I said in the OP, by an \"accelerated\" timelike trajectory I just mean a timelike trajectory that isn't a geodesic. Jan 10, 2017 at 0:49\n\nThe issue of coordinate time vs. proper time\/affine parameter is a bit of a red herring, since the former is a purely gauge (i.e. coordinate-dependent) quantity, while the latter is physical but uninteresting in the context of the asymptotic boundary. For instance, you say that null geodesics reach infinity in finite coordinate time, but for a given null geodesic I could of course choose a time coordinate that diverges when the null geodesic reaches infinity, making that geodesic reach the boundary in infinite coordinate time. Likewise, by definition any curve (of any signature) that reaches the asymptotic boundary does so in infinite proper time\/distance\/affine parameter.\n\nInstead, the covariant observation is that null geodesics always reach the asymptotic boundary of AdS, while timelike ones never do. Your question can then be stated covariantly as: do there exist timelike curves that reach the asymptotic boundary of AdS? The answer is clear from the conformal diagram of AdS:\n\n(ignore the two dots labeled $$i^+$$ and $$i^-$$; I just grabbed this picture off the web). The asymptotic (or conformal) boundary of AdS is the vertical line marked $$r = \\infty$$ (the line $$r = 0$$ is just one possible choice of origin), and the line moving at 45$$^\\circ$$ is a light ray (shown here reaching the boundary and then bouncing back in). With this picture, it's clear that we can draw a timelike trajectory (that is, a line whose angle with the vertical is always less than 45$$^\\circ$$) to and from the conformal boundary, so indeed, there do exist timelike curves that do reach asymptotic infinity.\n\nEdit: As Peter pointed out in a comment, a statement I made regarding proper time in my previous answer was slightly wrong. I believe the correct statement is that any timelike curve that reaches the asymptotic boundary must either do so in infinite proper time (e.g. a uniformly accelerated observer can eventually reach the boundary, but takes an infinite proper time to get there) or have divergent geodesic acceleration there (e.g. a timelike curve can get \"close enough\" to being null that it reaches the boundary in finite proper time, but it takes an infinitely large acceleration to do so). The physical interpretation, of course, is that no finitely-accelerated observer can reach the asymptotic boundary of AdS in finite proper time.\n\n\u2022 Why must it reach infinity in infinite proper time? There's time dilation to account for. Aug 7, 2019 at 0:59\n\u2022 You're right; if a timelike curve approaches a null one sufficiently fast asymptotically, you can engineer the proper time along it to be finite. But I think its geodesic acceleration would then necessarily need to diverge as it reaches the boundary, so the curve would be singular in that sense. (A timelike curve with constant but finite acceleration, such as those generated by Rindler time translation in the AdS-Rindler wedge, would asymptotically approach a null curve but would still take infinite proper time to reach the boundary, I believe.) Aug 8, 2019 at 2:33\n\u2022 It would be very good to give a reference or calculation saying that a time-like curve with constant acceleration can reach the boundary. I don't see why that should be the case. Doesn't just hovering a constant distance from the origin require arbitrarily large acceleration as you approach the boundary? AdS space has some extremely non-intuitive properties, and you can't just use your intuition. Aug 8, 2019 at 10:13\n\u2022 The \"AdS-Rindler curves\" I mentioned are such an example. These are the integral curves of a Killing vector field which leaves an AdS-Rindler wedge fixed; because they are generated by an isometry, their geodesic acceleration is constant, but from the structure of the AdS-Rindler wedge it's clear they still reach the asymptotic boundary. Aug 8, 2019 at 13:02\n\u2022 (Explicitly, the relevant portion of the AdS-Rindler metric is $ds^2 = -\\xi^2 dt^2 + d\\xi^2\/(1+\\xi^2)$, and the curves I'm talking about are curves of fixed $\\xi$. These curves have unit tangent $u^a = (\\partial_t)^a\/\\xi$, and it's easy to check that their acceleration $a^a = u^b \\nabla_b u^a$ has constant norm along each such curve. That they reach the asymptotic boundary of global AdS as $t \\to \\pm \\infty$ can be verified from e.g. equation (2.6) of arxiv.org\/pdf\/1211.7370.pdf .) Aug 8, 2019 at 13:04","date":"2022-07-05 06:48:56","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 6, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7869080305099487, \"perplexity\": 359.381689657536}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.3, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-27\/segments\/1656104514861.81\/warc\/CC-MAIN-20220705053147-20220705083147-00775.warc.gz\"}"} | null | null |
\section{Introduction}
There has recently been a renewal of interest in the equilibrium states (the KMS states) of operator-algebraic dynamical systems consisting of an action of the real line (the \emph{dynamics}) on a $C^*$-algebra. There has been particular interest in systems involving graph algebras and their Toeplitz extensions \cite{EL, KW, T, CL}.
Very satisfactory results have been obtained for sytems associated to finite directed graphs, and we now have concrete descriptions of the simplices of KMS$_\beta$ states on the Toeplitz algebras at all inverse temperatures $\beta$ \cite{aHLRS1, aHLRS2}. Here we review these results, and discuss some surprising applications to work of Thomsen on systems involving the Cuntz-Pimsner algebras of local homeomeorphisms \cite{Th1}. One main conclusion of our recent work with Afsar \cite{AaHR} is that lower and upper bounds for the possible inverse temperatures given by Thomsen are sharp. For these applications we do not need the full strength of the general results in \cite{aHLRS2}, and in this article we describe a more direct approach.
\section{The Toeplitz algebra of a graph}
We suppose that $E=(E^0,E^1,r,s)$ is a finite directed graph. A \emph{Toeplitz-Cuntz-Krieger $E$-family} consists of mutually orthogonal projections $\{P_v:v\in E^0\}$ and partial isometries $\{S_e:e\in E^1\}$ in a $C^*$-algebra such that $S_e^*S_e=P_{s(e)}$ for every $e\in E^1$ and
\begin{equation}\label{TCK}
P_v\geq \sum_{r(e)=v}S_eS_e^*\text{ for every $v\in E^0$}
\end{equation}
(where we interpret an empty sums as $0$). Since the vertex projections are mutually orthogonal, the relation \eqref{TCK} implies that the range projections $S_eS_e^*$ are also mutually orthogonal. (See \cite[Corollary~1.2]{aHLRS1}, for example.)
For $n\geq 2$, we write
\[
E^n:=\big\{\mu=\mu_1\mu_2\cdots\mu_n:s(\mu_i)=r(\mu_{i+1})\text{ for $1\leq i<|\mu|:=n$}\big\}
\]
for the set of paths of length $n$ in $E$, and note that $S_\mu:=S_{\mu_1}S_{\mu_2}\cdots S_{\mu_n}$ is a partial isometry for every $\mu\in E^n$. We write $E^*:=\bigcup_{n\geq 0} E^n$ for the set of finite paths. Then for $\mu,\nu,\alpha,\beta\in E^*$ we have the product formula
\begin{equation}\label{prodform}
(S_\mu S_\nu^*)(S_\alpha S_\beta^*)=\begin{cases}
S_{\mu\alpha'}S_\beta^* & \text{if $\alpha=\nu\alpha'$}\\
S_\mu S_{\beta\nu'}^* &\text{if $\nu=\alpha\nu'$}\\
0&\text{otherwise.}\end{cases}
\end{equation}
The \emph{Toeplitz algebra} $\mathcal{T} C^*(E)$ of $E$ is the $C^*$-algebra generated by a universal Toeplitz-Cuntz-Krieger $E$-family $(p,s)$. The product formula \eqref{prodform} implies that the elements $\{s_\mu s_\nu^*:\mu,\nu\in E^*\}$ span a $*$-subalgebra of $\mathcal{T} C^*(E)$, and hence we have
\[
\mathcal{T} C^*(E)=\overline{\operatorname{span}}\{s_\mu s_\nu^*:\mu,\nu\in E^*\}.
\]
The quotient of $\mathcal{T} C^*(E)$ by the ideal generated by the gap projections
\[
\Big\{p_v-\sum_{r(e)=v}s_es_e^*:v\in E^0\Big\}
\]
is the usual graph algebra or Cuntz-Krieger algebra $C^*(E)$.
For every graph $E$ there is a canonical Toeplitz-Cuntz-Krieger $E$-family $(Q,T)$ on the \emph{finite-path space} $\ell^2(E^*)$, characterised by the following actions on the usual orthonormal basis $\{h_\mu:\mu\in E^*\}$:
\[
Q_v h_\mu=\begin{cases} h_{\mu}&\text{if $v=r(\mu)$}\\
0&\text{otherwise} \end{cases}
\quad\text{and}\quad T_e h_\mu=\begin{cases} h_{e\mu}&\text{if $s(e)=r(\mu)$}\\
0&\text{otherwise.} \end{cases}
\]
The universal property of $\mathcal{T} C^*(E)$ then gives a representation $\pi_T=\pi_{Q,T}$ of $\mathcal{T} C^*(E)$ on $\ell^2(E^*)$ such that $\pi_T(p_v)=Q_v$ and $\pi_T(s_e)=T_e$; we call $\pi_T$ the \emph{finite-path representation}. The gap projections $Q_v-\sum_{r(e)=v}T_eT_e^*$ are the projections on $\C h_v$, and hence are all nonzero. Thus the uniqueness theorem for Toeplitz algebras \cite[Corollary~4.2]{FR} implies that $\pi_T$ is faithful.
There is a gauge action $\gamma:\mathbb{T}\to \operatorname{Aut} \mathcal{T} C^*(E)$ such that $\gamma_z(p_v)=p_v$ and $\gamma_z(s_e)=zs_e$, and this induces the usual gauge action on the quotient $C^*(E)$. We are interested in the dynamics $\alpha:\R\to \operatorname{Aut} \mathcal{T} C^*(E)$ given by $\alpha_t=\gamma_{e^{it}}$, and its analogue on $C^*(E)$. In particular, we wish to study the KMS states for this dynamics.
\section{KMS states on the Toeplitz algebra}
\label{sec:1}
The spanning elements $s_\mu s_\nu^*$ for $\mathcal{T} C^*(E)$ are are all analytic for the action $\alpha$. Hence if $\phi$ is a KMS$_\beta$ state on $(\mathcal{T} C^*(E),\alpha)$, we have
\begin{align*}
\phi(s_\mu s_\nu^*)&=\phi(s_\nu^*\alpha_{i\beta}(s_\mu))=e^{-\beta|\mu|}\phi(s_\nu^* s_\mu)\\
&=e^{-\beta(|\mu|-|\nu|)}\phi(s_\mu s_\nu^*).
\end{align*}
So $\phi(s_\mu s_\nu^*)\not=0\Longrightarrow |\mu|=|\nu|$, and then
\[
\phi(s_\mu s_\nu^*)\not=0\Longrightarrow\big(s_\nu^* s_\mu\not=0\text{ and }|\mu|=|\nu|\big)\Longrightarrow\mu=\nu.
\]
Now a routine computation using the product formula \eqref{prodform} gives the following:
\begin{lem}\label{nascKMS}\cite[Proposition~2.1]{aHLRS1} A state $\phi$ on $\mathcal{T} C^*(E)$ is KMS$_\beta$ for $\alpha$ if and only if
\[
\phi(s_\mu s_\nu^*)=
\delta_{\mu,\nu}e^{-\beta|\mu|}\phi(p_{s(\mu)}).
\]
\end{lem}
Suppose $\phi$ is a KMS$_\beta$ state on $(\mathcal{T} C^*(E),\alpha)$. Then for each $v\in E^0$ the Toeplitz-Cuntz-Krieger relation gives
\begin{align}\label{TCKineq}
\phi(p_v)\geq\sum_{r(e)=v}\phi(s_es_e^*)=\sum_{r(e)=v}e^{-\beta}\phi(p_{s(e)}),
\end{align}
where we interpret the empty sum as $0$ if $v$ is a source. The \emph{vertex matrix} of $E$ is the $E^0\times E^0$ integer matrix $A$ with entries \[
A(v,w)=|r^{-1}(v)\cap s^{-1}(w)|.\]
We can rewrite the inequality \eqref{TCKineq} as
\begin{equation}\label{subinv}
e^{\beta}\phi(p_v)\geq\sum_{w\in E^0}\;\sum_{r(e)=v,\;s(e)=w}\phi(p_w)=\sum_{w\in E^0}A(v,w)\phi(p_{w}),
\end{equation}
so $m=(m_v):=(\phi(p_v))\in [0,\infty)^{E^0}$ satisfies $Am\leq e^{\beta}m$; we say that $m$ is a \emph{subinvariant vector} for $A$.
If $\phi$ factors through a KMS$_\beta$ state of $C^*(E)$, then we have equality throughout \eqref{TCKineq} and \eqref{subinv}, and $m$ satisfies $Am= e^{\beta}m$. If $E$ is strongly connected, $A$ is irreducible and $e^\beta$ has to be the Perron-Frobenius eigenvalue of $A$. The Perron-Frobenius theorem then says many things: thus in particular we know that the eigenvalue is the spectral radius $\rho(A)$, that the eigenspace is one-dimensional, and that there is an eigenvector with positive entries (see \cite[Theorem~2.6]{DZ} or \cite[Theorem~1.6]{seneta}). Since $\phi$ is a state, we have
\[
1=\phi(1)=\sum_v \phi(p_v)=\sum_v m_v,
\]
and hence $m=\big(\phi(p_v)\big)_{v\in E^0}$ is the unique eigenvector in $(0,\infty)^{E^0}$ with $\|m\|_1=1$. The formula in Lemma~\ref{nascKMS} says that $\phi(s_\mu s_\nu^*)=
\delta_{\mu,\nu}e^{-\beta|\mu|}m_{s(\mu)}$ for all $\mu,\nu\in E^*$, so the vector $m$ completely determines the state $\phi$. Thus we recover the following elegant result of Enomoto, Fujii and Watatani \cite{EFW}:
\begin{theorem} Suppose that $E$ is a strongly connected graph with vertex matrix $A$. Then $(C^*(E),\alpha)$ has at most one KMS state. This state has inverse temperature $\ln\rho(A)$, where $\rho(A)$ is the spectral radius of $A$.
\end{theorem}
They proved existence of the KMS$_{\ln\rho(A)}$ state too, but we'll get to that.
For states on $\mathcal{T} C^*(E)$, the vector $m$ only satisfies the subinvariance relation $Am\leq e^{\beta}m$, but when $A$ is irreducible Perron-Frobenius theory has things to say about this too. For example:
\begin{itemize}
\item If $Am\leq e^{\beta}m \text{ and }\beta=\ln\rho(A)$, then $Am= e^{\beta}m$, so that $m$ is the Perron-Frobenius eigenvector.
\item Suppose that $Am\leq e^{\beta}m$. Then $Am\not=e^{\beta}m\Longleftrightarrow\beta>\ln\rho(A)$.
\end{itemize}
This suggests that we look more carefully at $\beta$ larger than the \emph{critical inverse temperature} $\beta_c:=\ln\rho(A)$.
So we consider $\beta>\ln\rho(A)$. We find it interesting that, although we were motivated to do so by the Perron-Frobenius theory, which applies only when $E$ is strongly connected, the following analysis does not require any connectivity hypothesis on $E$. Thus we consider an arbitrary finite directed graph $E$, which could have sinks or sources, and a KMS$_\beta$ state $\phi$ on $\mathcal{T} C^*(E)$.
Take $m=\big(\phi(p_v)\big)$ as before. Then $\epsilon:=(1-e^{-\beta}A)m$ has nonnegative entries, not all $0$. Since $e^{\beta}>\rho(A)$, $e^{\beta}$ is not in the spectrum of $A$, and $1-e^{-\beta}A$ is invertible. Thus we can recover $m$ as $(1-e^{-\beta}A)^{-1}\epsilon$. Our main point is that we can describe geometrically the set of $\epsilon\in [0,1]^{E^0}$ which arise from unit vectors $m$ in $\ell^1(E^0)$. For $v\in E^0$, define $y^\beta\in [1,\infty)^{E^0}$ by
\begin{equation}\label{ybeta}
y^\beta_v:=\sum_{n=0}^\infty\;\sum_{w\in E^0} e^{-\beta n}A^n(w,v)=(1-e^{-\beta}A)^{-1}\delta_v;
\end{equation}
the series converges because $\sum_ne^{-\beta n}A^n$ converges in the operator norm with sum $(1-e^{-\beta}A)^{-1}$. Then $m:=(1-e^{-\beta}A)^{-1}\epsilon$ has $\|m\|_1=1$ if and only if
\[
1=\epsilon\cdot y^\beta:=\sum_{v\in E^0}\epsilon_vy^\beta_v
\]
(see Theorem~3.1(a) of \cite{aHLRS1}).
Then the main theorem of \cite{aHLRS1} says:
\begin{theorem}\label{paraKMS}
Suppose $E$ is a finite graph with vertex matrix $A$, and $\beta>\ln \rho(A)$. Suppose $\epsilon\cdot y^\beta=1$. Then there is a KMS$_\beta$ state $\phi_\epsilon$ of $\mathcal{T} C^*(E)$ such that
\[
\phi_\epsilon(p_v)=\big((1-e^{-\beta}A)^{-1}\epsilon\big)_v\quad\text{for all $v\in E^0$.}
\]
The map $\epsilon\mapsto \phi_\epsilon$ is an isomorphism of $\Delta_\beta=\{\epsilon:\epsilon\cdot y^\beta=1\}$ onto the simplex of KMS$_\beta$ states of $(\mathcal{T} C^*(E),\alpha)$.
\end{theorem}
We proved existence of the KMS state $\phi_\epsilon$ in \cite[Theorem~3.1(b)]{aHLRS1} by a spatial argument using the finite-path representation $\pi_T$ of $\mathcal{T} C^*(E)$ on $\ell^2(E^*)$. Then surjectivity of $\epsilon\mapsto \phi_\epsilon$ amounts to our earlier observation that the subinvariant vector $m=\big(\phi(p_v)\big)_{v\in E^0}$ determines a KMS state $\phi$.
The set $\Delta_\beta=\{\epsilon:\epsilon\cdot y^\beta=1\}$ parametrising the KMS$_\beta$ states is a simplex in the positive cone $[0,\infty)^{E^0}$ of $\R^{E^0}$ with extreme points on the coordinate axes, and the vector $y^\beta$ is normal to this simplex. As $\beta$ decreases to the critical value $\beta_c=\ln\rho(A)$, the terms in the series on the right-hand side of \eqref{ybeta} get larger, and the simplex contracts towards the origin.
The preceding analysis does not apply when $\beta=\beta_c=\ln\rho(A)$ is critical, because then the matrix $1-e^{-\beta}A$ need not be invertible. However, we can take a sequence $\beta_n$ decreasing to $\ln\rho(A)$, and use weak* compactness of the state space to get a KMS$_{\ln\rho(A)}$ state of $\mathcal{T} C^*(E)$ \cite[Proposition~4.1]{aHLRS1}. When $E$ is strongly connected, this is the only KMS$_{\ln\rho(A)}$ state, and we can deduce from Perron-Frobenius that it factors through the graph algebra $C^*(E)$. In particular, we recover the existence of the KMS$_{\ln \rho(A)}$ state, first established by other methods in \cite{EFW}.
We can sum up our discussion as follows:
\begin{cor}\label{subinv2}
Suppose that $E$ is a directed graph with vertex matrix $A$, and that $\beta\in (0,\infty)$ satisfies $\beta\geq \ln\rho(A)$. Then the map $\phi\mapsto m^\phi:=\big(\phi(p_v)\big)$ is a bijection of the set of KMS$_\beta$ states of $(\mathcal{T} C^*(E),\alpha)$ onto the unit vectors $m$ in $[0,\infty)^{E^0}\subset\ell^1(E^0)$ satisfying the subinvariance relation $Am\leq e^{\beta}m$.
\end{cor}
For $\beta> \ln\rho(A)$, Theorem~\ref{paraKMS} is stronger, because it describes the solutions of the subinvariance relation. But for some applications, such as those in \S\ref{sec:dumb}, we can deal directly with the subinvariance relation in an \emph{ad hoc} manner.
\section{Dumbbell graphs}\label{sec:dumb}
We say that a graph $E$ is \emph{reducible} if it is not strongly connected, or equivalently if its vertex matrix $A$ is not irreducible. For $v,w\in E^0$, we write $v\leq w$ to mean that
\[
vE^*w:=\{\mu\in E^*: r(\mu)=v\text{ and }s(\mu)=w\}
\]
is nonempty (or in other words, that there is a path from $w$ to $v$). Then we define a relation $\sim$ on $E^0$ by
\[
v\sim w\Longleftrightarrow v\leq w\text{ and }w\leq v.
\]
This is an equivalence relation (it is reflexive because $v\in vE^*v$), and we write $E^0/\!\!\sim$ for the set of equivalence classes.
For each $C\in E^0/\!\!\sim$, we define $A_C$ to be the $C\times C$ matrix obtained by deleting all rows and columns involving vertices not in $C$. We can view $A_C$ as the vertex matrix of the subgraph $E_C:=(C, E^1\cap r^{-1}(C)\cap s^{-1}(C),r,s)$. Each $A_C$ is either a $1\times 1$ zero matrix (if $C$ is a singleton set $\{v\}$ and there is no loop at $v$) or an irreducible matrix (in which case we call $E_C$ a \emph{strongly connected component} of $E$). It is possible to order the set $E^0$ so that the vertex matrix $A$ is block upper-triangular with diagonal blocks $A_C$ (see \cite[\S2.3]{aHLRS2}), and it follows that $\rho(A)=\max_C\rho(A_C)$.
Now we consider the KMS states on $\mathcal{T} C^*(E)$ when $E$ is reducible. There are three situations that we have to deal with:
\begin{itemize}
\item For $\beta>\ln \rho(A)$, Theorem~\ref{paraKMS} applies, and we have a $(|E^0|-1)$-dimensional simplex of KMS$_\beta$ states on $\mathcal{T} C^*(E)$.
\item For $\beta=\ln\rho(A)$, we focus on the \emph{critical components} $C\in E^0/\!\!\sim$ that have $\rho(A_C)=\rho(A)$. The relation $\leq $ descends to a well-defined relation on the set of critical components, and then a critical component $C$ is \emph{minimal} if $D$ critical and $D\leq C$ imply $D=C$. The behaviour of the KMS$_{\ln\rho(A)}$ states of $\mathcal{T} C^*(E)$ depends on the location of the minimal critical components.
\item Recall that a subset $H$ of $E^0$ is \emph{hereditary} if $v\in H$ and $v\leq w$ imply $w\in H$, and that the Toeplitz algebra $\mathcal{T} C^*(E\backslash H)$ of the graph
\[
E\backslash H:=(E^0\backslash H, E^1\cap s^{-1}(E^0\backslash H), r, s)
\]
is a quotient of $\mathcal{T} C^*(E)$ \cite[Proposition~2.1]{aHLRS2}. For $\beta<\ln\rho(A)$, we consider the hereditary subset $H$ of $E^0$ generated by the critical components (which is also generated by the minimal critical components). If $H$ is not all of $E^0$, then we can apply Theorem~\ref{paraKMS} to $E\backslash H$ and get KMS$_\beta$ states of $\mathcal{T} C^*(E)$ for $\ln\rho(A_{E\backslash H})<\beta<\ln\rho(A)$ which factor through the quotient map onto $\mathcal{T} C^*(E\backslash H)$.
\end{itemize}
The first and third situations both require straightforward applications of Theorem~\ref{paraKMS}, and the interesting things happen when $\beta=\ln\rho(A)$ is critical. Then the phrase ``depends on the location of the minimal critical components'' needs clarification. We illustrate its meaning with some examples, which fortunately are enough for the main applications in \cite{AaHR}. The key feature of these examples is that the strongly connected components have just one vertex each. We call such graphs \emph{dumbbell graphs}.
\begin{example} We consider the following graph $E$:
\[
\begin{tikzpicture}
\node[inner sep=1pt] (v) at (0,0) {$v$};
\node[inner sep=1pt] (w) at (2,0) {$w$};
\draw[-latex] (v)--(w);
\foreach \x in {0,2} {
\draw[-latex] (v) .. controls +(1.\x,1.\x) and +(-1.\x,1.\x) .. (v);
}
\foreach \x in {0,2,4} {
\draw[-latex] (w) .. controls +(1.\x,1.\x) and +(-1.\x,1.\x) .. (w);
}
\end{tikzpicture}
\]
for which $\rho(A)=3$. In this example, the hereditary closure of the critical component $\{w\}$ is all of $E^0$, and hence the third situation does not arise.
If we list $E^0=\{w,v\}$, then $A=\big(\begin{smallmatrix}3&1\\0&2\end{smallmatrix}\big)$. For $\beta=\ln \rho(A)=\ln 3$ we have $e^\beta=3$, and the subinvariance relation $Am\leq e^\beta m$ says
\[
Am=\begin{pmatrix}3&1\\0&2\end{pmatrix}\begin{pmatrix}m_w\\m_v\end{pmatrix}=\begin{pmatrix}3m_w+m_v\\3m_v\end{pmatrix}\leq 3\begin{pmatrix}m_w\\m_v\end{pmatrix}.
\]
The only unit vector in $[0,\infty)^{E^0}\subset \ell^1(E^0)$ which satisfies this relation is $m=(1,0)$. Thus Corollary~\ref{subinv2} says there is a unique KMS$_{\ln 3}$ state on $\mathcal{T} C^*(E)$. This state factors through $C^*(E)$.
\end{example}
\begin{example}\label{2nddumb}
Next we switch the horizontal arrow, so $E$ is
\[
\begin{tikzpicture}
\node[inner sep=1pt] (v) at (0,0) {$v$};
\node[inner sep=1pt] (w) at (2,0) {$w$};
\draw[-latex] (w)--(v);
\foreach \x in {0,2} {
\draw[-latex] (v) .. controls +(1.\x,1.\x) and +(-1.\x,1.\x) .. (v);
}
\foreach \x in {0,2,4} {
\draw[-latex] (w) .. controls +(1.\x,1.\x) and +(-1.\x,1.\x) .. (w);
}
\end{tikzpicture}
\]
With $E^0=\{v,w\}$, $A=\big(\begin{smallmatrix}2&1\\0&3\end{smallmatrix}\big)$, and subinvariance for $\beta=\ln 3$ reduces to $m_v\leq m_w$. This graph also has just one critical component $\{w\}$, but this time $\{w\}$ is hereditary, and the graph $E\backslash H$ has vertex set $\{v\}$, so the third situation kicks in.
We find:
\begin{itemize}
\item For $\beta>\ln 3$, we have a one-dimensional simplex of KMS$_\beta$ states on $\mathcal{T} C^*(E)$, none of which factor through $C^*(E)$.
\item The simplex of KMS$_{\ln 3}$ states on $\mathcal{T} C^*(E)$ has extreme points $\phi_v$ ($m_v=m_w=\frac{1}{2}$) and $\phi_w$ ($m_v=0$); only $\phi_w$ factors through a state of $C^*(E)$.
\item For $\ln 2\leq \beta<\ln 3$, there is a unique KMS$_\beta$ state $\phi_v$ on $\mathcal{T} C^*(E)$ which factors through the quotient map corresponding to the hereditary set $\{w\}\subset E^0$.
\item For $\beta=\ln 2$, the state $\phi_v$ factors through $C^*(E)$.
\item For $\beta<\ln 2$, there are no KMS$_\beta$ states on $\mathcal{T} C^*(E)$.
\end{itemize}
\end{example}
When a minimal strongly connected component $E_C$ has more than one vertex, we organise the block form for $A$ in three pieces: we take the hereditary closure $H$ of the critical components, and decompose $E^0=(E^0\backslash H)\cup C\cup (H\backslash C)$. The Perron-Frobenius eigenvector for $A_C$ gives a KMS$_{\ln \rho(A)}$ state $\psi_C$ that has $\phi(p_v)=0$ for $v\in H\backslash C$, but has $\phi(p_v)\not=0$ for vertices $v$ such that $vE^*C\not=\emptyset$: the precise formula is given in \cite[Theorem~4.3(a)]{aHLRS2}. Since $\rho(A_{E\backslash H})<\rho(A)$, we can also use Theorem~\ref{paraKMS} to find KMS$_{\ln\rho(A)}$ states on $\mathcal{T} C^*(E\backslash H)$, and lift them to KMS$_{\ln\rho(A)}$ states of $\mathcal{T} C^*(E)$. Again the formulas and the complete classification are given in \cite[Theorem~4.3]{aHLRS2}.
To construct KMS states on the usual graph algebra $C^*(E)$, we need to know which states on $\mathcal{T} C^*(E)$ factor through $C^*(E)$. Here we hit another subtlety: distinct hereditary sets give distinct ideals in $\mathcal{T} C^*(E)$ but not necessarily in $C^*(E)$, where the ideal in $C^*(E)$ associated to a hereditary subset $H$ of $E^0$ depends only on the saturation of $H$. This problem is solved in \cite[Theorem~5.3]{aHLRS2}, which gives a recipe for finding all the KMS$_\beta$ states of $\mathcal{T} C^*(E)$ and $C^*(E)$ for fixed $\beta$.
\section{$C^*$-algebras from local homeomorphisms}\label{sec:local}
We consider a compact Hausdorff space $Z$ and a surjective local homeomorphism $h:Z\to Z$. In our main examples in the next section, $Z$ will be the infinite-path space $E^\infty$ of a finite directed graph with the topology inherited from the product space $(E^1)^\infty$, and $h$ will be the backward shift $\sigma$ defined by
\[
\sigma(e_1e_2e_3\cdots)=e_2e_3\cdots.
\]
If $E$ has no sources, then $\sigma$ is a homeomorphism on each cylinder set $Z(\mu)$, and hence is a local homeomorphism; if $E$ has no sinks, then $\sigma$ is also surjective.
So we shall suppose in the rest of this paper that $E$ is a finite graph with no sinks or sources, and then $\sigma:E^\infty\to E^\infty$ is a good example to bear in mind for this section.
We can view $C(Z)$ as a Hilbert bimodule $X$ over the $C^*$-algebra $C(Z)$, by setting $(a\cdot x\cdot b)(z)=a(z)x(z)b(h(z))$ and
\[
\langle x,y \rangle(z)=\sum_{h(w)=z}\overline{x(w)}y(w)\quad \text{for $x,y\in X$.}
\]
This Hilbert bimodule has both a Toeplitz algebra $\mathcal{T}(X)$ and a Cuntz-Pimsner algebra $\mathcal{O}(X)$: the Toeplitz algebra is generated by a representation $(\psi,\pi)$ characterised by $\psi(a\cdot x\cdot b)=\pi(a)\psi(x)\pi(b)$ and $\pi(\langle x,y \rangle)=\psi(x)^*\psi(y)$, and the Cuntz-Pimsner algebra \cite{P} is a quotient of $\mathcal{T}(X)$. For our purposes, all the necessary background material is in Chapter~8 of \cite{R}. The Cuntz-Pimsner algebra $\mathcal{O}(X)$ is an example of Katsura's topological-graph algebras: in the conventions of \cite[Chapter~9]{R} (which are a little different from those in Katsura's original paper \cite{K}), the graph is $(Z,Z,\id,h)$.
The Toeplitz algebra $\mathcal{T}(X)$ carries a gauge action $\gamma$ of the circle characterised by $\gamma_z(\psi(x))=z\psi(x)$ and $\gamma_z(\pi(a))=\pi(a)$, and this lifts to a dynamics $\alpha:t\mapsto \gamma_{e^{it}}$. The kernel of the quotient map onto $\mathcal{O}(X)$ is invariant under $\gamma$, and hence we also get a dynamics on $\mathcal{O}(X)$ (still denoted by $\alpha$).
Thomsen \cite{Th1} has studied the KMS states of the quotient system $(\mathcal{O}(X),\alpha)$ (and he worked with much more general systems $(Z,h)$\,). He showed that the possible inverse temperatures of the KMS states all lie in a finite interval $[\beta_l,\beta_c]$, and gave formulas for upper and lower bounds:
\begin{align*}\label{defb}
\beta_c&=\limsup_{n\to \infty}\Big(n^{-1}\ln\Big(\max_{z\in Z}|h^{-n}(z)|\Big)\Big),\ \text{and}\\
\beta_l&=\limsup_{n\to \infty}\Big(n^{-1}\ln\Big(\min_{z\in Z}|h^{-n}(z)|\Big)\Big)
\end{align*}
(applying \cite[Theorem~6.8]{Th1} with the function $F\equiv 1$; see \cite[Remark~6.3]{AaHR} for the connections with Thomsen's notation). We are not aware that Thomsen has discussed the extent to which these bounds might be sharp.
In our recent work with Afsar \cite{AaHR}, we have studied the KMS states of the Toeplitz system $(\mathcal{T}(X),\alpha)$. We viewed $C(Z)$ as a continuous analogue of the (finite-dimensional) space $C(E^0)$, and followed the strategy of \cite{aHLRS1}. We found that, for inverse temperatures $\beta$ larger than Thomsen's $\beta_c$, the KMS$_\beta$ states are parametrised by a simplex $\Sigma_\beta$ of finite measures $\epsilon$ on $Z$ satisfying a normalisation condition of the form
\[
\int f_\beta\,d\epsilon=1,
\]
where $f_\beta$ is a fixed continuous function defined by summing a series like that defining $y_\beta$ in \eqref{ybeta} \cite[Theorem~5.1]{AaHR}. At $\beta_c$, there is a phase transition: we can see by passing to limits as $\beta$ decreases to $\beta_c+$ that there exist KMS$_{\beta_c}$ states on $\mathcal{T}(X)$, and can argue by mimicking our earlier results in \cite{aHLRS1} that at least one of them factors through $\mathcal{O}(X)$. (This is Theorem~6.1 in \cite{AaHR}.) So, in our generality at least, Thomsen's upper bound is sharp.
If $E$ is a finite graph, then there is a natural Hilbert bimodule $X(E)$ over the commutative $C^*$-algebra $C(E^0)$, and the Toeplitz algebra $\mathcal{T}(X(E))$ was the original model of the Toeplitz-Cuntz-Krieger algebra $\mathcal{T} C^*(E)$ (see \cite{FR} and \cite[Chapter~8]{R}). This bimodule is not given by a local homeomorphism, so it does not quite fit the set-up of the present section, but the analysis of \cite{AaHR} was inspired by analogy with that of \cite{aHLRS1}. As we mentioned earlier, we can also directly apply the results of \cite{AaHR} to the shift $\sigma$ on the compact path space $E^\infty$, and this gives another connection to the results of \cite{aHLRS1} and \cite{aHLRS2}.
\section{Shifts on path spaces}\label{sec:shift}
We consider again a finite directed graph $E$ with no sinks or sources, and the infinite-path space $E^\infty$. Then $E^\infty$ is a compact Hausdorff space and the backward shift $\sigma:E^\infty\to E^\infty$ is a surjective local homeomorphism. So as in \S\ref{sec:local}, we can consider the Hilbert bimodule over the commutative $C^*$-algebra $C(E^\infty)$ with underlying space $X=C(E^\infty)$. At this point we choose to write $X(E^\infty)$ for $X$ to emphasise that this is not the graph bimodule $X(E)$ studied in \cite{FR} and \cite[Chapter~8]{R}.
The topology on $E^\infty$ arises from viewing it as a subset of the infinite product $(E^1)^\infty$ of the finite set $E^1$, and the cylinder sets
\[
Z(\mu)=\{x\in E^\infty: x_i=\mu_i\text{ for $i\leq |\mu|$}\}
\]
associated to finite paths $\mu\in E^*$ form a basis of compact-open sets for the topology on $E^\infty$. Then a straightforward calculation shows:
\begin{lem}\label{includeTalgs}
The elements $P_v:=\pi(\chi_{Z(v)})$ and $S_e:=\psi(\chi_{Z(e)})$ of $\mathcal{T}(X(E^\infty))$ form a Toeplitz-Cuntz-Krieger $E$-family.
\end{lem}
The universal property of the Toeplitz algebra $\mathcal{T} C^*(E)$ now gives a homomorphism $\pi_{P,S}:\mathcal{T} C^*(E)\to \mathcal{T} (X(E^\infty))$. Corollary~4.2 of \cite{FR} implies that this homomorphism is injective, and it is equivariant for the gauge actions, and hence for the various dynamics $\alpha$ studied in \S\ref{sec:1} and \S\ref{sec:local}. So composing with $\pi_{P,S}$ takes KMS$_\beta$ states of $(\mathcal{T}(X(E^\infty)),\alpha)$ to KMS$_\beta$ states of $(\mathcal{T} C^*(E),\alpha)$. Now we have KMS$_\beta$ states of $\mathcal{T}(X(E^\infty))$ for $\beta$ larger than Thomsen's $\beta_c$, and KMS$_\beta$ states of $\mathcal{T} C^*(E)$ for $\beta>\ln \rho(A)$, where $A$ is the vertex matrix of $E$. We reconcile this in the following reassuring lemma, which is Proposition~7.3 of \cite{AaHR}. (Note that the condition on $E$ is there to ensure that $\rho(A)>0$, so that $\ln \rho(A)$ makes sense.)
\begin{lem}\label{reassure}
Suppose that $E$ is a directed graph with at least one cycle. Then
\[
\frac{1}{n}\ln\Big(\max_{x\in E^\infty}|\sigma^{-n}(x)|\Big)\to \ln \rho(A)\quad\text{as $n\to \infty$.}
\]
\end{lem}
Thus Thomsen's $\beta_c$ is our $\ln\rho(A)$, and the range of possible $\beta$ in Theorem~\ref{paraKMS} is the the same as that in \cite[Theorem~5.1]{AaHR}. Suppose that $\beta>\ln\rho(A)$, that $\mu$ is a measure on $E^\infty$ satisfying the hypothesis $\int f_\beta\,d\mu=1$ of \cite[Theorem~5.1]{AaHR}, and that $\phi^\mu$ is the corresponding state of $\mathcal{T}(X(E^\infty))$. Then Proposition~7.4 of \cite{AaHR} says that $\phi^\mu\circ\pi_{P,S}$ is the state $\phi_{\epsilon}$ of \cite[Theorem~2.1]{aHLRS1} associated to the vector $\epsilon=\epsilon(\mu)=\big(\mu(Z(v))\big)$ in $[0,\infty)^{E^0}$.
Every state $\phi_\epsilon$ of $(\mathcal{T} C^*(E),\alpha)$ has the form $\phi^\mu\circ\pi_{P,S}$ for some measure $\mu$ on $E^*$ satisfying $\int f_\beta\,d\mu=1$ \cite[Corollary~7.6]{AaHR}. In the proof of this result, such a measure $\mu$ is constructed as a measure on the inverse limit $E^\infty=\varprojlim_nE^n$, and an examination of the construction shows that there is considerable leeway in building such a measure. Indeed, for each $\epsilon$ satisfying the normalisation relation $y^\beta\cdot\epsilon=1$ of \cite{aHLRS1},
\[
\Big\{\lambda\in M(E^\infty)_+:\int f_\beta\,d\lambda=1\text{ and }\lambda(Z(\lambda))=\epsilon_v \text{ for }v\in E^0\Big\}
\]
is a simplex of codimension $|E^0|+1$ in the cone $M(E^\infty)_+$ of positive measures. Thus there are many more KMS$_\beta$ states on $\mathcal{T}(X(E^\infty))$ than on $\mathcal{T} C^*(E)$.
The injection $\pi_{P,S}:\mathcal{T} C^*(E)\to \mathcal{T}(X(E^\infty))$ is certainly not surjective --- if for no other reason, because $\mathcal{T}(X(E^\infty))$ has many more KMS states.
However, Proposition~7.1 of \cite{AaHR} says that $\pi_{P,S}$ induces an isomorphism of the Cuntz-Krieger algebra $C^*(E)$ \emph{onto} $\mathcal{O}(X(E^\infty))$! (This observation is essentially due to Exel \cite{E} and Brownlowe \cite{BRV}.) Since this isomorphism also intertwines the dynamics of \cite{aHLRS1} and that of \cite{AaHR}, the latter algebra has effectively the same KMS states as $C^*(E)$.
We now return to the dumbbell graph $E$
\[
\begin{tikzpicture}
\node[inner sep=1pt] (v) at (0,0) {$v$};
\node[inner sep=1pt] (w) at (2,0) {$w$};
\draw[-latex] (w)--(v);
\foreach \x in {0,2} {
\draw[-latex] (v) .. controls +(1.\x,1.\x) and +(-1.\x,1.\x) .. (v);
}
\foreach \x in {0,2,4} {
\draw[-latex] (w) .. controls +(1.\x,1.\x) and +(-1.\x,1.\x) .. (w);
}
\end{tikzpicture}
\]
which we discussed in Example~\ref{2nddumb} of \S\ref{sec:dumb}. The system $(C^*(E),\alpha)$ has KMS$_\beta$ states for $\beta=\ln 3=\ln\rho(A)$ and $\beta=\ln 2=\ln\rho(A_{\{v\}})$. Thus so does $\mathcal{O}(X(E^\infty))$. We have already seen in Lemma~\ref{reassure} that $\beta_c=\ln\rho(A)$ in general. For this $E$ and $x\in E^\infty$, we can compute
\[
|\sigma^{-n}(x)|=|E^nr(x)|=\begin{cases}
2^n&\text{if $r(x)=v$}\\
3^n+\sum_{j=0}^{n-1}3^j2^{n-1-j}&\text{if $r(x)=w$.}
\end{cases}
\]
Thus $\min_x|\sigma^{-n}(x)|=2^n$ is attained when $r(x)=v$, and Thomsen's $\beta_l$ is $\ln 2$. So for the local homeomorphism $\sigma:E^\infty\to E^\infty$, the lower bound $\beta_l$ in \cite[Theorem~6.8]{Th1} is also sharp.
It is easy to see with dumbbell graphs that there can be KMS$_\beta$ states at inverse temperatures strictly between $\beta_l$ and $\beta_c$. For example, with $E$ the following graph
\[
\begin{tikzpicture}
\node[inner sep=1pt] (u) at (-2,0) {$u$};
\node[inner sep=1pt] (v) at (0,0) {$v$};
\node[inner sep=1pt] (w) at (2,0) {$w$};
\draw[-latex] (w)--(v);
\draw[-latex] (v)--(u);
\foreach \x in {0,2} {
\draw[-latex] (u) .. controls +(1.\x,1.\x) and +(-1.\x,1.\x) .. (u);
}
\foreach \x in {0,2,4} {
\draw[-latex] (v) .. controls +(1.\x,1.\x) and +(-1.\x,1.\x) .. (v);
}
\foreach \x in {0,2,4,6} {
\draw[-latex] (w) .. controls +(1.\x,1.\x) and +(-1.\x,1.\x) .. (w);
}
\end{tikzpicture}
\]
both $C^*(E)$ and $\mathcal{O}(X(E^\infty))$ have KMS states at inverse temperatures $\ln2$, $\ln 3$ and $\ln 4$.
There are, however, interesting constraints on the possible inverse temperatures $\beta$. First, since $e^\beta$ has to be the spectral radius of an irreducible integer matrix, it has to be an algebraic number. But there are also other, more subtle constraints. The issue is discussed, along with relevant results of Lind \cite{L}, in \cite[\S7.1]{aHLRS2}.
\begin{acknowledgement}
This research was supported by the Marsden Fund of the Royal Society of New Zealand. We also thank our collaborators Zahra Afsar, Marcelo Laca and Aidan Sims, the referee for some constructive suggestions, and the organisers of the Abel symposium for a marvellous experience.\end{acknowledgement}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,355 |
{"url":"https:\/\/brilliant.org\/problems\/an-inequality-problem\/","text":"# An inequality problem\n\nAlgebra Level 4\n\nLet $$a,b,x,y$$ be real numbers such that $$a^2 +b^2 =81$$, $$x^2 + y^2 = 121$$ and $$ax+by=99$$.\n\nThen what is the set of all possible values of $$ay-bx$$?\n\n###### KVPY problems.\n\u00d7\n\nProblem Loading...\n\nNote Loading...\n\nSet Loading...","date":"2017-05-28 10:38:41","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7001122236251831, \"perplexity\": 1286.2599029067992}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-22\/segments\/1495463609613.73\/warc\/CC-MAIN-20170528101305-20170528121305-00455.warc.gz\"}"} | null | null |
\section{Introduction}
In a common form of competition, a group of judges scores contestants' performances to determine their ranking. Unlike one-on-one pairwise direct competitions such as football or basketball where strict rules for scoring points must be followed and accordingly a clear winner is produced in the open, a complete reliance on the judges' subjective judgments can often lead to dissatisfaction by the fans and accusations of bias or even corruption~\cite{birnbaum1979source, zitzewitz2006nationalism,whissell1993national}. Examples abound in history, including the Olympics that heavily feature the said type of competitions. A well-documented example is the figure skating judging scandal at the 2002 Salt Lake Olympics that can said to have been a prototypical judging controversy where the favorites lost under suspicious circumstances, which led to a comprehensive reform in the scoring system~\cite{looney2003evaluating,kang2015dealing}. A more recent, widely-publicized example can be found in the prestigious 17th International Chopin Piano Competition of 2015 in which judge Philippe Entremont gave contestant Seong-Jin Cho an ostensibly poor score compared with other judges and contestants. That Cho went on to win the competition nonetheless rendered the low score from Entremont all the more noteworthy, if not determinant of the final outcome~\cite{justin2015, onejuror2015}. Given that the competition format depends completely on human judgment, these incidents suggest that the following questions will persist: How do we detect a biased score? How much does a bias affect the outcome of the competition? What is the effect of the bias in our understanding of system's behavior? Here we present a network framework to find answers and insights into these problems.
\begin{figure}
\resizebox{\figurewidth}{!}{\includegraphics{01_definition.eps}}
\caption{ (a) The bipartite network representation of the judge--contestant competition. The edge weight is the score given from a judge to a contestant. (b) The one-mode projection onto the judges produces a weighted complete network whose edge weights are the similarity between the judges. We use the cosine similarity in our work.}
\label{definition}
\end{figure}
\begin{table*}[ht]
\caption{The final round scores from the 17th International Chopin Piano Competition. Judge Dang was not allowed to score the three contestants that were his former students (Liu, Lu, and Yang), noted ``NA''. The expected scores $\hat{b}$ of Eq.~\eref{expscore} in these cases are given in parentheses.}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
& Cho & Hamelin & Jurinic & Kobayashi & Liu & Lu & Osokins & Shiskin & Szymon & Yang \\ \hline
Alexeev & 10 & 8 & 2 & 1 & 7 & 9 & 3 & 6 & 4 & 5 \\ \hline
Argerich & 9 & 9 & 4 & 6 & 4 & 5 & 4 & 5 & 4 & 5 \\ \hline
Dang & 8 & 8 & 2 & 7 & \begin{tabular}{@{}c@{}}NA \\ (6.124) \end{tabular} & \begin{tabular}{@{}c@{}}NA \\ (5.673) \end{tabular} & 1 & 5 & 4 & \begin{tabular}{@{}c@{}}NA \\ (4.776) \end{tabular} \\ \hline
Ebi & 9 & 9 & 3 & 5 & 3 & 4 & 5 & 5 & 3 & 8 \\ \hline
Entremont & 1 & 8 & 3 & 2 & 5 & 8 & 4 & 7 & 4 & 6 \\ \hline
Goerner & 9 & 10 & 2 & 5 & 5 & 8 & 2 & 6 & 2 & 6 \\ \hline
Harasiewicz & 6 & 7 & 6 & 2 & 9 & 3 & 5 & 7 & 2 & 2 \\ \hline
Jasiński & 9 & 6 & 3 & 8 & 10 & 6 & 2 & 3 & 5 & 2 \\ \hline
Ohlsson & 9 & 8 & 6 & 1 & 9 & 4 & 5 & 7 & 2 & 3 \\ \hline
Olejniczak & 10 & 7 & 1 & 5 & 9 & 8 & 3 & 2 & 6 & 4 \\ \hline
Paleczny & 9 & 6 & 1 & 4 & 10 & 8 & 2 & 3 & 5 & 7 \\ \hline
Pobłocka & 9 & 7 & 1 & 6 & 8 & 8 & 2 & 5 & 2 & 6 \\ \hline
Popowa-Zydroń & 9 & 10 & 1 & 6 & 9 & 8 & 1 & 1 & 4 & 6 \\ \hline
Rink & 9 & 9 & 5 & 3 & 8 & 4 & 7 & 6 & 2 & 1 \\ \hline
Świtała & 9 & 8 & 1 & 5 & 10 & 7 & 4 & 1 & 5 & 5 \\ \hline
Yoffe & 9 & 9 & 5 & 3 & 8 & 7 & 6 & 2 & 4 & 2 \\ \hline
Yundi & 9 & 9 & 4 & 5 & 6 & 6 & 2 & 4 & 3 & 5 \\ \hline
\end{tabular}
\label{BB}
\end{table*}
\section{Methodology and Analysis}
The judge--contestant competition can be modeled as a bipartite network with weighted edges representing the scores, shown in Fig.~\ref{definition}~(a). It is a graphical representation of the $l\times r$--bipartite adjacency matrix
\begin{align}
\mathbf{B} = \set{b_{ij}},
\end{align}
whose actual values from the 17th International Chopin Piano Competition are given in Table~\ref{BB}~\cite{finaloceny2015}, composed of $l=17$ judges and $r=10$ contestants. The entries ``NA'' refer to the cases of judge Thai Son Dang ($i=3$) and his former pupils Kate Liu ($j=4$), Eric Lu ($j=5$), and Yike (Tony) Yang ($j=10$) whom he was not allowed to score. For convenience in our later analysis, we nevertheless fill these entries with expected scores based on their scoring tendencies using the formula
\begin{align}
\hat{b}_{ij} = \sqrt{\frac{\sum'_ib_{ij}}{l-1}\times\frac{\sum''_jb_{ij}}{r-3}},
\label{expscore}
\end{align}
where the summations $\sum'$ and $\sum''$ indicate omitting these individuals. It is the geometric mean of Dang's average score given to the other contestants and the contestant's average score obtained from the other judges. The values are given inside parentheses in Table~\ref{BB}. A one-mode projection of the original bipartite network onto the judges is shown in Fig.~\ref{definition}~(b), which is also weighted~\cite{zhou2007bipartite}. The edge weights here indicate the similarity between the judges, for which we use the cosine similarity
\begin{align}
\sigma_{ij} \equiv \frac{\vec{b}_i\cdot\vec{b}_j}{|\vec{b}_i||\vec{b}_j|} = \frac{\sum_kb_{ik}b_{jk}}{\sqrt{\sum_kb_{ik}^2}\sqrt{\sum_kb_{ik}^2}}
\label{cosine}
\end{align}
with $\hat{b}$ naturally substituted for $b$ when applicable. This defines the $17\times 17$ adjacency matrix $\mathbf{S}=\set{\sigma_{ij}}$ of the one-mode projection network.
\begin{figure}
\resizebox{\figurewidth}{!}{\includegraphics{02_simlarity.eps}}
\caption{The mutual average similarity between the judges. (a) In the full data Philippe Entremont is the most dissimilar, atypical judge. (b) In the truncated data with Cho removed, Entremont now becomes the seventh most similar judge, placing himself as the more typical one. This abrupt change indicates the outsize effect of the single uncharacteristic score given to Cho by Entremont.}
\label{meansimilarity}
\end{figure}
\subsection{Determining the Atypicality of Judges}
Perhaps the most straightforward method for determining the atypicality of a judge before analyzing the network (i.e., using the full matrix) is to compare the judges' average mutual similarities (average similarity to the other judges), shown in Fig.~\ref{meansimilarity}. Using the full data set (Fig.~\ref{meansimilarity}~(a)) we find Yundi to be the most similar to the others with $\av{\sigma}=0.94\pm0.04$, and Entremont to be the least so with $\av{\sigma}=0.83\pm 0.03$. The global average similarity is $0.90\pm 0.05$, indicated by the red dotted line. Yundi is not particularly interesting for our purposes, since a high overall similarity indicates that he is the most typical, average judge. Entremont, on the other hand, is the most interesting case. Given the attention he received for his low score to Cho, this makes us wonder how much of this atypicality of his was a result of it. To see this, we perform the same analysis with Cho removed from the data, shown in Fig.~\ref{meansimilarity}~(b). Entremont is now ranked 7th in similarity, indicating that his score on Cho likely was a very strong factor for his atypicality first seen in Fig.~\ref{meansimilarity}~(a).
\begin{figure*}[htpb]
\begin{center}
\includegraphics[scale=0.5]{03_dendrogram.eps}
\caption {Clustering dendrogram of the judges in 17th Chopin Competition. (a) Using the full data. Entremont joins the dendrogram at the last possible level ($z=16$). (b) Using the truncated data with Cho removed. Entremont joins the dendrogram early, at level $z=3$. The elimination of a single contestant has rendered Entremont to appear to be one of the more typical judges, consistent with Fig.~\ref{meansimilarity}~(b).}
\label{clusterDendro}
\end{center}
\end{figure*}
Although the effect of a single uncharacteristic score was somewhat demonstrated in Fig.~\ref{meansimilarity}, by averaging out the edge weights we have incurred a nearly complete loss of information on the network structure. We now directly study the network and investigate the degree to which biased scores affect its structure and our inferences about it. While there exists a wide variety of analytical and computational methods for network analysis~\cite{newman2010networks,barabasi201609}, here we specifically utilize \emph{hierarchical clustering} for exploring our questions at hand. Hierarchical clustering is most often used in classification problems by identifying clusters or groups of objects based on similarity or affinity between them~\cite{johnson1967hierarchical,newman2004fast,murtagh2012algorithms}. The method's name contains the word ``hierarchical'' because it produces a hierarchy of groups of objects starting from each object being its own group at the bottom to a single, all-encompassing group at the top. The hierarchy thus found is visually represented using a dendrogram such as the one shown in Fig.~\ref{clusterDendro}, generated for the judges based on cosine similarity $\sigma_{ij}$ of Eq.~\eref{cosine}. We used agglomerative clustering with average linkage~\cite{eisen1998cluster,newman2004finding}. Before we use the dendrogram to identify clusters, we first focus on another observable from the dendrogram, the level $z$ at which a given node joins the dendrogram. A node with small $z$ joins the dendrogram early, meaning a high level of similarity with others; a large $z$ means the opposite. This $z$ is consistent with Fig.~\ref{meansimilarity}: For Entremont $z=16$ (the maximum possible value with 17 judges) in the full data set, being the last one to join the dendrogram in the full data set, while $z=3$ when Cho is removed. The two dendrograms and Entremont's $z$ are shown in Fig.~\ref{clusterDendro}~(a)~and~(b). $z$ is therefore a simple and useful quantity for characterizing a node's atypicality. To see if any other contestant had a similar relationship with Entremont, we repeat this process by removing the contestants alternately from the data and measuring Entremont's $z$, the results of which are shown in Fig.~\ref{entryPoint}. No other contestant had a similar effect on Entremont's $z$, once again affirming the uncharacteristic nature of Entremont's score of Cho's performance.
\subsection{Racism as a Factor in Scoring}
A popular conjecture regarding the origin of Cho's low score was that Entremont may have been racially motived. We can perform a similar analysis to find any such bias against a specific group (e.g., non-Caucasians) of contestants. To do so, we split the contestants into two groups, non-Caucasians and Caucasians plus Cho (the ethnicities were inferred from their surnames and, when available, photos) as follows:
\begin{itemize}
\item Non-Caucasians (5): Cho, Kobayashi, Liu, Lu, and Yang
\item Caucasians plus Cho (6): Cho, Hamelin, Jurinic, Osokins, Shiskin, and Szymon.
\end{itemize}
We then plot figures similar to Fig.~\ref{entryPoint}. If Entremont had truly treated the two racial groups differently, the effect of his score to Cho would have had significantly different effects on each group. The results are shown in Fig.~\ref{R5_EastWestEntryPoint}. As before, Entrement's low score of Cho stands out amongst the non-Caucasian contestants, a strong indication that the race hadn't played a role, although it should be noted that Entremont appears to have been more dissimilar overall from the other judges in scoring the non-Caucasian contestants when Cho was not considered ($z=8$ compared with $z=2$ in the Caucasian group).
\begin{figure}
\resizebox{\figurewidth}{!}{\includegraphics{04_entrypoint.eps}}
\caption{Entremont's entry point $z$ into the dendrogram as the contestants are alternately removed from the data one by one. The removal of any contestant other than Cho has no visible effect on the typicality of of Entremont.}
\label{entryPoint}
\end{figure}
\begin{figure*}[htpb]
\begin{center}
\includegraphics[scale=0.5]{05_caucasian.eps}
\caption {Entremont's entry point into the clustering dendrogram in two distinct groups of contestants, the non-Caucasian group (a) and the Caucasian group plus Cho (b). In both cases, Entremont's $z$ decreases from the maximum value only when Cho is removed. This suggests that Entremont's uncharacteristic score of Cho's performance was not ethnically motivated.}
\label{R5_EastWestEntryPoint}
\end{center}
\end{figure*}
\subsection{Impact of Biased Edges on Inference of Network's Modular Structure}
As pointed out earlier, hierarchical clustering is most often used to determine the modular structure of a network. This is often achieved by making a ``cut'' in the dendrogram on a certain level~\cite{langfelder2008defining}. A classical method for deciding the position of the cut is to maximize the so-called \emph{modularity} $Q$ defined as
\begin{align}
Q = \frac{1}{2m}\sum_{ij}\biggl[A_{ij}-\frac{k_ik_j}{2m}\biggr]\delta(c_i,c_j)
\label{modularity}
\end{align}
where $m$ is the number of edges, $c_i$ is the module that node $i$ belongs to, and $\delta$ is the Kronecker delta~\cite{newman2006modularity}. The first factor in the summand is the difference between the actual number of edges ($0$ or $1$ in a simple graph) between a node pair and its random expectation based on the nodes' degrees. We now try to generalize this quantity for our one-mode projection network in Fig.~\ref{definition}~(b) where the edge values are the pairwise similarities $\sigma\in[0,1]$. At first a straightforward generalization of Eq.~\eref{modularity} appears to be, disregarding the $(2m)^{-1}$ which is a mere constant,
\begin{align}
Q' = \sum_{ij}\bigl(\sigma_{ij}-\av{\sigma_{ij}}\bigr)\delta(c_i,c_j)\equiv\sum_{ij}q'_{ij}\delta(c_i,c_j)
\label{qtemp}
\end{align}
where $\av{\sigma_{ij}}$ is the expected similarity obtained by randomly shuffling the scores (edge weights) in the bipartite network of Fig.~\ref{definition}~(a). In the case of the cosine similarity this value can be computed analytically using its definition Eq.~\eref{cosine}: it is equal to the average over all permutations of the elements of $\vec{b}_i$ and $\vec{b}_j$. What makes it even simpler is that permutating either one is sufficient, say $\vec{b}_j$. Denoting by $\vec{b}_j^{(k)}$ the $k$-th permutation of $\vec{b}$ out of the $r!$ possible ones, we have
\begin{align}
\av{\sigma_{ij}}
&= \frac{1}{r!|\vec{b}_i||\vec{b}_j|} \biggl(\vec{b}_i\cdot\vec{b}_j^{(1)}+\cdots+\vec{b}_i\cdot\vec{b}_j^{(r!)}\biggr) \nonumber \\
&= \frac{1}{r!|\vec{b}_i||\vec{b}_j|}\vec{b}_i\cdot\biggl(\vec{b}_j^{(1)}+\cdots+\vec{b}_j^{(r!)}\biggr)\nonumber \\
&= \frac{1}{r!|\vec{b}_i||\vec{b}_j|}\biggl(b_{i1}\bigl(b_{j1}^{(1)}+\cdots+b_{j1}^{(r!)}\bigr) \nonumber \\
&~~~+b_{i2}\bigl(b_{j2}^{(1)}+\cdots+b_{j2}^{(r!)}\bigr)+\cdots\bigr)\nonumber \\
&=\frac{(\sum_{k=1}^rb_{ik})(\sum_{k=1}^rb_{jk})}{r!|\vec{b}_i||\vec{b}_j|}\equiv\frac{B_iB_j}{r!|\vec{b}_i||\vec{b}_j|}.
\label{expectation}
\end{align}
When we insert this value into Eq.~\eref{qtemp} and try to maximize it for our network, however, we end up with a single module that contains all the judges as the optimal solution, a rather uninteresting and uninformative result. On closer inspection, in turns out, this stems from the specific nature of summand $q'$ with regards to our network. For a majority of node pairs the summand is positive (even when Entremont is involved), so that it is advantageous to have $\delta(c_i,c_j)=1$ for all $(i,j)$ for $Q'$ to be positive and large, i.e. all judges belonging to a single, all-encompassing module, as noted. The reason why $Q$ of Eq.~\ref{modularity} has worked so well for sparse simple networks was that most summands were negative (since $A_{ij}=0$ for most node pairs in a sparse network, and $k_ik_j/(2m)>0$ always), so that including all nodes in a single group was not an optimal solution for $Q$. To find a level of differentiation between the judges, therefore, we need to further modify $Q'$ so that we have a reasonable number of negative as well as positive summands. We achieve this by subtracting a universal positive value $q'_0$ from each summand, which we propose to be the mean of the $q'$, i.e.
\begin{align}
q'_0 &= \mean{q'}=\mean{\sigma_{ij}-\av{\sigma_{ij}}}
= \frac{2}{l(l-1)}\sum_{i<j}\bigl(\sigma_{ij}-\av{\sigma_{ij}}\bigr) \nonumber \\
&=\mean{\sigma}-\mean{\av{\sigma}}.
\end{align}
At this point one must take caution not to be confused by the notations: $\mean{\sigma}$ is the average of the actual similarities from data, while $\av{\sigma}$ is the pairwise random expectation from Eq.~\eref{expectation}, and therefore $\mean{\av{\sigma}}$ is the average of the pairwise random expectations. Then our re-modified modularity is
\begin{align}
Q'' &\equiv\sum_{ij}q_{ij}''\delta(c_i,c_j) \equiv \sum_{ij}\bigl(q'_{ij}-q'_0\bigr)\delta(c_i,c_j)\nonumber \\
&=\sum_{ij}\bigl[(\sigma_{ij}-\av{\sigma_{ij}})-\overline{(\sigma_{ij}-\av{\sigma_{ij}})}\bigr]\delta(c_i,c_j)
\end{align}
This also has the useful property of vanishing to $0$ at the two ends of the dendrogram (i.e. all nodes being separate or forming a single module), allowing us to naturally avoid the most trivial or uninformative cases.
\begin{figure*}[htpb]
\begin{center}
\includegraphics[scale=0.75]{06_networks.eps}
\caption {Modified modularity $Q''$ and the modular structure of the judges' network. (a) In the full network, maximum $Q''$ occurs at $z=14$, resulting in three modules shown in (c). (b) In the truncated network with Cho removed the optimal solution is at $z=15$, resulting in two modules shown in (d). A comparison of (c) and (d) tells us that the single biased score can be powerful enough to produce cause Entremont to form his own module, and also present the solution as the dominant one; in the absence of the edge, several comparable solutions can exist (marked by an encompassing rectangle) in (b).}
\label{clusterNetworks}
\end{center}
\end{figure*}
We now plot $Q''$ as we traverse up the dendrograms from Figs.~\ref{clusterNetworks}. For the full data with Cho, maximum $Q''$ occurs at level $z=14$, yielding $3$ modules (Fig.~\ref{clusterNetworks}~(c)). With Cho removed, in contrast, maximum $Q''$ occurs at level $z=15$, resulting in $2$ modules (Fig.~\ref{clusterNetworks}~(d)). In the full data Entremont forms an isolated module on his own, but otherwise the $Q''$-maximal modular structures are identical in both cases. This is another example of how a single uncharacteristic, biased score from Entremont to Cho is responsible for a qualitatively different observed behavior of the system. There is another issue that warrants further attention, demonstrating the potential harm brought on by a single biased edge: We see in Fig.~\ref{clusterNetworks}~(a) that the $Q''$-maximal solution ($z=14$) eclipses all the possibilities ($\Delta Q''=2.3687$ between it and the second optimal solution, for a relative difference $\Delta Q''/Q''_{\textrm{max}}=0.2653$), compared with Fig.~\ref{clusterNetworks}~(b) where the difference between the two most optimal solutions is much smaller ($\Delta Q''=1.8430$ and $\Delta Q''/Q''_{\textrm{max}}=0.0554$). Furthermore, there are at least three other solutions with comparable $Q''$ $(z=13,~12,~11)$ in Fig.~\ref{clusterNetworks}~(b). Given the small differences in $Q''$ between these solutions, it is plausible that had we used slightly a different definition of modularity or tried alternative clustering methods, any of these or another comparable configuration may have presented itself as the optimal solution. But a single biased edge was so impactful that not only an apparently incorrect solution was identified as the most optimal, but also much more dominant than any other.
\section{Discussions and Conclusions}
Given the prevalence of competition in nature and society, it is important to understand the behaviors of different competition formats know their strengths, weakness, and improve their credibility. Direct one-on-one competitions are the easiest to visualize and model as a network, and many centralities can be applied either directly or in a modified form to produce reliable rankings~\cite{park2005network, shin2014ranking}. Such competition formats are mostly free from systematic biases, since the scores are direct results of one competitor's superiority over the other. The jury--contestant competition format, while commonly used, provides a more serious challenge since it relies completely on human judgement; when the public senses unwarranted bias they may lose trust in the fairness of the system, which is the most serious threat against the very existence of a competition.
Here we presented a network study of the jury-contestant competition, and showed how we can use the hierarchical clustering method to detect biased scores and measure their impact on the network structure. We began by first identifying the most abnormal jury member in the network, i.e. the one that is the least similar. While using the individual jury member's mean similarity to the others had some uses, using the dendrogram to determine the atypicality of a judge graphically was more intuitive and allowed us gain a more complete understanding of the network. After confirming the existence of a biased score, we investigated the effect of the bias on the network structure. For this analysis, we introduced a modified modularity measure appropriate for our type of network. This analysis revealed in quite stark terms the dangers posed by such biased edges; even a single biased edge that accounted for less than 1\% of the edges led us to make unreliable and misleading inferences about the network structure.
Given the increasing adoption of the network framework for data modeling and analysis in competition systems where fairness and robustness are important, we hope that our work highlights the importance of detecting biases and understanding their effect on network structure.
\acknowledgements{
This work was supported National Research Foundation of Korea (NRF-20100004910 and NRF-2013S1A3A2055285), BK21 Plus Postgraduate Organization for Content Science, and the Digital Contents Research and Development program of MSIP (R0184-15-1037, Development of Data Mining Core Technologies for Real-time Intelligent Information Recommendation in Smart Spaces)
}
\bibliographystyle{apsrev4-1}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,223 |
{"url":"https:\/\/gamedev.stackexchange.com\/questions\/117264\/how-to-make-illusion-of-round-world\/117267","text":"# How to make illusion of round world?\n\nI want to make a flat world, but i want to split it into pieces which will load in segments (for better optimization), and when you are at the end of map it will start loading segments from the beginning again. And I want to make an illusion of roundness (only optical effect if possible). For example, when you watch ships on the horizon, you see their masts first.\n\nI'm asking only for theoretical ideas, so you don't need to send any scripts.\n\n\u2022 Something like youtube.com\/watch?v=_kY4v-L3rvY ? Uses shaders to present a flat environment as curved. \u2013\u00a0fadden Feb 25 '16 at 18:26\n\u2022 There was an old game that I use to play called Populous 3 that had round worlds. They would tile a rectangular map around the world so that the tops and sides of the rectangle would connect (even though it is impossible to wrap a rectangle around a sphere in this way). It was a very clever illusion and they pulled it off very well. \u2013\u00a0JSideris Feb 28 '16 at 20:06\n\u2022 Thanks, but for me is vertex shader better option. \u2013\u00a0T. R\u016f\u017ei\u010dka Feb 28 '16 at 21:56\n\nYou can do this purely in a vertex shader. You'd want to apply this shader to everything you render.\n\nOne trick though that you can do is weight it so that the nearby objects are flat out to say 100 meters. I'd recommend this because in an FPS game the distortion on objects requires you to change things. (Players will aim at things wrong). If you keep the nearby regions flat then start the curve at a distance it'll look the same without having interaction problems.\n\nHere's an image to understand. (I don't have the code at the moment on this machine, but it's only a few lines if I remember correctly).\n\nSince you asked for code. I can't vet this code 100%, but I did see images of it working. (I wrote pseudocode for a friend who converted it to HLSL and the images showed it working).\n\ncbuffer matrix_buffer\n{\nmatrix world;\nmatrix view;\nmatrix projection;\n};\n\nstruct vertex_input_type\n{\nfloat4 position : POSITION;\nfloat3 normal : NORMAL;\n};\n\nstruct pixel_input_type\n{\nfloat4 position : SV_POSITION;\nfloat3 normal : NORMAL;\n};\n\n{\npixel_input_type output;\n\ninput.position.w = 1.0f;\n\n#if 0\noutput.position = mul(world, input.position);\noutput.position = mul(view, output.position);\noutput.position = mul(projection, output.position);\n#else\nfloat4 viewPosition = float4(0, 20.0, 0, 1);\nfloat seaLevel = 0.0;\nfloat4 vertex = input.position;\nmatrix model = world;\n\nvertex = mul(model, vertex);\nfloat2 diff = vertex.xz - viewPosition.xz;\nfloat angleX = -length(diff) \/ radius;\nfloat angleY = atan2(diff.x, diff.y);\nfloat3x3 rotateX =\n{\n1, 0, 0,\n0, cos(angleX), -sin(angleX),\n0, sin(angleX), cos(angleX)\n};\nfloat3x3 rotateY =\n{\ncos(angleY), 0, sin(angleY),\n0, 1, 0,\n-sin(angleY), 0, cos(angleY)\n};\nvertex = float4(mul(rotateY, mul(rotateX, float3(0, radius + vertex.y - seaLevel, 0))) + float3(0, -radius, 0), 1);\nvertex = mul(projection, mul(view, vertex));\noutput.position = vertex;\n#endif\n\noutput.normal = input.normal;\n\nreturn output;\n}\n\n\u2022 Thanks a lot. Is it called somehow? So i can look for code on my own. \u2013\u00a0T. R\u016f\u017ei\u010dka Feb 25 '16 at 19:21\n\u2022 It'll be a few hours until I get home. In the mean-time here's another image: i.imgur.com\/RKzQifZ.png This one shows the regions that require loading based on the maximum height a camera can get to. Also en.wikipedia.org\/wiki\/Tangent_lines_to_circles \u2013\u00a0Sirisian Feb 25 '16 at 19:47\n\u2022 @T.R\u016f\u017ei\u010dka I updated with the only code sample I have in my old notes. I hope it helps. \u2013\u00a0Sirisian Feb 26 '16 at 8:50\n\u2022 Thaks, it helped \u2013\u00a0T. R\u016f\u017ei\u010dka Feb 26 '16 at 8:54\n\u2022 Do you know how to use it in Unity please? \u2013\u00a0T. R\u016f\u017ei\u010dka Mar 1 '16 at 13:59","date":"2019-08-25 14:06:31","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.292248010635376, \"perplexity\": 3378.8818647692033}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2019-35\/segments\/1566027330233.1\/warc\/CC-MAIN-20190825130849-20190825152849-00020.warc.gz\"}"} | null | null |
Category: Dassault Systèmes
3DEXPERIENCE, Consumer Goods, Dassault Systèmes Ken Smith 0 comment
Consumer Goods: Moving at the Speed of Social Media
Customers today can be fickle. Our attention spans—conditioned by years of bite-size news, messages, video clips, and posts—are notoriously short. It's both a boon and a hazard to manufacturers of consumer goods that the power of social media can make trends viral in the blink of an eye—and discards them just as quickly. Today's hot product is tomorrow's "over it" post, and brands have to be quick to respond to stay relevant.
That's why manufacturers with hopes of competing in the global marketplace must be able to communicate, design, and produce faster than ever before. They have to deliver not just at the speed of today's global business, but at the pace of social media.
Of course, most manufacturers aren't merely watching cultural trends go past and hoping to jump on the merry-go-round, they're also being bombarded with opinions, feedback, criticism, kudos, and requests for help. Their customers around the world are demanding safe, high-quality, and timely products. And most manufacturers are handling all of that while also dealing with a multitude of internal, disconnected systems. It's an ever-increasing challenge to imagine, design, and deliver innovative consumer goods, especially for small to medium-sized businesses.
The Communication Challenge
Manufacturers don't typically establish their operations with a fully planned, cohesive network of information. Instead, they tend to grow from tiny operations, adding on software systems and databases of information as necessary to house a litany of ideas, specifications, CAD models, and more. It's an organic means of growing a business that tends to result in siloed information in a variety of disconnected systems—and difficulty in maintaining a single, shared vision.
Disconnected islands of information make it difficult to design and manufacture products quickly, much less to be agile enough to design and produce a product based on customer feedback. But that's where a single, integrated platform can be a manufacturer's game-changer.
The 3DEXPERIENCE Platform Solution
A product lifecycle management (PLM) platform can form the basis of a manufacturer's operations. With multiple components seamlessly integrated together—everything from 3D CAD software, project management, simulation, and manufacturing—you can sustain and preserve all of your operational data in one place. The "single source of truth" allows you to exchange data with such widely flung and disparate groups as R&D, production, procurement, marketing, and even customers.
In fact, PLM leader, Dassault Systèmes has developed My Product Portfolio, a unique solution designed for consumer goods companies based on the 3DEXPERIENCE platform. This solution takes advantage of cloud-based technology to provide a solution for global manufacturers. The solution gives product managers the ability to track customer requests (features) from inception through production—providing an unparalleled opportunity for follow-through and customer satisfaction. Internal teams can engage customers, gather insights, conduct user studies and product tests—then store the information where it can be accessed by any party involved in the product lifecycle. The same is true for design data, marketing information, production schedules, and more. An integrated PLM platform isn't merely one source of truth, it's also one source for communication, innovation, and collaboration.
The Bottom-Line Benefits
A solution like My Product Portfolio makes it easy for small and medium retail goods manufacturers to collaborate and produce with the resources of much larger corporations. It provides a collaborative cloud-based system that ensures better communication between all stakeholders. A project management solution for tracking product enhancements and changes throughout the manufacturing process. More efficient engineering and simulation tools reduce the need for physical prototypes. Shortening development and production time. All of these tools improve business processes to save money and accelerate new product time-to-market. No longer do manufacturers have to look at "right, fast, and cheap" and only choose two. With the right tools, they can make the product right for the customer, deliver it fast—at the speed of cultural trends and social media—and save money through collaboration and increased communication.
Consumer Goods, Dassault Systèmes Ken Smith 0 comment
Adaptive to Join Dassault Systèmes at IHA Smart Home Pavilion
Adaptive Corporation representatives will be joining Dassault Systèmes at the "Smart Home Pavilion", part of the International Home & Housewares 2018 Show. The show will be held March 10-13 at the McCormick Place Convention Center in Chicago.
How Smart Kitchens will improve our lifestyle experience.
The Smart Home Pavilion will demonstrate how the future of housewares is quickly moving toward the smart home. Connectivity is being incorporated into nearly every corner of the home – from light bulbs to coffee brewers, from thermostats to ovens – connected products, once only a dream, are fast becoming a reality. Smart products too are making an impact – from Alexa to Siri, from vacuuming robots to trash cans – intelligent sensors are changing the way we live in, and interact with, our homes.
Listen to Dassault Systèmes session on Sunday, March 11 at 2.30 PM in the Smart Pavilion and watch a connected food robot come to life.
Susan Olivier, Worldwide Business Development for the Consumer Goods & Retail Industry at Dassault Systèmes, will lead a talk about How Smart Kitchens will improve our lifestyle experience.
When: Sunday March 11, at 2.30 PM
Where: Smart Home Pavilion, Hall of Global Innovation – Lakeside Center Lobby
Kitchens are becoming more and more intelligent, helping us improve our culinary skills like never before. With the rise of the Internet of Things, appliances are increasingly connected to each other, to the Internet and to our smartphones.
Discover the amazing journey of Nestor, a connected food robot, from initial market trends and customer requirements to freeform and detail design all using groundbreaking software applications. During our talk, we will show how industrial designers and engineers can ideate, design, engineer and produce smart kitchen appliances like Nestor by blending creativity and technical function.
Business, Dassault Systèmes Ken Smith 0 comment
Adaptive Corporation Receives Platinum Designation in the Dassault Systèmes Partner Program
Adaptive Corporation, the leading Digital to Physical Product Lifecycle Company, was recently named a Platinum Partner in Dassault Systèmes Value Solutions channel for 2018. The Platinum Partner designation is reserved for Partners that are highly engaged in Dassault Systèmes' business and identified as best-in-class performers in the 3DS ecosystem. The award is based on Key Performance Indicators (KPIs), which measure expertise in sales performance and efficiency, strategic alignment, and commitment. Other partner designations are Gold, Silver, and Bronze.
"Receiving this recognition from Dassault Systèmes is an honor for us at Adaptive," said Eric Doubell, CEO of Adaptive Corporation. "We have tough competition in the Value Solutions channel and we are in great company at the Platinum level. We look forward to continuing our participation in this program as we further build upon our strengths as a reseller for Dassault. Ultimately, this effort helps us improve our ability to execute as an organization and ensures a positive customer experience when companies choose Adaptive Corporation."
Stay up-to-date on all the latest industry and Adaptive news. Subscribe to our newsletter now.
Dassault Systèmes, Life Sciences, White Papers Juliann Grant 0 comment
White Paper: Optimizing Medical Device Development with Full Regulatory Compliance
How to Integrate Quality Throughout Your Product Lifecycle
A variety of factors are vital to the long-term success of a company and a product line, including price/cost, time-to-market, and more. But in this age of global communication—particularly in this era of social media usage, when an opinion or comment can go viral—one of the most important priorities for any company is product quality. That's especially true for medical device manufacturers—companies whose customers' lives often depend on the quality of the manufactured product.
The challenge many manufacturers face, however, is maintaining quality, as well as traceability and transparency, not just at one point in the product lifecycle, but throughout. That challenge is often compounded by siloed design, production, and change systems that don't easily share information with each other or provide accessibility to all stakeholders in the process—something that impacts more than just the product itself.
As a new paper from Dassault Systèmes, "Optimizing Medical Device Development with Full Regulatory Compliance," notes:
"Quality information must be highly visible throughout an organization to ensure that any and all decisions…are informed in a timely, efficient, and accurate fashion."
Unfortunately, even when companies know that quality is so important, they don't always make it the focus, as they scramble to get products to market or as different teams struggle with poor cross-functional communication. And that's a problem. As the article points out:
"Achieving product quality is a multidimensional challenge and failure to manage quality in an integrated way throughout the total product lifecycle jeopardizes a company's profitability and reputation."
The ideal solution is total transparency of the product lifecycle across functions, organizations, teams, stakeholders, and more. And that's exactly what a PLM system—an enterprise-wide, cross-functional solution that provides a "formalized, systematic approach for managing all aspects of product quality, reliability, and risk"—can deliver.
PLM platforms also help organizations optimize design controls, communication, and product/technology reuse. By handling requirements management for both mass-market manufacturing and specialized, configure-to-order business models, as well as requirements validation through simulation and systems engineering, PLM solutions enable manufacturers to maintain traceability of customer needs being met throughout the lifecycle, from concept to design to finished product feature. In addition, search tools and integrated processes such as quality management solutions save manufacturers money and ensure communication and transparency organization-wide.
In short, a platform-based PLM solution "breaks down organizational boundaries so companies can achieve the ultimate goal of increased patient safety while delivering innovative healthcare breakthroughs."
To learn more about how a PLM solution can help your organization, download the whitepaper:
← Previous1…45 | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,023 |
Hot and Cold Penguin is a 1955 Chilly Willy cartoon directed by Alex Lovy and produced by Walter Lantz.
It was the third Chilly Willy entry in the series and was the first Alex Lovy directed at the Walter Lantz Studio since his departure in 1943. Although Tex Avery had departed the year prior, he left behind several storyboards ultimately utilized by Lovy for Hot and Cold Penguin, Room and Wrath and Hold That Rock. Lovy remained director of the series for the remainder of the decade.
Plot
Chilly Willy is outside in the snow keeping himself warm with a campfire. A blizzard suddenly blows in and freezes the fire solid. Another blizzard blows in, sending Chilly Willy flying to a "Little America" sign. He looks up and sees a log cabin with a furnace inside and races toward it.
Smedley forces the penguin out with a bayonet pointing at his back. Chilly is then standing in front of a field of signs, with Smedley holding up a "Beware of Dog" sign. He then makes a face to scare the penguin and retreats back to his cabin to rest.
Chilly Willy drills a hole underneath Smedley's head and pushes him off to the side. He shushes him and goes in front of the furnace to get warm. He suddenly realizes what he did and Smedley forces him out by kicking him further away from the cabin.
Smedley goes back to rest. Chilly Willy swipes the rug and Smedley falls down a hole. Outside, Smedley unscrews a cork and plays "Taps" on his trumpet while Chilly Willy sinks into the water. Smedley returns to his cabin to take another rest, but he immediately wakes up after seeing Chilly Willy on the furnace. Back outside, Smedley unscrews another cork. However, as he plays "Taps", the ice sinks along with him.
Back inside the cabin, Smedley wrings out his tail and before going back to his nap, he checks the furnace for Chilly Willy. After confirmation, he returns to sleep. Chilly Willy pulls on the chimney, pulling the furnace along with it. Smedley forces the furnace down, but Chilly Willy forces it back up. Smedley climbs to the rooftop and gets an idea. He takes several packs of dynamite and loads them in the furnace. Chilly Willy pulls the furnace up. Nothing happens, and Smedley goes to see Chilly Willy warming himself up. He opens the top of the furnace and gets an explosion to his face.
Back inside the cabin, Smedley hammers the furnace down to the floor as a precautionary measure. However, Chilly Willy sees the furnace from beneath and pulls it down. Smedley peeks down the hole and is hit with another explosion. Angry, Smedley yanks the chimney up from the hole.
He ties Chilly Willy to a firework launcher and sends the penguin into orbit. Smedley heads back inside the cabin but heads back out to see Chilly Willy relaxing with a group of aliens around the furnace. Smedley ties himself to a firework launcher, plays "Taps" in a sad pitch, and is launched into orbit. Chilly Willy watches him from the cabin. He then performs the same dance Smedley does and rests on the furnace.
See also
Chilly Willy-First entry from 1953
The Legend of Rockabye Point-Oscar-nominated 1955 CW short
I'm Cold-1954 classic featuring the debut of Smedley Dog
References
External links
Video
1955 animated films
Films directed by Alex Lovy
1955 films
Universal Pictures animated short films
Animated films about animals
Animated films about penguins
Walter Lantz Productions shorts
1950s English-language films
1950s American films | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,623 |
\section*{Introduction}
Let $X$ be a smooth projective variety of dimension $n$ and $E$ a locally free sheaf of $\mathcal{O}_X$-modules on $X$. We are interested in the deformations of $E$ together with some of its sections.
Much is known about the classical case of a line bundle $L$ on a smooth projective curve $C$.
The classical Brill-Noether theory concerns with the subvarieties $W_d^k(C)$ of $\Pic^d(C)$ of linear systems on $C$ of degree $d$ and projective dimension at least $k$ or equivalently of line bundles on $C$ of degree $d$ having at least $k+1$ independent sections. Properties of $W_d^k(C)$ like non emptiness, connectedness, irreducibility and dimension were largely investigated, successfully determined and summarised in \cite{ACGH}.
During the last years, several generalisations of this problem were investigated.
Many efforts have been carried out to analyse the moduli space of stable vector bundles of fixed rank and degree on a curve, having at least $k$ independent sections.
In this context, less is known, about dimension, connected components and singular locus, see for instance \cite{Gt} and reference therein for an overview on this case.
To overcome the difficulties of the Brill-Noether theory of vector bundles, the concept of coherent systems was introduced, see \cite{nt,king,lepoit, bgmm03, bgmm, newsteadquestion} and reference therein.
A coherent system on an algebraic variety is the pair of a vector
bundle $E$ of fixed rank $n$ and degree $d$ together with a linear subspace $U$ of sections of $E$ of dimension $k$.
There is a notion of stability which allows to construct the moduli spaces of coherent systems fixing the parameters $(n,d,k)$, see \cite{king,lepoit}.
The relation between these moduli spaces and Brill-Noether theory is obvious:
any vector bundle which occurs as part of a coherent system must have at least a prescribed number of independent sections. Conversely, a vector bundle with a prescribed number of linearly independent sections
determines, in a natural way, a coherent system.
This defines a forgetful map $(E,U) \to E$ surjecting to the corresponding Brill-Noether locus. This map is an obvious generalisation of the classical projection $G^k_d(C) \to W^k_d(C)$, where $G^k_d(C)$ is the variety that parametrises the linear systems of degree $d$ and projective dimension exactly $k$ on a curve $C$. In many of the above works [loc.cit.], the aim is to deduce as much information as possible on the Brill-Noether loci from the moduli spaces of coherent systems that are easier to describe.
In \cite{he}, the infinitesimal study of the moduli space of coherent system on varieties was carried out, allowing a description of the tangent space and an obstruction space, see also \cite[Section 3]{bgmm}.
On the other hand, in \cite{pardini} the authors generalised the Brill-Noether theory to line bundles on smooth projective varieties of dimension greater than one. They are able to prove non emptiness and find the dimension of the Brill-Noether loci of a curve $C$ over a smooth surface $X$ of maximal Albanese dimension, under the hypothesis that a properly defined Brill-Noether number is positive and under some mild additional assumptions.
Finally, the general case of vector bundles on varieties of higher dimension is still quite mysterious.
In \cite{costa}, the authors prove the existence of a Brill-Noether type stratification of the moduli spaces of stable vector bundles on a smooth projective varieties with fixed Chern classes under the assumption that all the cohomology groups of degree greater than one vanish.
Some properties known in the classical Brill-Noether theory for line bundles on curves are expected to hold for the general case of vector bundles on higher dimensional varieties too. Many of them are known to experts but often there are not reference for them.
In this paper, we are interested in the infinitesimal deformations of a locally free sheaf $E$ of $\mathcal{O}_X$-modules on a smooth variety $X$ that preserve at least a prescribed number of independent sections. We focus on the local study of the Brill-Noether loci, on all properties we can predict using deformation theory and we do not concentrate on its global structure.
It is nowadays almost accepted that the most appropriate way to local analyse a moduli problem through infinitesimal deformations is via derived algebraic geometry.
The philosophy behind may be formulated in the following way: every deformation problem is controlled by a differential graded Lie algebra (dgLa) via the Maurer-Cartan equation and gauge equivalence.
A rigorous proof of this philosophy was independently given by Lurie \cite{lurie} and Pridham \cite{pridham} via an equivalence of infinity categories between dgLa and formal moduli problem.
The dgLa associated with a certain deformation problem is defined only up to quasi-isomorphism and it encodes many information about the problem. For instance, its first cohomology group coincides with the Zariski tangent space of the moduli space and its second cohomology group is an obstruction space for the problem.
This approach has been succesfully applied in many cases as deformations of locally free sheaves \cite{Fuk}, locally free sheaves with prescribed cohomological dimensions \cite{ElenaFormal}, coherent sheaves \cite{FIM}, pairs of manifold and coherent sheaves \cite{Dona-Marco}.
Inspired by this philosophy, we apply the dgLa techniques to the analysis of infinitesimal deformations of a locally free sheaf on a smooth projective variety, such that at least a certain number of independent sections lifts to the deformed sheaf.
Our main motivation was to test the powerful of the derived techniques in this very classical context, where the usual theory has not yet answered all questions and predict some properties the associated moduli spaces has to satisfy.
In particular, using this different approach, we are able to show some results, probably expected by the experts but without sufficient references.
The article is organised as follows. For the convenience of the reader, we first collect some basic notions on deformation functors, differential graded Lie algebras and the link between them.
In the second section, we briefly recall the definition of deformations of a locally free sheaf and exhibit the dgLa that controls these deformations following \cite{Fuk}.
The third section is finally devoted to the study of deformations of pairs $(E,U)$, where $E$ is a locally free sheaf of $\mathcal{O}_X$-modules on a smooth variety $X$ and $U$ is a linear subspace of its sections. For the basic definitions and the identification of the dgLa that controls these deformations, we follow \cite{elenatesi}.
Moreover, we are able to generalise some classical results: the condition for a section of a locally free sheaf to be extended to a first order deformation and the description of the image of the Petri map (Proposition \ref{prop.sezione si estende se cup product va a zero}). We also describe the tangent space to the functor of deformations of $(E,U)$ in the case $U=H^0(E)$ (Corollary \ref{Cor. TDef(E,H0(E))}).
In Section $4$, we specialize the study of deformations of pairs $(E,U)$ to the case of a smooth curve. In Lemma \ref{lemma.equiv h2 zero e petri iniettiva}, we find two equivalent conditions to the injectivity of the Petri map, which is known to be crucial in the classical study of Brill-Noether loci.
In Proposition \ref{prop.beta e liscezza}, we compute the dimension of the tangent space to the functor of deformations of a pair $(E,U)$ and find equivalent conditions to its smoothness, generalising the classical results concerning the variety $G^r_d(C)$.
Section $5$ is devoted to our main aim. Let $E$ be a locally free sheaf $E$ of $\mathcal{O}_X$-modules on a smooth variety $X$, such that $\dim H^0(X,E) \geq k$. We study infinitesimal deformations of $E$ such that at least $k$ independent sections of $E$ lift.
First we define this kind of deformations and observe that the functor $\Def_E^k$ associated to them is not a deformation functor in the meaning of Definition \ref{def. def functor}. Theorem \ref{teorema tangente Def^r} describes the first order deformations $\Def_E^k(\mathbb{C}[\epsilon])$ and the vector space generated by them, suggesting that the locally free sheaves with at least $k+1$ independent sections are singular points in the moduli space of sheaves with at least $k$ sections.
Propositions \ref{prop.alpha sur equivalenza di liscezze} and \ref{prop.H2=0 liscezza} deal with the smoothness of the functor $\Def_E^k$, linking it with other known conditions.
\medskip
We indicate with $\mathbb{K}$ an algebraic closed field of characteristic zero.
We will work often over the field $\mathbb{C}$ of complex numbers. We denote by $\mathbb{K}[\epsilon]$ the ring of dual number, meaning $\epsilon^2=0$.
\subsection*{Acknowledgements}
We wish to thank Marco Manetti for some inspiring mathematical discussions, Andrea Petracci for answering our questions and Peter Newstead for precious comments and suggestions on a first draft of this paper.
\section{Preliminaries on deformation functors}
The first part of this section is dedicated to some preliminaries on functors of Artin rings and deformation functors we will need in the article.
Secondly we introduce the basic definitions and properties of differential graded Lie algebras and the deformation theory associated to them.
For a complete presentation of the topics, we refer the reader to \cite{Schlessinger, FantechiManetti, Man Pisa, Man Roma, ManettiSeattle}.
\medskip
$\Set$ denotes the category of sets in a fixed universe and $\Art_{\mathbb{K}}$ the category of local Artinian $\mathbb{K}$-algebras with residue fields $\mathbb{K}$.
\bigskip
\subsection{Theory of deformation functors}
\begin{definition}
A \emph{functor of Artin rings} is a covariant functor $F :\Art_\mathbb{K} \to \Set$,
such that $F(\mathbb{K})=* $, where $*$ is the one point set.
\end{definition}
Consider the following diagram whose objects and arrows are in $\Art_\mathbb{K}$
\[ \xymatrix{ B \times_A C \ar[r]\ar[d] & C \ar[d]\\ B \ar[r] & A,} \]
applying a functor $F: \Art_\mathbb{K} \to \Set$, we get a map
\[\eta: F(B\times_A C) \to F(B) \times_{F(A)} F(C). \]
\begin{definition} \label{def. def functor}
A functor of Artin rings $F$ is called a \emph{deformation functor} if it satisfies the following conditions:
\begin{itemize}
\item $\eta$ is surjective whenever $B\to A$ is surjective
\item $\eta$ is an isomorphism whenever $A=\mathbb{K}$.
\end{itemize}
The functor $F$ is called \emph{homogeneous}, if $\eta$ is an isomorphism, whenever $B\to A$ is surjective.
\end{definition}
The name comes from the fact that most functors arising by deforming geometric objects are deformation functors and some of them are actually homogeneous.
\begin{remark}
Our definition of a deformation functor follows \cite{Man Pisa}. The first condition here is the classical Schlessinger's condition (H1) in \cite{Schlessinger}, while the second is slightly more restrictive then the (H2) of \cite{Schlessinger}. The main motivations of assuming these conditions are the good properties that tangent space and obstruction theory have if the functor satisfies them, as stated in Proposition \ref{prop.sp tg} and Theorems \ref{teo.univ ob} and \ref{teo.univ rel ob}.
For more details see \cite[Example 6.8]{FantechiManetti}.
\end{remark}
\begin{proposition} \label{prop.sp tg}
Let $F$ be a deformation functor, the set $t_F=F(\mathbb{K}[\epsilon]) $ has a natural structure of $\mathbb{K}$-vector space. If $\varphi: F \to G$ is a morphism of deformation functors the induced map $\varphi: t_F \to t_G$ is linear.
\end{proposition}
\begin{definition}
Let $F$ be a deformation functor.
The vector space $t_F=F(\mathbb{K}[\epsilon])$ is called the \emph{tangent space} to $F$.
\end{definition}
\begin{definition} \label{def.smoothness}
A morphism of functors of Artin rings $\varphi: F \to G$ is called \emph{smooth} if
for every surjection $B \to A$ in $\Art_\mathbb{K}$, the map
\[F(B) \to G(B) \times_{G(A)} F(A)\] is also surjective.
A functor of Artin rings $F$ is \emph{smooth} if the morphism $F \to *$ is smooth, i.e. if $F(B)\to F(A)$ is surjective for every surjective morphism $B\to A$ in $\Art_\mathbb{K}$.
\end{definition}
\begin{remark}
Note that, if $\varphi: F \to G$ is smooth, then the induced map $F(A) \to G(A)$ is surjective for all $A\in \Art_\mathbb{K}$.
\end{remark}
\begin{proposition}\label{prop liscezza funtori}
Let $\varphi: F \to G$ a smooth morphism of functors of Artin rings. Then:
$F$ is smooth if and only if $G$ is smooth.
\end{proposition}
\begin{proof}
Let $ B \to A$ be a surjection in $\Art_\mathbb{K}$.
$(\Rightarrow):$
Consider the following commutative diagram
\[ \xymatrix{ F(B) \ar@{>>}[r] \ar@{>>}[d]^{\varphi_B} & F(A) \ar@{>>}[d]^{\varphi_A} \\
G(B) \ar[r] & G(A) } \]
in which the vertical arrow are surjective by smoothness of $\varphi$ and the upper horizontal arrow is surjective by smoothness of $F$. Thus the lower arrow is surjective too and $G$ is smooth.
$(\Leftarrow):$
Let $f_A \in F(A)$. Since $G$ is smooth, there exists an element $g_B \in G(B)$ that lifts $\varphi_A(f_A) \in G(A)$. By smoothness of $\varphi$, the element $(f_A, g_B) \in F(A) \times_{G(A)} G(B)$ has a pre-image $f_B\in F(B)$, that assures the surjectivity of $F(B) \to F(A)$ and then the smoothness of $F$.
\end{proof}
We now introduce the notion of obstruction theory that is crucial in the study of deformations.
By a \emph{small extension} in $\Art_\mathbb{K}$ we mean an exact sequence
\[ e: 0\to J \to B \stackrel{\varphi}{\to} A \to 0\]
where $\varphi: B \to A$ is a morphism in $\Art_\mathbb{K}$ and $J$ is an ideal of $B$
annihilated by the maximal ideal $m_B$. In particular $J$ is a finite dimensional vector space over $B/m_B = \mathbb{K}$.
\begin{definition}
Let $F$ be a functor of Artin rings. An \emph{obstruction theory} $(V, v_e)$ for $F$ is the
data of a $k$-vector space $V,$ called \emph{obstruction space}, and for every small extension in $\Art_\mathbb{K}$:
\[ e: 0\to J \to B \stackrel{\varphi}{\to} A \to 0\]
of an obstruction map $v_e : F(A) \to V \otimes_\mathbb{K} J$ satisfying the following properties:
\begin{itemize}
\item If $ a\in F(A)$ can be lifted to $F(B)$ then $v_e(a) = 0$.
\item (base change) For every morphism $\alpha: e_1\to e_2$ of small extensions, i.e. for every commutative diagram
\begin{equation} \label{morph of small ex}\xymatrix{ 0 \ar[r]& J_1 \ar[r]\ar[d]^{\alpha_J} & B_1 \ar[r]\ar[d]^{\alpha_B} & A_1 \ar[r]\ar[d]^{\alpha_A} & 0 \\
0 \ar[r]& J_2 \ar[r] & B_2 \ar[r] & A_2 \ar[r] & 0 } \end{equation}
we have $v_{e_2}(\alpha_A(a))=(Id_V\otimes \alpha_J)(v_{e_1}(a))$ for every $a\in F(A_1)$.
\end{itemize}
An obstruction theory $(V, v_e)$ for $F$ is called \emph{complete} if the converse of
the first condition holds, i.e. the lifting exists if and only if the obstruction vanishes.
\end{definition}
\begin{remark}
Note that, if $F$ is smooth then all the obstruction maps are trivial.
The inverse holds if the obstruction theory is complete.
Clearly if $F$ admits a complete obstruction theory then it admits infinitely ones; it is in
fact sufficient to embed $V$ in a bigger vector space. One of the main interest is to look for
the smallest complete obstruction theory.
\end{remark}
\begin{definition} A \emph{morphism of obstruction} theories $(V, v_e) \to (W,w_e)$ is a linear map
$\varphi: V \to W$, such that $w_e = \varphi(v_e)$ for every small extension $e$.
An obstruction theory $(O_F , ob_e)$ for $F$ is called \emph{universal} if for every obstruction theory $(V, v_e)$ for $F$ there exists an unique morphism $(O_F , ob_e)\to(V, v_e)$.
\end{definition}
\begin{theorem}\cite[Theorem 3.2]{FantechiManetti} \label{teo.univ ob}
Let $F$ be a deformation functor, then there exists an universal obstruction
theory $(O_F , ob_e)$ for $F$. Moreover the universal obstruction theory is complete and every element of the vector space $O_F$ is of the form $ob_e(a)$ for some small extension
\[ e: 0\to \mathbb{K} \to B \to A \to 0\]
and some $a \in F(A)$.
\end{theorem}
In the following, we will also need the notion of relative obstruction theory.
\begin{definition}
Let $\varphi: F\to G$ be a morphism of functors of Artin rings and suppose
$G$ to be a deformation functor. A \emph{relative obstruction theory} $(V,v_e)$ for $\varphi$ is the data of a $\mathbb{K}$-vector space $V,$ called \emph{obstruction space} and for every small extension
in $\Art_\mathbb{K}$:
\[ e: 0\to J \to B \stackrel{\varphi}{\to} A \to 0\]
of an obstruction map $v_e : F(A) \times_{G(A)} G(B) \to V \otimes_\mathbb{K} J$ satisfying the following properties:
\begin{itemize}
\item If $(a, \beta) \in F(A) \times_{G(A)} G(B)$ can be lifted to $F(B)$ then $v_e( a, \beta) =0$.
\item (base change) For every morphism $\alpha: e_1\to e_2$ of small extensions, i.e. for every commutative diagram as (\ref{morph of small ex}), the following diagram is also commutative
\[ \xymatrix{ F(A_1) \times_{G(A_1)} G(B_1) \ar[r]^-{v_{e_1}} \ar[d]^{(\alpha_A,\alpha_B)} & V\times_{\mathbb{K}} J_1 \ar[d]^{Id_V \otimes \alpha_J} \\
F(A_2) \times_{G(A_2)} G(B_2) \ar[r]^-{v_{e_2}} & V\times_{\mathbb{K}} J_2. } \]
A relative obstruction theory is called \emph{complete} if the converse of
the first condition holds, i.e. the lifting exists if and only if the obstruction vanishes.
\end{itemize}
\end{definition}
\begin{remark}
Note that, if $\varphi: F\to G$ is smooth then all the relative obstruction maps are trivial. The inverse holds if the relative obstruction theory is complete.
\end{remark}
\begin{theorem}\cite[Theorem 3.2]{FantechiManetti} \label{teo.univ rel ob}
Let $\varphi: F \to G$ be a morphism of deformation functors, then there exists a unique universal relative obstruction theory for $\varphi$.
\end{theorem}
\begin{theorem}\cite[Proposition 2.17]{Man Pisa} \label{teo. liscio se tangete suriettivo e iniettivo ostruzione}
Let $\varphi: F \to G$ be a morphism
of deformation functors and $\varphi': (V, v_e) \to (W, we) $ be a compatible morphism between obstruction theories. If $(V, v_e)$ is complete, $\varphi': V \to W$ is injective and $t_\varphi: t_F\to t_G$ is surjective then $\varphi$ is smooth.
\end{theorem}
\bigskip
\subsection{Differential graded Lie algebras and deformation functors}
\begin{definition}
A \emph{differential graded Lie algebra}, briefly a \emph{dgLa}, is the data $(L,d,[\ ,\ ])$, where $L=\bigoplus_{i\in \mathbb {Z}} L^i$ is a $\mathbb Z$-graded vector space over $\mathbb{K}$, $d:L^i \rightarrow L^{i+1}$ is a linear map, such that $d \circ d=0$, and $[\ ,\ ]:L^i \times L^j \rightarrow L^{i+j}$ is a bilinear map, such that:
\begin{enumerate}
\item[-] $[\ ,\ ]$ is graded skewsymmetric, i.e. $[a,b]=-(-1)^{\deg a\deg b}[b,a]$,
\item[-] $[\ ,\ ]$ verifies the graded Jacoby identity, i.e. $[a,[b,c]]=[[a,b],c]+(-1)^{\deg a\deg b}[b,[a,c]]$,
\item[-] $[\ ,\ ]$ and $d$ verify the graded Leibniz's rule, i.e. $d[a,b]=[da,b]+(-1)^{\deg a}[a,db]$,
\end{enumerate}
for every $a, b$ and $c$ homogeneous.
\end{definition}
\begin{definition}
Let $(L,d_L, [\ ,\ ]_L)$ and $(M, d_M, [\ ,\ ]_M)$ be two dgLas, a \emph{morphism of dglas} $\varphi:L\to M$ is a degree zero linear morphism that commutes with the brackets and the differentials.
A \emph{quasi-isomorphism} of dgLas is a morphism of dgLas that induces an isomorphism in cohomology.
\end{definition}
Let $L$ be a differential graded Lie algebra, then it is defined a deformation functor $\Def_L: \Art_{\mathbb{K}}\to \Set$ canonically associated to it, as follows
\begin{definition}
For all $(A,\mathfrak{m}_A)\in \Art_{\mathbb{K}}$, we define:
$$\Def_L(A)=\frac{\MC_L(A)}{\sim_{\textrm{gauge}}},$$
where:
$$\MC_L(A)=\left\{x\in L^1\otimes \mathfrak{m}_A \mid dx+\frac{1}{2}[x,x]=0\right\}$$
and the gauge action is the action of $\exp (L^0\otimes \mathfrak{m}_A)$ on $\MC_L(A)$, given by:
$$e^a * x= x+\sum_{n=0}^{+\infty} \frac{([a,-])^n}{(n+1)!}([a,x]-da).$$
\end{definition}
We recall that the tangent to the deformation functor $\Def_L$ is the first cohomology space $H^1(L)$ of the dgLa $L$. Moreover, a complete obstruction theory for the functor $\Def_L$ can be naturally defined and its obstruction space is the second cohomology space $H^2(L)$ of the dgLa $L$.
If the functor of deformations of a geometrical object $\mathcal{X}$ is isomorphic to the deformation functor associated to a dgLa $L$, then we say that $L$ controls the deformations of $\mathcal{X}$.
By definition, any morphism $\varphi: L \to M$, induces a morphism $\varphi: \Def_L \to \Def_M$, that is an isomorphism whenever $\varphi$ is a quasi-isomorphism.
\section {Deformation of locally free sheaves}
Let $X$ be a smooth projective variety of dimension $n$ and $E$ a locally free sheaf of $\mathcal{O}_X$-modules on $X$. First of all we recall some notions about the deformations of the locally free sheaf $E$.
\begin{definition}
Let $A$ be a local Artinian $\mathbb{K}$-algebra with residue field $\mathbb{K}$.
An \emph{infinitesimal deformation} of $E$ over $A$ is a locally free sheaf $E_A$ of $\mathcal{O}_X \otimes A$-modules over $X\times \Spec A$, with a morphism $\pi_A: E_A \to E$ such that the obvious restriction of scalars $\pi_A: E_A \otimes_A \mathbb{K} \to E$ is an isomorphism. The deformation will be indicated with $(E_A, \pi_A)$ or, shortly, with $E_A$.
Two of such deformations $E_A$ and $E'_A$ are \emph{isomorphic} if there exists an isomorphism $\phi$ of sheaves of $\mathcal{O}_X \otimes A$-modules that makes the following diagram commutative:
\begin{equation} \label{def(E)}
\xymatrix{ E_A \ar[rr]^{\phi} \ar[dr]_{\pi_A} & & E'_A \ar[dl]^{\pi'_A} \\
&E.& }\end{equation}
The \emph{functor} of infinitesimal deformations of $E$ is
\[ \Def_E: \Art_\mathbb{K} \to \Set.\]
\end{definition}
It is classically known that $\Def_E$ is a deformation functor. Moreover its tangent space is $t_{\Def_E}=\Def_E(\mathbb{K}[\epsilon])= H^1(X,\End (E))$ and the obstructions are contained in $H^2(X, \End (E))$, see for example \cite{Sernesi}.
\medskip
Let $E$ be a locally free sheaf of $\mathcal{O}_X$-modules on $X$ and let $\End E$ be the locally free sheaf of its endomorphisms.
Over the ground field $\mathbb{C}$, consider
\[ A_X^{0,*}(\End E) := \bigoplus_{i=0}^n A_X^{0,i}(\End E):= \bigoplus_{i=0}^n \Gamma\left(X, {\mathcal A}_X^{0,i}(\End E)\right), \]
the graded vector space of global sections of the sheaf of differential forms with values on the sheaf $\End E$.
The Dolbeault differential on forms and the bracket defined as the wedge product on forms and the composition of endomorphisms induce a structure of dgLa on it.
It is well known that this dgLa is the one that controls the deformations of $E$.
\begin{proposition}\cite [Theorem 1.1.1]{Fuk} \label{dgla che governa Def E}
The dgLa $A_X^{0,*}(\End E)$ controls deformations of $E$.
The isomorphism of functors is given, for all $A\in \Art_{\mathbb{C}}$, by
$$\begin{array}{rrll}
\Psi: & \Def_{A_X^{0,*}(\End E)}(A)& \longrightarrow &\Def_{E}(A) \\
&x& \longrightarrow & \ker(\bar{\partial}+x)
\end{array}$$
\end{proposition}
In particular, the tangent space to $\Def_{E}$ is $\Def_{E}(\mathbb{C}[\epsilon])=H^1(X, \End E)$ and the obstructions to deformations are contained in $H^2(X, \End E)$, that fits in the classical picture.
\begin{remark} \label{rmk.Thom-Whitney}
If the ground field is any algebraically closed field of characteristic zero, instead of Dolbeault forms, the associated dgLa is defined via the Thom-Whitney complex associated with the sheaf of endomorphisms $\End E$ (see \cite{FMM}).
\end{remark}
\section {Deformation of locally free sheaves with a fixed subspace of sections} \label{sect.def(E,U)}
Let $E$ be a locally free sheaf of $O_X$-modules on a smooth projective variety $X$ and fix a subspace $U \subseteq H^0(X,E)$.
In this section, we study infinitesimal deformations of $E$ which preserves the subspace $U$.
We point out that in the literature such a pair $(E,U)$ is called a \emph{local system} of type $(n=\rk E,d=\deg E, k=\dim U)$. Deformations of local systems, stability conditions for them and the concerned moduli space are studied in \cite{lepoit, king,bgmm03, he}.
\smallskip
We start with some definitions and results of \cite{elenatesi, ElenaFormal}.
\begin{definition} \label{def.(E,U)}
Let $A$ be a local Artinian $\mathbb{K}$-algebra with residue field $k$. An \emph{infinitesimal deformation} of the pair $(E, U)$ over $A$ is the data $(E_A,\pi_A, i_A)$ of:
\begin{itemize}
\item a deformation $(E_A, \pi_A)$ of $E$ over $A$,
\item a morphism $i_A:U\otimes A \rightarrow H^0(E_A)$,
\end{itemize}
such that the following diagram commutes
\begin{equation} \label{def(E,U)}
\xymatrix{ U\otimes A \ar[d]^{\pi} \ar[r]^{i_A} & H^0(E_A) \ar[d]^{\pi_A}\\
U \ar@{^{(}->}[r]^{i} & H^0(E). }
\end{equation}
Two of such deformations $(E_A,\pi_A,i_A)$, $(E'_A,\pi'_A,i'_A)$ are \emph{isomorphic} if there exist an isomorphism $\phi:E_A \rightarrow E'_{A}$ of sheaves of $\mathcal{O}_X \otimes A$-modules, such that
$\pi'_A \circ \phi=\pi_A$ as in diagram \eqref{def(E)},
and an isomorphism $\psi:U\otimes A \to U\otimes A$, that makes the diagram commutative:
\begin{equation} \label{isodef(E,U)}
\xymatrix{ U\otimes A \ar[d]^{\psi} \ar[r]^{i_A}& H^0(E_A) \ar[d]^{\phi} \\
U\otimes A \ar[r]^{i'_A}& H^0(E'_A) . }
\end{equation}
Note that, this implies that $\phi$ induces an isomorphism $\phi: i_A(U\otimes A) \rightarrow i'_A(U\otimes A)$.
The \emph{functor} of infinitesimal deformations of $(E,U)$ is
\[ \Def_{(E,U)}: \Art_\mathbb{K} \to \Set,\]
that associates with every $A\in \Art_\mathbb{K}$ a deformation $(E_A,\pi_A, i_A)$ as defined above. In the following, we will often shorten the notation of such a deformation with $(E_A, i_A)$.
\end{definition}
\begin{proposition}
The functor $\Def_{(E,U)}: \Art_\mathbb{K} \to \Set$ defined above is a deformation functor.
\end{proposition}
\begin{proof}
First observe that $\Def_{(E,U)}(\mathbb{K})=\{(E,i)\}$, where $i:U \to H^0(E)$ is the inclusion and so $\Def_{(E,U)}$ is a functor of Artin rings.
To prove it is a deformation functor, we verify the two conditions of Definition \ref{def. def functor}.
\begin{itemize}
\item Let $B \rightarrow A$ and $C \rightarrow A$ two morphisms of Artin rings, suppose the first one to be surjective, we have to prove that
\[ \eta: \Def_{(E,U)}(B \times_A C) \rightarrow \Def_{(E,U)}(B) \times_{\Def_{(E,U)}(A)} \Def_{(E,U)}(C) \] is surjective.
Let $((E_B,i_B), (E_C,i_C)) \in \Def_{(E,U)}(B) \times_{\Def_{(E,U)}(A)} \Def_{(E,U)}(C)$ and let $(E_A, i_A)$ be the deformation over $A$ to which both reduce. It is classically known (see for example \cite[Prop.3.2]{Schlessinger} for the line bundle case), that $\widetilde{E}:= E_B \times_{E_A} E_C$ is a locally free sheaf of ${\mathcal O}_{B\times_A C}$-modules that deforms $E$ and which reduces to $E_B$ and $E_C$ over $B$ and $C$, respectively. By hypothesis, $i_B \otimes_B \Id_A = i_C \otimes_C \Id_A = i_A: U \otimes A \to H^0(E_A)$, that means that $U$ is a subspace of sections of $E$ that lift to $E_B$ and $E_C$. Thus, there exists $\tilde{i} :=i_B \times i_C: U \otimes (B\times_A C) \to H^0({\widetilde E})$ and $({\widetilde E}, \tilde{i}) \in \Def_{(E,U)}(B \times_A C)$ proves the surjectivity of $\eta$.
\item Let now $A=\mathbb{K}$, we have to prove that $\eta$ is bijective. The surjectivity is done. Suppose now that $(\hat{E}, \hat{i}) \in \Def_{(E,U)}(B\times_\mathbb{K} C)$ is an other deformation of $(E,U)$ sent to $((E_B,i_B), (E_C,i_C)) $ under $\eta$. Since $\hat{E}$ and $\widetilde{E}$ both reduce to $E_B$, $E_C$, $E$ over $B$, $C$ and $k$ respectively, it is classically known (see \cite[Prop.3.2]{Schlessinger}), that they are isomorphic. Note now that $\hat{i}: U \otimes (B\times_\mathbb{K} C) \to H^0(\hat{E})$ is completely determined by its reductions over $B$ and $C$, that are respectively $\hat{i}\otimes_{B\times_\mathbb{K} C} B=i_B$ and $\hat{i}\otimes_{B\times_\mathbb{K} C} C=i_C$. Thus $\hat{i}$ and $\widetilde{i}$ have to coincide.
\end{itemize}
\end{proof}
\medskip
There is a natural transformation of functors
\[ \Def_{(E,U)} \to \Def_E,\]
that associates with every deformation of the pair $(E, U)$ over $A\in \Art_\mathbb{K}$, the deformation of the sheaf $E$ over $A$ forgetting the deformed space of sections.
\begin{lemma} \label{rel obst def functors}
The relative obstruction theory of the natural transformation $\Def_{(E,U)} \to \Def_E$ is contained in $\Hom(U, H^1(X,E))$.
\end{lemma}
\begin{proof}
Let $0 \to J \to B \to A \to 0$ be a small extension.
Let
\[ \left( (E_A, i_A), E_B \right) \in \Def_{(E,U)}(A) \times_{\Def_{E}(A)} \Def_{E}(B), \]
thus $E_A$ is a deformation of $E$ over $A$ that lifts to a deformation $E_B$ over $B$.
Consider the exact sequence
\[ 0 \to E \otimes J \to E_B \to E_A \to 0, \]
that induces the exact sequence in cohomology
\[ 0 \to H^0(E) \otimes J \to H^0(E_B) \to H^0(E_A) \stackrel{\delta}{\to} H^1(E) \otimes J \to \ldots. \]
Note that a section $s \in H^0(E_A)$ lifts to a section of $E_B$ if and only if its image under the boundary map $\delta$ in $H^1(X,E)\otimes J$ is zero.
Thus, the obstructions of $\Def_{(E,U)}$ relative to $\Def_E$ are contained in $\Hom(U, H^1(X,E)) \otimes J$ and the obstruction theory is complete.
\end{proof}
\medskip
From now on, the base field will be $\mathbb{C}$.
Consider the complex of sheaves of differential forms on $X$ with values in the sheaf $E$ with the Dolbeault differential
\[ 0 \to \mathcal{A}_X^{0,0}(E) \stackrel{\bar{\partial}}{\to} \mathcal{A}_X^{0,1}(E) \stackrel{\bar{\partial}}{\to} \mathcal{A}_X^{0,2}(E) \stackrel{\bar{\partial}}{\to} \ldots \]
and the sheaf ${\mathcal H}om( \mathcal{A}_X^{0,*}(E), \mathcal{A}_X^{0,*}(E))$ of homorphisms of this complex.
Note that the graded vector space of global sections of the sheaf ${\mathcal H}om( \mathcal{A}_X^{0,*}(E), \mathcal{A}_X^{0,*}(E))$ is the same as the graded vector space of homomorphisms of the complex of global sections
\[ 0 \to A_X^{0,0}(E) \stackrel{\bar{\partial}}{\to} A_X^{0,1}(E) \stackrel{\bar{\partial}}{\to} A_X^{0,2}(E) \stackrel{\bar{\partial}}{\to} \ldots \]
We denote it as $\Hom^*(A_X^{0,*}(E),A_X^{0,*}(E))$.
As always, when one considers the homomorphism of a complex, one can endow $\Hom^*(A_X^{0,*}(E),A_X^{0,*}(E))$ with an obvious structure of dgLa using as bracket the wedge product on forms and the composition of homomorphism and as differential
the bracket with the differential of the complex.
The dgLa $\Hom^*(A_X^{0,*}(E),A_X^{0,*}(E))$ controls the deformation of the complex $(A_X^{0,*}(E), \bar{\partial})$, as proved in \cite[Section 4]{ManettiSemireg}.
Note that there exists an inclusion of dgLas
\begin{equation} \label{morfismo da end in hom(h0,h1)}\phi: A_X^{0,*}(\End E) \to \Hom^*(A_X^{0,*}(E),A_X^{0,*}(E)), \end{equation}
defined for $\omega \cdot f \in A_X^{0,p}(\End E) $ and $\eta \cdot s \in A_X^{0,q}(E)$ as
\[\phi ( \omega \cdot f)(\eta \cdot s)= \omega \wedge \eta \cdot f(s) \in A_X^{0,p+q}(E).
\]
It is easy to see that the elements in $A_X^{0,*}(\End E)$ correspond to the morphism of the complex $A_X^{0,*}(E)$ that are $A_X^{0,*}$-linear. Moreover, the Maurer-Cartan elements of $A_X^{0,*}(\End E)$ which are equivalent to zero in $\Hom^*(A_X^{0,*}(E),A_X^{0,*}(E))$ under the inclusion $\phi$ correspond to the deformations of $E$ that preserve the dimension of the cohomology spaces $H^i(X,E)$ for every index $i$, as proved in \cite[Lemma 4.1]{ManettiSemireg}.
\medskip
Next, consider the complex
\[Q_U: 0\to U \stackrel{i}{\hookrightarrow} A^{0,0}_X(E) \stackrel{\bar{\partial}}{\to} A^{0,1}_X(E) \stackrel{\bar{\partial}}{\to} A_X^{0,2}(E) \stackrel{\bar{\partial}}{\to} \ldots, \]
where $U$ is in degree -1.
We define the graded vector space
\[ D_U = \left\{ f\in \Hom^*(Q_U,Q_U) \mid f|_{A^{0,*}_X(E) } \in {A}^{0,\ast}_X(\End E) \right\}. \]
For any element $f \in D_U^j$, we use the notation as pair $f=(f_{-1}, f_i)$, where $f_{-1}:U \to A^{0,j-1}_X(E)$ and $f_i \in A^{0,j}_X(\End E) $.
Endowed with the same differential and bracket as $\Hom^*(Q_U,Q_U)$, $D_U$ is a dgLa.
In particular, the tangent space to $\Def_{D_U}$ is $ \Def_{D_U}(\mathbb{C}[\epsilon])=H^1(D_U)$ and the obstructions to deformations are contained in $H^2(D_U)$.
Consider the morphism:
\[r: D_U\to A^{0,\ast}_X(\End E), \]
that associates with any $f=(f_{-1}, f_i)\in D_U$, the element $f_i \in A^{0,*}_X(\End E)$. By definition, it is a morphism of dgLas and it is clearly surjective.
Denoting by $M^*=\ker r= \{ f \in D_U\ \mid \ f|_{ A^{0,*}_X(E)}=0 \}$, we have the following short exact sequence of dgLas
\[
0 \to M^* \to D_U \to A^{0,\ast}_X(\End E) \to 0,
\]
that induces the following exact sequence in cohomolgy
\begin{equation}
\begin{split} \label{successione lunga comologia DU}
0 \to H^0(M^*) \to H^0(D_U) \to H^0(A^{0,\ast}_X(\End E)) \to \\
\to H^1(M^*) \to H^1(D_U) \to H^1(A^{0,\ast}_X(\End E)) \to \\
\to H^2(M^*) \to H^2(D_U) \to H^2(A^{0,\ast}_X(\End E)) \to \ldots \\
\end{split}
\end{equation}
Since $ A^{0,\ast}_X(\End E)$ is the Dolbeault resolutions of the sheaf $\End E$, there are isomorphisms $H^j(A^{0,\ast}_X(\End E)) \cong H^j(X, \End E)$, for all $j \geq 0$.
Note that as dg vector space $M^*$ is isomorphic to $\Hom^*(U, Q_U)$, where $U$ is considered as a dg-vector space concentrated in degree -1, thus $H^0(M^*)\cong \Hom (U, H^{-1}(Q_U))=0$, $H^1(M^*)\cong \Hom (U, H^0(X,E)/U )$ and $H^j(M^*)\cong \Hom (U, H^{j-1}(X,E))$, for $j \geq 2 $.
Therefore the long exact sequence \eqref{successione lunga comologia DU} becomes
\begin{equation}
\begin{split} \label{seconda successione lunga comologia DU}
0 \to H^0(D_U) \to H^0( X,\End E) \to \\
\to \Hom (U, H^0(X,E)/U ) \to H^1(D_U) \to H^1(X,\End E) \stackrel{\alpha}{\to} \\
\to \Hom (U, H^{1}(X,E)) \stackrel{\beta}{\to} H^2(D_U) \stackrel{\gamma}{\to} H^2(X,\End E) \to \cdots \\
\end{split}
\end{equation}
where the map $\alpha$ is the restriction to $U$ of the morphism induced in cohomology by the inclusion $\phi$ defined in \eqref{morfismo da end in hom(h0,h1)}.
\smallskip
Note, that the dgLa morphism $r: D_U\to A^{0,\ast}_X(\End E)$ induces a natural transformation of functors:
\[ \Def_{D_U} \to \Def_{A^{0,*}_X(\End E)}.\]
\begin{lemma} \label{rel obst dgla functors}
A complete relative obstruction theory of the natural transformation
$\Def_{D_U} \to \Def_{A^{0,*}_X(\End E)}$ is contained in $\Hom(U, H^1(X,E))$.
\end{lemma}
\begin{proof}
Let $0 \to J \to B \to A \to 0$ be a small extension.
Let
\[
x=\left((x_{-1}, x_i), \tilde{x}_i)\right) \in \Def_{D_U}(A) \times_{\Def_{A^{0,*}_X(\End E)}(A)} \Def_{A^{0,*}_X(\End E)}(B),\]
thus $x_i \in \MC_{A^{0,*}_X(\End E)} (A)$ lifts to $\tilde{x}_i \in \MC_{A^{0,*}_X(\End E)}(B)$.
Choose a lifting $\tilde{x}_{-1} \in \Hom(U, A^{0,0}_X(E)) \otimes B$ of $x_{-1}$ and define $\tilde{x}=(\tilde{x}_{-1}, \tilde{x}_i)$.
The relative obstruction of $x$ is the class of $ob(x)=d\tilde{x} + \frac{1}{2}[\tilde{x}, \tilde{x}] \in H^2(D_U) \otimes J$.
Tensoring the sequence in \eqref{seconda successione lunga comologia DU} with $J$, we get the exact sequence:
\[ \ldots \to \Hom (U, H^{1}(X,E))\otimes J \to H^2(D_U) \otimes J \stackrel{\gamma}{\to} H^2(X,\End E) \otimes J \to \cdots \]
Since the element $ob(x)$ goes to zero under the map $\gamma$,
the relative obstruction $ob(x)$ is contained in $\Hom (U, H^{1}(X,E)) \otimes J$.
The defined obstruction is complete. Indeed, if there exists a lifting $\tilde{x}\in \Def_{D_U}(B)$ of $x$, it satisfies the Maurer-Cartan equation, thus $ob (x) =d\tilde{x} + \frac{1}{2}[\tilde{x}, \tilde{x}]=0$. \end{proof}
The following proposition is one of the main result of this section.
\begin{proposition}\cite[Corollary 4.1.14]{elenatesi} \label{dgla D controlla def (E,U)}
The dgLa $D_U$ controls deformations of the pair $(E,U)$.
The isomorphism of functors is given, for all $A\in \Art_\mathbb{C}$, by
$$\begin{array}{rrll}
\Phi: & \Def_{D_U}(A)& \longrightarrow &\Def_{(E,U)}(A) \\
& x& \longrightarrow & \left( (\ker(\bar{\partial}+x_0), \Id+x_{-1} \right)
\end{array}$$
\end{proposition}
\begin{proof}
For completeness and clearness we write here the proof.
We leave to the reader the classically known calculations for
the isomorphism of the functors of Proposition \ref{dgla che governa Def E}.
We divide the proof in two steps.
\smallskip
\noindent{\bf{First step: the natural transformation of functors $\Phi$ is well defined.}}
Let $x=(x_{-1},x_i)\in D_U^1 \otimes m_A$ be a Maurer-Cartan element and prove that it defines a deformation of the pair $(E,U)$.
It is a classical fact that $E_A:=\ker(\bar{\partial}+x_0)$ with the map $\pi_A := \Id \otimes \pi$ defines a locally free sheaf that is deformation of the sheaf $E$ (Proposition \ref{dgla che governa Def E}). The map
$i_A:= \Id+x_{-1}$
fits in the diagram \eqref{def(E,U)}, in particular $i_A(U\otimes A) \subset H^0(X, E_A)$. Indeed,
\begin{eqnarray*}
(\bar{\partial}+x_0)\circ(\Id+x_{-1})|_{U\otimes A} &= &\bar{\partial}\circ\Id+ \bar{\partial}\circ x_{-1}+x_0\circ\Id+x_0\circ x_{-1}\\
&=& 0+(\bar{\partial}\circ x_{-1}+x_0\circ\Id)+x_0\circ x_{-1}\\
&=&(dx)_{-1}+\frac{1}{2}[x,x]_{-1}=0,
\end{eqnarray*}
since $U\subset H^0(X,E)$ and $x \in \MC_{D_U}(A)$.
Then, the maps $i_A$ and $\pi_A$ makes the diagram \eqref{def(E,U)} commutative. Indeed, since $x_{-1} \in D_U \otimes m_A$:
\[ \pi_A \circ i_A|_{U\otimes A} = (\Id \otimes \pi) \circ (\Id + x_{-1})|_{U\otimes A} = (\Id \otimes \pi)|_{U\otimes A} + (\Id \otimes \pi) \circ x_{-1}
= \pi + 0= i \circ \pi. \]
Moreover, the morphism above is well defined on deformation functors. Let $x,y \in \MC_{D_U}(A)$ be two gauge equivalent elements via $z\in D_U^0 \otimes m_A$, i.e. $e^z *x=y$.
For $i\geq 0$, the elements $e^{z_i}: A^{0,i}_X(E) \otimes A \to A^{0,i}_X(E) \otimes A $ define an isomorphism of degree zero and, as classically know, the gauge relation is equivalent to the commutativity
\[ \bar{\partial}+y_0= e^{[z_i,-]}(\bar{\partial}+x_0)=e^{z_{i+1}}\circ(\bar{\partial}+x_0)\circ e^{-z_i}. \]
Thus, $\phi:=e^{-z_0}$ defines an isomorphism between the deformed sheaves $\ker(\bar{\partial} + x_0)$ and $\ker(\bar{\partial} + y_0)$.
Similarly, the element $\psi:=e^{z_{-1}}: U \otimes A \to U\otimes A$ defines an isomorphism and the gauge relation is equivalent to the commutativity of the diagram \eqref{isodef(E,U)}. Indeed,
\begin{eqnarray} \label{eqgauge2}
y_{-1} &=& e^{z}* x_{-1} = x_{-1}+\sum_{n=0}^{+\infty} \frac{([z,-])^n}{(n+1)!}([z,x]_{-1}-(dz)_{-1})=\nonumber \\
&=& x_{-1}+\sum_{n=0}^{+\infty} \frac{([z,-])^n}{(n+1)!}([z,x]_{-1}+[z,\Id]_{-1})=
x_{-1}+\sum_{n=1}^{+\infty} \frac{([z,-])^n}{n!}(\Id+x_{-1})=\nonumber \\
&=& \sum_{n=0}^{+\infty} \frac{([z,-])^n}{n!}(\Id+x_{-1})-\Id= e^{[z,-]}(\Id+x_{-1})-\Id \ ,
\end{eqnarray}
where we use $(dz)_{-1}=i\circ z_{-1}-z_0\circ i=-[z,\Id]_{-1}$. Thus:
$$ \Id+ y_{-1}= e^{[z,-]}(\Id+x_{-1})=e^{z_{0}}\circ(\Id+x_{-1})\circ e^{-z_{-1}},$$
as we wanted.
\smallskip
\noindent{\bf{Step two: $\Phi$ is an isomorphism of functors.}}\\
First the injectivity of $\Phi(A)$ for every $A\in \Art_\mathbb{C}$.
Suppose that $x=(x_{-1}, x_i)$ and $ y=(y_{-1}, y_i) \in \MC_{D_U}(A)$ induce isomorphic deformations $(\ker(\bar{\partial} + x_0), \Id+ x_{-1})$ and $ (\ker(\bar{\partial} + y_0), \Id+ y_{-1})$ via the isomorphisms $(\phi, \psi)$, as in Definition \ref{def.(E,U)}.
It is classical to lift $\phi$ to an isomorphism of the form $e^z$, with $z \in A^{0,0}(\End E) \otimes m_A$ and to get the following commutative diagram
\begin{equation} \label{iniett}
\xymatrix{
0 \ar[r]& U\otimes A \ar[d]^{\psi}\ar[r]^{\Id+x_{-1}\ \ \ }& \ker(\bar{\partial}+x_0)\ar[r]^{i}\ar[d]^{\phi=e^z} & A_X^{(0,0)}(E)\otimes A \ar[r]^{\ \ \ \ \ \bar{\partial}+x_0}\ar[d]^{e^z} & \cdots \\
0 \ar[r]& U\otimes A \ar[r]^{\Id+y_{-1} \ \ \ } &\ker(\bar{\partial}+y_0)\ar[r]^{i} & A_X^{(0,0)}(E)\otimes A \ar[r]^{\ \ \ \ \ \bar{\partial}+y_0} & \cdots }
\end{equation}
The isomorphism $\psi$ is of the form $e^w$, with $w \in \Hom(U,U)\otimes m_A$ too, because it is the identity on the residue field.
Thus there exists an element $t=(w,z) \in D_U^0\otimes m_A$, such that $e^t$ is an isomorphism that makes the diagram (\ref{iniett}) commutative. It is an easy calculation, similar to (\ref{eqgauge2}), to see that the commutativity is equivalent to the gauge relation $y=e^t* x$.
Moreover, by next Proposition \ref{liscezza morf funtori}, the morphism of functor $\Phi$ is smooth, thus $\Phi(A)$ is surjective, for all $A\in \Art_\mathbb{C}$.
\end{proof}
\begin{proposition} \label{liscezza morf funtori}
The morphism of functors
$\Phi: \Def_{D_U} \longrightarrow \Def_{(E,U)}$ defined in Proposition \ref{dgla D controlla def (E,U)}
is smooth.
\end{proposition}
\begin{proof} Let $0\to J \to B\to A \to 0$ be a small extension. Let $x =(x_{-1}, x_i) \in \Def_{D_U}(A)$ and $\Phi(x)=(E_A,i_A) \in \Def_{(E,U)}(A)$. The smoothness of $\Phi$ is equivalent to say that $x$ lifts to an element $\tilde{x}\in \Def_{D_U}(B)$
if and only if $(E_A,i_A)$ lifts to a pair $(E_B,i_B)\in \Def_{(E,U)}(B)$.
One direction is obvious.
For the other one, we recall that the morphism of functors
$\Psi: \Def_{A^{0,*}(\End E)} \to \Def_E$, defined in Proposition \ref{dgla che governa Def E}, is smooth. Thus it is enough to show that the relative obstruction theories of Lemmata \ref{rel obst def functors} and \ref{rel obst dgla functors} are isomorphic via the correspondence between the Dolbeault and \v{C}ech cohomology.
As in Lemma \ref{rel obst dgla functors}, let
\[
x=\left((x_{-1}, x_i), \tilde{x}_i)\right) \in \Def_{D_U}(A) \times_{\Def_{A^{0,*}_X(\End E)}(A)} \Def_{A^{0,*}(\End E)}(B)
\]
and let $ob(x)\in \Hom(U, H^1(X, E))\otimes J$ be its obstruction. Observe that here $H^1(X, E)$ is the Dolbeault cohomology group and let find the element in \v{C}ech cohomology that corresponds to $ob(x)$.
For every $s \in U \otimes A$, $ob(x)(s) \in H^1(X,E)\otimes J$, since it is closed, it is locally exact, i.e. there exist an open cover $\mathcal W=\{ W_i\}$ of $X$ and $\tau_i(s) \in A_{W_i}^{0,0}(E) \otimes J$, such that $\bar{\partial} \tau_i(s)= ob(x)(s)|_{W_i} $.
Define on $W_i \cap W_j$ the elements $\sigma_{ij}(s)=\tau_i(s)- \tau_j(s)$, they are \v{C}ech cocycles and their class $[\{\sigma_{ij}(s)\}_{ij}] \in H^1(X,E)\otimes J$ defines the correspondent element to $ob(x)(s)$ in \v{C}ech cohomology.
As in Lemma \ref{rel obst def functors}, let
\[ \left( (E_A, i_A), E_B \right) \in \Def_{(E,U)}(A) \times_{\Def_{E}(A)} \Def_{E}(B), \]
where $\Phi(x)=(E_A,i_A)$ and $E_B=\Psi( \tilde{x}_i)$. For every $s \in U\otimes A$, the obstruction to lift $i_A(s)\in H^0(E_A)$ to a section of $E_B$ lives in $H^1(X,E)\otimes J$ and is given by $\delta(i_A)(s)$, where $\delta$ is the coboundary map
\[\ldots \to H^0(E_B) \to H^0(E_A) \stackrel{\delta}{\to} H^1(E) \otimes J\to \ldots. \]
Recall that the construction of the coboundary map consists in chasing the following diagram
$$\xymatrix{ 0\ar[r] & \check{C}^0(\mathcal{W},E)\otimes J\ar[r]\ar[d]_{\check{\delta}}& \check{C}^0(\mathcal{W},E_B) \ar[r]\ar[d]_{\check{\delta}}& \check{C}^0(\mathcal{W},E_A)\ar[r]\ar[d]_{\check{\delta}}& 0 \\
0\ar[r] & \check{C}^1(\mathcal{W},E)\otimes J\ar[r]& \check{C}^1(\mathcal{W},E_B) \ar[r]& \check{C}^1(\mathcal{W},E_A) \ar[r]& 0. }
$$
The element $(i_A)(s)=\{ i_A(s)|_{W_i}\}_i \in H^0(E_A)$ can be lifted to an element $i_A(s)|_{W_i} - \tau_i (s) \in \check{C}^0(\mathcal{W}, E_B)$. Applying the \v{C}ech differential to it, we get $\check{\delta} (i_A(s)|_{W_i} - \tau_i (s))= \{i_A(s)|_{W_i}-\tau_i (s) - i_A(s)|_{W_j}+\tau_j (s)\}_{ij} =\{ \tau_i (s)- \tau_j (s)\}_{ij} = \{\sigma_{ij}(s)\}_{ij}$.
As we state, the two obstructions coincides.
\end{proof}
As a direct consequence of Proposition \ref{dgla D controlla def (E,U)}, we get the following result, already obtained in \cite[Th\'eoreme 3.12]{he}. See also \cite[Proposition 3.4]{bgmm03} for the curve case.
\begin{corollary} \label{cor.sp tang e ostr Def(E,U)}
The tangent space to $\Def_{(E,U)}$ is $ H^1(D_U)$ and all obstructions are contained in $H^2(D_U)$.
\end{corollary}
\begin{remark}
If the ground field is any algebraically closed field of characteristic zero, we expect we can define a dgLa that controls deformations of $(E,U)$ using the Thom-Whitney complex associated with the sheaf of endomorphisms $\End E$ instead of the Dolbeault forms, as observed in Remark. \ref{rmk.Thom-Whitney} \end{remark}
\smallskip
In the following, we briefly focus on smoothness of the forgetful morphism $r: \Def_{(E,U)} \to \Def_E$.
The following corollary is a direct consequence of Lemmata \ref{rel obst def functors} and \ref{rel obst dgla functors}. Otherwise, it can be obtained applying Theorem \ref{teo. liscio se tangete suriettivo e iniettivo ostruzione} to the exact sequence \eqref{seconda successione lunga comologia DU}.
\begin{corollary} \label{prop.rel obstr classica}
If $\Hom(U, H^1(E))=0$, the forgetful morphism of functors $r:\Def_{(E,U)} \to \Def_E$ is smooth.
\end{corollary}
\begin{remark} \label{cor. alpha sur}
By Proposition \ref{prop liscezza funtori}, the smoothness of the forgetful morphism $r: \Def_{(E,U)} \to \Def_E$ implies the equivalence between the smoothness of the two functors $\Def_E$ and $\Def_{(E,U)}$.
\end{remark}
\begin{corollary} \label{corollario alpha su implica r liscio}
If the map $\alpha: H^1(X,\End E)
\to \Hom (U, H^{1}(X,E))$ that appears in \eqref{seconda successione lunga comologia DU} is surjective, then the forgetful morphism $r: \Def_{(E,U)} \to \Def_E$ is smooth.
\end{corollary}
\begin{proof}
Let $0\to J \to B \to A \to 0$ be a small extension in $\Art_\mathbb{C}$ and consider
\[
x=\left((x_{-1}, x_i), \tilde{x}_i)\right) \in \Def_{D_U}(A) \times_{\Def_{A^{0,*}_X(\End E)}(A)} \Def_{A^{0,*}_X(\End E)}(B).\]
Since $x_i$ lifts to $\tilde{x}_i$, from diagram of obstruction theories
\begin{equation} \label{ostr}
\xymatrix{ \Def_{D_U}(A) \ar[r]^-{ob} \ar[d] & H^2(D_U) \otimes J \ar[d]^{\gamma} \\
\Def_{A^{0,*}_X(\End E)} (A)\ar[r]^-{ob} & H^2(\End E) \otimes J }
\end{equation}
we get that the relative obstructions to lift $x$ to an element in $\Def_{(E,U)}(B)$ is contained in $\ker \gamma$, that is trivial. Indeed, looking at \eqref{seconda successione lunga comologia DU},
the surjectivity of the map $\alpha: H^1(X,\End E) \to \Hom (U, H^{1}(X,E))$ implies that the morphism $\gamma : H^2(D_U)
\to H^2(\End E) $ is injective.
\end{proof}
\begin{remark}\label{remark alpha su allora Hom(U, H^1(E))=0}
The condition $\Hom(U, H^1(E))=0$ is equivalent to the surjectivity of the map $\alpha: H^1(X,\End E) \to \Hom (U, H^{1}(X,E))$.
Indeed, by Corollary \ref{corollario alpha su implica r liscio}, if $\alpha$ is surjective, $r$ is smooth, then also the map $H^1(D_U) \to H^1(X,\End E) $ on the tangent spaces of the functors is surjective. By the exact sequence \eqref{seconda successione lunga comologia DU}, the map $\alpha$ is actually the zero map and so $ \Hom (U, H^{1}(X,E)=0$.
The other implication is obvious.
\end{remark}
\begin{corollary} In the notation above, we have
\[ \dim t_{\Def_{(E,U)}} \geq \dim t_{\Def_{E}}
- k \cdot \dim H^1(X,E),\]
where $k$ is the dimension of $U \subseteq H^0(X,E)$.
\end{corollary}
\begin{proof}
By the long exact sequence \eqref{seconda successione lunga comologia DU},
\[
\cdots \to \Hom (U, H^0(X,E)/U ) \to H^1(D_U) \stackrel{\beta}{\to} H^1(X,\End E) \stackrel{\alpha}{\to} \Hom (U, H^{1}(X,E)) \to \cdots \\
\]
we have
\[
\dim t_{\Def_{(E,U)}} = \dim H^1(D_U) \geq \dim \im \ \beta = \dim \ker \ \alpha= \dim H^1(X,\End E) - \dim \im \alpha
\]
\[
\geq \dim H^1(X,\End E) - \dim \Hom (U, H^{1}(X,E))= \dim t_{\Def_{E}} -k \cdot \dim H^1(X,E).
\]
\end{proof}
Using our description of deformations via dgLas, we can generalise a classical result.
Fix a section $s \in H^0(X,E)$, the morphism $\phi$ of \eqref{morfismo da end in hom(h0,h1)} induces in cohomology the cup product
\[
- \cup s: H^1(X, \End E) \to H^1(X,E),
\]
where $a\cup s=\alpha(a)(s)$, for every $a \in H^1(X, \End E)$.
\begin{proposition} \label{prop.sezione si estende se cup product va a zero}
Let $E$ be a locally free sheaf over a projective variety $X$. A section $s \in H^0(X,E)$ can be extended to a section of a first order deformation of $E$ associated to an element $a \in H^1(X, \End E)$ if and only if $a \cup s =0 \in H^1(X,E)$.
\end{proposition}
\begin{proof}
Let $s \in H^0(X,E)$ be a section and define $U=\langle s \rangle$.
Recalling our descriptions via dgLas of the first order deformations given after Proposition \ref{dgla che governa Def E} and in Corollary \ref{cor.sp tang e ostr Def(E,U)},
we can rewrite the exact sequence (\ref{seconda successione lunga comologia DU}) as
\[ \ldots \to H^1(D_U)= \Def_{(E,U)}(\mathbb{C}[\epsilon])\stackrel{r}{\to} H^1(X, \End E)= \Def_E(\mathbb{C}[\epsilon]) \stackrel{\alpha}{\to} \Hom(U, H^1(X,E)) \to \ldots \]
The section $s$ can be extended to a deformation associated to $a \in H^1(X, \End E)= \Def_E(\mathbb{C}[\epsilon])$ if and only if $a \in \im r$. Since $\im r= \ker \alpha$ we have the required description.
\end{proof}
The same result is classically known for line bundles over a curve (see \cite[Lemma page 186]{ACGH}) and for line bundles over a projective variety (see \cite[Proposition 3.3.4]{Sernesi}).
\smallskip
This result can be reinterpreted in terms of some special maps and it can be seen as a generalization of \cite[Proposition 4.2 (i)]{ACGH}, \cite[Section 2]{Gt} and \cite[Section 4.3]{pardini}. In the spirit of \cite[Section 4.3]{pardini}, we define a generalization of the Petri map - we will properly introduce in the next section - as the map induced by the cup product:
\[ \mu_0: H^0(X,E) \otimes H^0(X, K_X \otimes E^*) \to H^0(X, K_C \otimes E \otimes E^*), \]
where $K_X$ is the canonical bundle of X, $E^*$ is the dual bundle of $E$
and the map
\[ \alpha_n: H^1(X, \End E) \otimes H^{n-1}(\mathcal{O}_X) \to H^n(\End E), \]
is given by the cup product.
Proposition \ref{prop.sezione si estende se cup product va a zero} can be stated saying that for all $\sigma \in H^1(X, \End E) \otimes H^{n-1}(\mathcal{O}_X)$ and for all $\psi \in H^0(X,E) \otimes H^0(X, K_X \otimes E^*)$ the following cup product vanishes:
\[ \alpha_n(\sigma) \cup \mu_0(\psi) =0, \]
or equivalently that $\alpha_n\left( H^1(X, \End E) \otimes H^{n-1}(\mathcal{O}_X)\right)\subset H^n(\mathcal{O}_X)$ is orthogonal to $\im \mu_0 \subset H^0(X, K_C \otimes E \otimes E^*).$
\bigskip
In the particular case of deformations of pairs $(E, H^0(E))$, the exact sequence
\eqref{seconda successione lunga comologia DU} splits
\[ 0 \to H^1(D_U) \to H^1(X,\End E) \stackrel{\alpha}{\to} \Hom (H^0(X,E), H^{1}(X,E)) \to \ldots \]
Thus the tangent space $t_{\Def_{(E,H^0(E))}}= H^1(D_U)$ can be identified with the kernel of the morphism $\alpha: H^1(X,\End E) \to \Hom (H^0(E), H^{1}(X,E))$.
\begin{corollary} \label{Cor. TDef(E,H0(E))}
The tangent space to the deformations of the pair $(E, H^0(E))$ can be identified with
\[ t_{\Def_{(E,H^0(E))}} = \{ a \in H^1(X,\End E) \ \mid \ a \cup s =0, \ \forall \ s \in H^0(X,E) \}. \]
\end{corollary}
In the case of line bundles, the description of the tangent space above is also given in \cite[Proposition 3.3, (i)]{pardini}.
\section{Deformations of the pair $(E,U)$ over a curve}
In this section, we restrict our attention on curves, i.e., we fix a smooth projective curve $C$ of genus $g$ and we study deformations of the pair $(E,U)$, where $E$ is a locally free sheaf of rank $n$ and degree $d$ on $C$ and $U\subseteq H^0(C,E)$ is a subspace of sections of dimension $k$.
\smallskip
First suppose $E=L$ to be a line bundle on $C$. The Petri map, introduced first by Petri in \cite{Petri} and studied deeply in \cite{arbarellocornalba} and \cite{ACGH}, is classically defined as the map induced by the cup product:
\[\mu_0: U \otimes H^0(C, K_C\otimes L^*) \to H^0(C, K_C), \]
where $K_C$ denotes the canonical sheaf of $C$ and $L^*$ the dual line bundle of $L$.
In \cite{bgmm03, Gt, pardini} a generalization of $\mu_0$ to the case of a vector bundle $E$ is introduced as the map induced by the cup product:
\[ \mu_0: U \otimes H^0(C, K_C \otimes E^*) \to H^0(C, K_C \otimes E \otimes E^*), \]
where $E^*$ is the dual of the vector bundle $E$.
Classically for line bundles and also in the successive generalizations [loc. cit.], the Petri map plays a role in the study of the smoothness of the deformations of the pair $(E,U)$ over a curve $C$. We aim to recover and generalise these kind of results.
Consider the sequence \eqref{seconda successione lunga comologia DU}; in the case of curves, it reduces to
\begin{equation}
\begin{split} \label{curva succesione lunga comologia DU}
0 \to H^0(D_U) \to H^0( C,\End E)
\to \Hom (U, H^0(C,E)/U ) \to\\
\to H^1(D_U) \to H^1(C,\End E)
\stackrel{\alpha}{\to} \Hom (U, H^{1}(C,E)) \to H^2(D_U) \to 0.
\end{split}
\end{equation}
So we are able to recover \cite[Proposition 3.4 (i)]{bgmm03}.
\begin{lemma} \label{lemma.equiv h2 zero e petri iniettiva}
In the above notations, the following conditions are equivalent:
\begin{itemize}
\item $H^2(D_U)=0$,
\item the map $\alpha$ is surjective,
\item $\Hom(U, H^1(E))=0$,
\item the Petri map $\mu_0$ is injective.
\end{itemize}
\end{lemma}
\begin{proof}
The equivalence between the first two conditions follows from the exact sequence (\ref{curva succesione lunga comologia DU}). The equivalence between the second and the third is Remark \ref{remark alpha su allora Hom(U, H^1(E))=0}. Finally, the second and the last condition are equivalent because $\alpha$ and $\mu_0$ are dual map. Indeed, by Serre duality $H^1(C,\End E)^* \cong H^0(C, K_C \otimes E \otimes E^* )$ and
$ (\Hom (U, H^{1}(C,E)) )^*\cong (U^* \otimes H^{1}(C,E))^*\cong U \otimes H^{1}(C,E)^*\cong U \otimes H^0(C, K_C \otimes E^*)$.
\end{proof}
Aiming to link these conditions with the smoothness of the functor of deformations of $(E,U)$, we prove the following result.
\begin{lemma} \label{lemma.calcolo beta}
In the above notations
\[ h^1(D_U)= h^2(D_U)+h^0(D_U) + k \chi(E) -\chi(\End E) -k^2,\]
where $\chi(E)$ and $\chi(\End E)$ denote the Euler characteristics of $E$ and $\End E$ respectively.
\end{lemma}
\begin{proof}
From the above exact sequence \eqref{curva succesione lunga comologia DU}, we obtain that
\[
h^0(D_U) - h^0(\End E)+ k \cdot \left(h^0(E) -k\right) - h^1(D_U) + h^1(\End E) - k \cdot h^1(E) + h^2(D_U)=0;\]
therefore
\[
\begin{split}h^1(D_U)& = h^2(D_U) + h^0(D_U) +k \cdot\left(h^0(E) -h^1(E)\right) +h^1(\End E) -h^0(\End E) -k^2\\
& = h^2(D_U)+h^0(D_U) +k \cdot \chi(E) -\chi(\End E) -k^2.
\end{split}
\]
\end{proof}
\begin{remark} \label{rmk.calcolo beta}
Let $E$ be a vector bundle of rank $n$ and degree $d$ on a curve $C$ of genus $g$, then
$\chi(E) = d+n(1-g) $ (see \cite{HarrisMorrison} page 154), then $\chi(\End E) = n^2(1-g) $.
Therefore
\[
\begin{split} k \chi(E) -\chi(\End E) - k^2&= k\left(d+n(1-g)\right) -n^2(1-g) -k^2 \\
&= k (d+n(1-g)) +n^2(g-1) - k^2
\end{split}
\]
\end{remark}
Then, as in \cite[Definition 2.7]{bgmm03} and \cite[Definition 2.1]{Gt}, we can introduce the Brill-Noether number.
\begin{definition}
Let $E$ be a vector bundle of rank $n$ and degree $d$ on a curve $C$ of genus $g$ and let $U$ be a subspace of sections of dimension $k$.
The \emph{Brill-Noether number} is
\[\beta(n,d,k)= n^2(g-1) -k (k- d + n(g-1)) +1.\]
\end{definition}
\begin{remark}
This number is a generalization to vector bundles of the well known \emph{Brill-Noether} number $\rho$ for the data of a degree $d$ line bundle over a curve of genus $g$ with a subspace of sections of dimension $k$:
\[ \rho= g-k(g-d+k), \]
defined in \cite{arbarellocornalba} and \cite{ACGH}.
As for the classical case of $\rho$, $\beta$ gives an estimate of the dimension of the Brill-Noether loci in the corresponding moduli spaces.
\end{remark}
We are now ready to prove our main result of this section. It generalises \cite[Proposition 4.1]{ACGH}, that for a line bundle $L$ on a curve connects the injectivity of the Petri map with the smoothness of the deformations of the pair $(L,U)$ and calculates the dimension of the concerned moduli space in the smooth case.
\begin{proposition} \label{prop.beta e liscezza}
Let $E$ be a vector bundle of rank $n$ and degree $d$ on the curve $C$ of genus $g$ and let $U$ be a subspace of sections of dimension $k$.
Then, the tangent space to deformations of the pair $(E,U)$ has dimension
\[ \beta(n,d,k)-1+h^0(D_U) +h^2(D_U). \]
Moreover, the functor $\Def_{(E,U)}$ is smooth and its tangent space has dimension $\beta(n,d,k)-1+h^0(D_U)$ if and only if $H^2(D_U)=0$ if and only if the Petri map is injective.
\end{proposition}
\begin{proof}
The tangent space to the deformations of the pair $(E,U)$ is $H^1(D_U)$. Then, according to Lemma \ref{lemma.calcolo beta} and Remark \ref{rmk.calcolo beta}, the dimension of it is given by
\begin{eqnarray}
h^1(D_U) &=& h^2(D_U)+h^0(D_U) +k \chi(E) -\chi(\End E) -k^2 =\nonumber \\
&=& h^2(D_U) + h^0(D_U) + k(d+n(1-g)) +n^2(g-1) -k^2 \nonumber \\
&= & h^2(D_U) + h^0(D_U) -1 + \beta(n,d,k), \nonumber
\end{eqnarray}
As already noticed in Lemma \ref{lemma.equiv h2 zero e petri iniettiva}, the Petri map is injective if and only if its dual map $\alpha$ is surjective, that is equivalent to the condition that $H^2(D_U)=0$.
Since the obstructions to deform the pair $(E,U)$ are contained in $H^2(D_U)$, if it vanishes, then the functor $\Def_{(E,U)}$ is smooth and the dimension of the tangent space is easily calculated by the above formula.
For the other direction, the condition on the dimension of the tangent space implies that $H^2(D_U)=0$.
\end{proof}
\begin{remark}
Proposition \ref{prop.beta e liscezza} is the analogous to \cite[Proposition 3.10]{bgmm03}.
In this article, the author focus their attention on the moduli space of coherent systems from the global point of view. In order to construct a moduli space, they need a suitable notion of stability. The stability conditions, they define, imply that $h^0(D_U)=1$. Thus
the formula for the dimension of the tangent space reduces to $\beta(n,d,k) +h^2(D_U) $ (see Lemma 3.5 [loc. cit]).
\end{remark}
\section{Deformations of a locally free sheaves and some of its sections}
In this section, we consider a locally free sheaf $E$ of $\mathcal{O}_X$-modules on a smooth projective variety $X$, such that $\dim H^0(X, E) \geq k$ and study infinitesimal deformations of $E$ such that at least $k$ independent sections of $E$ lift to the deformed locally free sheaf.
These deformations correspond to the infinitesimal deformations of the locally free sheaf $E$ induced by an infinitesimal
deformation of a pair $(E,U)$, for some subspace $U\subseteq H^0(X, E)$ with $\dim U = k$.
In other words, they are the deformations in the image of the forgetful maps of functors:
\[ r_U: \Def_{(E,U)} {\to} \Def_E, \]
for some $U\subseteq H^0(X,E)$, with $\dim U = k$. We denote this subfunctor of $\Def_E$ with $\Def^{k}_E$.
More explicitly, we give the following definition.
\begin{definition}
Let $E$ be a locally free sheaf of $\mathcal{O}_X$-modules on a smooth projective variety $X$, such that $h^0(X,E) \geq k$.
Let $Gr(k,H^0(E))$ be the grassmannian of all subspaces of $H^0(X, E)$ of dimension $k$. We define the functor $\Def^{k}_E:\Art_\mathbb{K} \to \Set$, that associates with every $A \in \Art_\mathbb{K}$ the set
\[ \Def^{k}_E (A)= \bigcup_{U \in Gr(k,H^0(E))} r_U(\Def_{(E,U)}(A)).
\]
and call it the \emph{functor of deformations of $E$ with at least $k$ sections}.
\end{definition}
\begin{remark} \label{rmk.no def funct}
In the case $h^0(X,E)=k$, all sections are required to lift to the deformed locally free sheaf and the functor $\Def^k_E$ is in one-to-one correspondence via the forgetful morphism with the functor $\Def_{(E,H^0(E))}$, analysed at the end of Section \ref{sect.def(E,U)}.
Thus, our study of $\Def_{(E,H^0(E))}$ applies completely to it and in particular $\Def_E^k$ is in this case a deformation functor.
In general, the functor $\Def_E^k$ is a functor of Artin rings, but unfortunately, it is not a deformation functor. Indeed, by definition, if $\mathbb{K}$ is the ground field, we have
\[\Def_E^k(\mathbb{K})= \bigcup_{U \in Gr(k,H^0(E))} r_U(\Def_{(E,U)}(\mathbb{K}) )= \{E\}, \]
since each of the functors $\Def_{(E,U)}$ are of Artin rings.
Consider now two morphisms of Artin rings $B \rightarrow A$ and $C \rightarrow A$ and suppose one of them to be surjective.
The map
\[ \eta: \Def_E^k(B\times_A C) \to \Def_E^k(B) \times_{\Def_E^k(A)} \Def_E^k(C) \]
will be in general not surjective. Indeed, let $(E_B, E_C) \in \Def_E^k(B) \times_{\Def_E^k(A)} \Def_E^k(C)$ and let $U$ and $V$ subspaces of sections of $E$ that lift to $E_B$ and to $E_C$ respectively, such that $U \cap V$ has maximal dimension and suppose $\dim U\cap V <k$. Then the existence of a lift of $(E_B, E_C)$ in $ \Def_E^k(B\times_A C)$ will contradict the maximality of $\dim U\cap V$.
\end{remark}
From now on, we restrict ourself to the field of complex numbers $\mathbb{C}$. Even if the description of the locus $\Def_E^k(A)$ for $A \in \Art_\mathbb{C}$ is still quite mysterious, we can determine the first order deformations and the vector space they generate.
\begin{theorem}\label{teorema tangente Def^r}
In the above notations, if $h^0(X, E)=k$, the tangent space to the deformation functor $\Def_E^k$ is
\[ t_{\Def^k_E} = \Def_E^k(\mathbb{C}[\epsilon]) = \{ a \in H^1(X,\End E) \ \mid \ a \cup s =0, \ \forall \ s \in H^0(X,E) \}. \]
If, instead $h^0(X, E) \geq k+1$,
the first order deformations of $E$ with at least $k$ sections are described by the cone
\[ \Def_{E}^k(\mathbb{C}[\epsilon]) = \{\nu \in H^1(X, \End E) \mid \exists U \in {Gr(k,H^0(E))} \mbox{ such that } \nu \cup s =0, \forall s \in U\} \]
and the vector space generated by it, that we call the tangent space to $\Def_E^k$, is
\[ t_{\Def_{E}^k} = H^1(X, \End E). \]
\end{theorem}
\begin{proof}
As already noticed, in the case $h^0(X, E)=k$, the functor $\Def^k_E$ is in one-to-one correspondence with the functor $\Def_{(E,H^0(E))}$ and the tangent space is described in Corollary \ref{Cor. TDef(E,H0(E))} to be
\[t_{\Def^k_E}\cong t_{\Def_{(E,H^0(E))}} = \{ a \in H^1(X,\End E) \ \mid \ a \cup s =0, \ \forall \ s \in H^0(X,E) \}. \]
If $h^0(X, E) \geq k+1$, by definition,
\[\Def_E^k(\mathbb{C}[\epsilon]) = \bigcup_{U \in Gr(k,H^0(E))} r_U(\Def_{(E,U)}(\mathbb{C}[\epsilon])).\]
For each $U \in Gr(k,H^0(E))$, we calculate the image of the tangent space to deformations of the pair $(E,U)$ using the exact sequence
\eqref{seconda successione lunga comologia DU}:
\[ \ldots \to H^1(X,D_U) \stackrel{r_U}{\to} H^1(X,\End E) \stackrel{\alpha_U}{\to} \Hom (U, H^{1}(X,E)) \ldots \]
Thus
\[ r_U(\Def_{(E,U)}(\mathbb{C}[\epsilon]))= \ker \alpha_U = \{ \nu \in H^1(X, \End E) \mid \nu \cup s =0, \forall s \in U\} \]
and the first statement is proved.
For the second statement, we have to prove that the vector space generated by $\Def_E^k(\mathbb{C}[\epsilon])$ is the whole space $H^1(X,\End E)$.
One inclusion is obvious. For the other one, it is enough to prove that, for all $s \in H^0(X,E)$ non zero section and for all $w \in H^1(X, E)$, there exists an element $\nu \in \Def_E^k(\mathbb{C}[\epsilon]) $ such that $\nu (s)=w$.
Since $\dim H^0(X, E) \geq k+1$, it is always possible to find a subspace $U \in Gr(k,H^0(E))$, such that $s \notin U$ and to build the matrix of $\nu$.
\end{proof}
\begin{remark}
This theorem generalises the classical results for line bundles on curves \cite[Proposition 4.2]{ACGH} and line bundles on a smooth projective varieties \cite[Proposition 3.3]{pardini}.
Moreover, our result is coherent with the well known fact that the locally free sheaves $E$ such that $h^0(X, E) \geq k+1$ are contained in the singular locus of the moduli space of locally free sheaves with al least $k$ independent sections. That is classically obtained defining that moduli space as a determinantal variety (see \cite[Proposition 4.2]{ACGH}, \cite[Theorem 2.8]{bgmm03}, \cite[Corollary 2.8]{costa}, et. al.)
\end{remark}
In the setting of deformation functors, the next step after the description of the tangent space is the study of an obstruction space. As well known, in the deformation functors case both spaces have a meaning in term of the corresponding moduli space. Unfortunately, our functor $\Def_E^k$ is not a deformation functor (see Remark \ref{rmk.no def funct}). However, Definition \ref{def.smoothness} holds for $\Def_E^k$ and in the following we try to get some geometrical information linked to its smoothness.
\begin{proposition} \label{prop.alpha sur equivalenza di liscezze}
As above, let $E$ be a locally free sheaf of $\mathcal{O}_X$-modules on the projective variety $X$, such that $h^0(X,E) \geq k$.
If there exists an $U \in Gr(k,H^0(E))$ such that $\Hom(U, H^1(E))=0$ or, that is equivalent, such that the map $\alpha_U:H^1(X, \End E) \to \Hom(U, H^1(X,E)) $ that appears in \eqref{seconda successione lunga comologia DU} is surjective, then
\[ \Def_E \mbox{ is smooth } \Leftrightarrow \Def_{(E,U)} \mbox{ is smooth } \Leftrightarrow \Def^k_E \mbox{ is smooth. } \]
\end{proposition}
\begin{proof}
From Corollaries \ref{prop.rel obstr classica} and \ref{corollario alpha su implica r liscio}, the two equivalent hypothesis imply that the forgetful morphism $r_U$ is smooth. Then, the first equivalence is a direct consequence of Remark \ref{cor. alpha sur}. As regard the second equivalence, since the obstruction is complete, each $E_A \in \Def_{E}^k(A)$ comes from a pair $(E_A, i_A) \in \Def_{(E,U)}(A)$, for every $A\in \Art_\mathbb{K}$. The above argument implies obviously the equivalence between the smoothness of $\Def_{(E,U)}$ and $\Def_E^k$ .
\end{proof}
\begin{proposition} \label{prop.H2=0 liscezza}
In the above notation, if there exists an $U \in Gr(k,H^0(E))$ such that $H^2(D_U)=0$, then both the functors $\Def_{(E,U)}$ and $\Def_E^k$ are smooth.
\end{proposition}
\begin{proof}
Since $H^2(D_U)=0$, the functor $\Def_{(E,U)}$ is smooth and relative obstruction to $r_U$ is zero, thus $r_U$ is smooth too.
These two properties assure that $\Def_E^k$ is smooth too.
\end{proof}
\begin{remark}
In general, the hypothesis $H^2(D_U)=0$ implies strictly that $\alpha_U$ is surjective. Since for a curve they are both equivalent to the injectivity of the Petri map (see Lemma \ref{lemma.equiv h2 zero e petri iniettiva}), Proposition \ref{prop.H2=0 liscezza} assures that on a curve $C$, if there esxists $U \in Gr(k,H^0(E))$, such that the Petri map $\mu_0: U \otimes H^0(C, K_C \otimes E^*) \to H^0(C, K_C \otimes E^*\otimes E)$ is injective, then both the functors $\Def_{(E,U)}$ and $\Def_E^k$ are smooth. See \cite[Proposition 2.1]{casalaina texidor} for a similar result, here the authors assume the injectivity of the Petri map for every $U\in Gr(k,H^0(E))$.
\end{remark}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,512 |
Das Emery-Nelson-Syndrom ist eine sehr seltene angeborene Erkrankung mit den Hauptmerkmalen Minderwuchs, Deformation von Händen und Füssen sowie Gesichtsdysmorphie mit flachem Profil.
Synonyme sind: Hand- und Fußdeformitäten – flaches Gesichtsprofil;
Die Bezeichnung bezieht sich auf die Autoren der Erstbeschreibung aus dem Jahre 1970 durch die schottischen Humangenetiker Alan E. H. Emery und M. M. Nelson.
Das Syndrom ist nicht zu verwechseln mit dem auch Nelson-Syndrom genannten Nelson-Tumor.
Verbreitung
Die Häufigkeit wird mit unter 1 zu 1.000.000 angegeben, bislang wurde nur eine Familie beschrieben. Vererbungsmodus und Ursache sind bislang nicht bekannt.
Klinische Erscheinungen
Klinische Kriterien sind:
Manifestation im Neugeborenen- bis Kleinkindesalter
Minderwuchs
Deformation der Hände und Füße mit Beugekontraktur der ersten 3 Metacarpophalangealgelenke, Streckkontraktur des Daumens, "Klauenzehen"
Gesichtsauffälligkeiten mit flachem Gesichtsprofil, hoher Stirn, abgeflachter Nasenbrücke, langem Philtrum, hohem Gaumenbogen
Hinzu können Muskelhypotonie beim Säugling, geistige Behinderung, dünne Haut über Hand und Fuss, Auffälligkeiten der Nägel und Haare kommen.
Einzelnachweise
Weblinks
Fehlbildung
Seltene Krankheit
Erbkrankheit
Krankheitsbild in der Kinderheilkunde
Krankheitsbild in Orthopädie und Unfallchirurgie | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,642 |
Q: Best way to display images in Xamarin Forms I am developing an Android app which retrive PC's informations from a database, upload the relative images of the PC to the server and also get back the PC's URL of the images for displaying. Everything works like a charm, for all of the 3 part I use a WCF service, deployed on remote IIS server.
The images are stored in a server's virtual directory, so you can copy the URL and paste it in the browser and the image appear without problems.
As I use a dynamic view of the images, I implemented the method below for creating them:
private void DisplayAttechedIMages(List<string> list_images_url)
{
for (int i = 0; i < list_images_url.Count; i++)
{
Image pic = new Image
{
HeightRequest = 250,
WidthRequest = 150,
Source = ImageSource.FromUri(new Uri(list_images_url[i])),
};
}
}
This is only the part where I create them, now I need to add them to a container, I tried to use <Grid> inside a <ScrollView>, but the result isn't good, because the visualization results with low performance (lagging, low response and bad resize).
Also I tried <ViewCell> inside <TableView> but the results are pretty the same.
This results could depend by the device?
So what is the best way to display image using the URLs?
A:
but the result isn't good, because the visualization results with low performance (lagging, low response and bad resize).
About lagging and low response , this need cache for Image .And bad resize , there is a property inside Image :
The Aspect property determines how the image will be scaled to fit the display area:
*
*Fill - Stretches the image to completely and exactly fill the display area. This may result in the image being distorted.
*AspectFill - Clips the image so that it fills the display area while preserving the aspect (ie. no distortion).
*AspectFit - Letterboxes the image (if required) so that the entire image fits into the display area, with blank space added to the top/bottom or sides depending on whether the image is wide or tall.
You can choose one to fit your best wants .Here is the forms doc about displaying images.
Here , I will recommand you FFImageLoading Nuget Packaget to have a try , it optimizeds the url image with cache used .
var cachedImage = new CachedImage() {
HorizontalOptions = LayoutOptions.Center,
VerticalOptions = LayoutOptions.Center,
WidthRequest = 300,
HeightRequest = 300,
CacheDuration = TimeSpan.FromDays(30),
DownsampleToViewSize = true,
RetryCount = 0,
RetryDelay = 250,
BitmapOptimizations = false,
LoadingPlaceholder = "loading.png",
ErrorPlaceholder = "error.png",
Source = "http://loremflickr.com/600/600/nature?filename=simple.jpg"
};
You can refer to its official sample to have a try .
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 0 |
\section{Introduction}\label{sec:introduction}
\vspace*{-2mm}
Hybrid systems are concerned about the discrete control mode transitions,
the continuous physical behavior, and the interaction between these two parts.
As mentioned in \cite{dorf2011modern},
the design of a system is the process that building a concrete to carry out some goals.
Meanwhile, people in the hybrid systems domain have the ambition to control their environment, i.e.,
the physical world.
For hybrid systems, numerous modeling approaches had been proposed, the hybrid automata \cite{ACHH93,alur1996automatic},
Hybrid CSP \cite{jifeng1994hybrid,ChaoChen96}, HyPA (hybrid process algebra) \cite{cuijpers2005hybrid}, and hybrid program \cite{PlatzerBook}, etc.
Regarding the formal verification on hybrid systems, various tools can be used, for instance,
HyTech \cite{henzinger1997hytech}, d/dt \cite{asarin2002d}, PHAVer \cite{Frehse08}, SpaceEx \cite{FrehseGDCRLRGDM11}, and KeYmaera \cite{platzer2008keymaera}.
These works are respectable and formal, the common feature is that most of them are focus on the high level abstraction of hybrid systems.
However, industrial applications of formal methods need a great level of abstraction
in existing development processes and an easier manner to adopt for users.
In other words, usability and complexity hiding are the major concerns for
designers and developers in industry.
Modelica \cite{fritzson1998modelica} is a multi-domain object-oriented modeling language,
it involves systems relating electrical, mechanical, control, and thermal components, etc.
And, one of the characteristics of Modelica is that, the class in Modelica can not be executed explicitly, but simulated by a simulation engine.
From the 1.0 release in 1997 when it began to model continuous dynamic systems to the 3.3
release in May, 2012 the addition of periodic and non-periodic synchronous controllers,
the revision of Modelica has never been ceased.
The description capability of Modelica is powerful, and the applications of Modelica is pervasive.
Nevertheless, it is not designed for formal verification, although it is quite suitable for simulation.
The reason is that the semantics of Modelica is prone to be deterministic,
however in the area of hybrid systems, it is prone to consider the non-deterministic evolution of the system behavior.
\vspace*{-1mm}
The motivation to propose the language Apricot is that,
we want to construct an object-oriented language for modeling hybrid systems.
The language should satisfy the following requirements.
First, clear and simple syntax.
We know that binary code is accurate and precise,
so why people in the highly developed modern society do not use
binary code as the communication language in life.
Because binary code is closed to hardware, it is far from daily life and hard to be acquainted.
The same is in the area of hybrid systems.
A language that is close to the designers and developers in industry is needed and worthy to be developed.
Second, distinct structure. As an object-oriented language, we can employ design patterns \cite{designpatterns1993} in the system design process. For instance, to demonstrate the hierarchical structure of complex hybrid systems, we utilize the composition pattern to build the ownership relation between
global system and subsystems. Composition pattern in Apricot constructs the tree structure with respect to objects of {\em System}, {\em Plant}, {\em Dynamic} and the subsystems of {\em Plant} object. We treat objects of {\em Dynamic} and {\em System} as a similar way under the compositional relationship, it results in the ownership between plant
and subsystem, and then the relationship between system and subsystem.
The third is an explicit semantics. We propose the operational semantics for Apricot. As the highly structural style of Apricot models, the semantics is clear and compositional.
The contributions of our work can be elaborated as follows.
The first is about the innovation on the Interface conception.
Interface is an abstraction of the type,
a suitable Interface for hybrid systems should consider the relations for system components and in favor of the
hierarchical structure construction for complex systems.
The common constraints and conventions are better to be defined in the abstract level than in the implementation part. Because, the higher the common knowledge is the easier the developer to know well.
Traditionally, in object-oriented languages, the Interface
only contains methods and no instance variable declaration or just the constant (in Java, or property in C\#, etc.) is allowed. In Apricot, we allow variable requirements, constraint indications and built-in block statements in the Interface.
The variable requirements define the relationships between the current type and other types. Therefore, it has the ability to describe the ownership among different components.
The constraint indications denotes the behavior that is forced to conform. For instance, the {\em clock} constraint
indication for the {\em Controller} Interface set the derivative of the variable of {\em Controller} to be the constant number one.
The built-in block statement denotes the right usage and position that the block should be.
In Apricot, for example, the {\em Condition} block is positioned in the {\em Composition} method of the Interface {\em Plant}.
As a consequence,
the innovation enhances and clarifies the relationship for various system components by variable requirements, specifies the limitation of some components by constraint indications, and explicitly
states the proper usages of blocks by the built-in block statement declaration in Interface.
Moreover, we apply the principle of {\em Architecture as Language}, and build the combination of the features from Domain Specific Language (abbreviated as DSL, \cite{DSL2013,fowler2010domain}) and Object-Oriented Language (abbreviated as OOL). The DSL notations (such as the variable requirements and constraint indications) used in Apricot are good for the building of component architecture, and as a result, it makes easier to communicate with domain experts during the system design process. On the other hand, the OOL is familiar to developers in industry,
and close to the implementations of the system. The combination of DSL and OOL in Apricot
fill the gap between the design at higher level and the implementation for the concrete.
This paper is organized as follows.
Section \ref{sec:syntax-of-apricot} describes the syntax of Apricot and an example (bouncing ball)
modeling under Apricot.
The operational semantics is demonstrated in Section \ref{sec:operational-semantics}.
In addition, Section \ref{sec:design-by-convention} discusses the features of design by convention in Apricot.
And, we make the conclusions in Section \ref{sec:conclusions}.
\begin{figure}
\begin{subfloat}
\begin{minipage}[b]{0.45\textwidth}
\begin{tikzpicture}[rounded corners, thick,shading=ball]
\draw[blue] (0,0) -- (5,0);
\draw[blue] (0,-.05) -- (5,-.05);
\foreach \x in {0,0.07,...,5}
{
\draw (\x,0) -- (\x+.05,-.05);
}
\draw[black, |<->|] (1.5,2.75) -- (1.5,0) node [midway, left, blue] {{\em h}};
\shade[ball color=red!50!green] (2,3) circle (2ex);
\shade[ball color=red!50!green] (3,.28) circle (2ex);
\draw[densely dotted] (3,.28) circle (2ex);
\draw[black,->] (2,2.5) -- (2,2) node [right,blue] { {\em g}};
\draw[black,->] (3,.28) -- (3,.8) node [right,blue] {{\em R}};
\draw[black,->] (3,.28) -- (3,-.3) node [left,blue] {{\em F}};
\filldraw [black] (3,.28) circle (.5pt);
\end{tikzpicture}
\caption{The ball. {\em h} denotes the height of the ball, {\em g} is for the acceleration of gravity. }
\label{fig:BALLView}
\end{minipage}
\end{subfloat}
~
\begin{subfloat}
\begin{minipage}[b]{0.5\textwidth}
\begin{Verbatim}[commandchars=\\\{\},fontsize=\fofo,numbers=left,numbersep=0pt,frame=lines]
\Dynamic Moving\{
\Real height,velocity,acceleration;
/*Constructor*/
Moving(\Real height,\Real velocity,\Real acceleration)\{
\this.height=height;
\this.velocity=velocity;
\this.acceleration=acceleration;
\}
\Continuous()\{
dot(height,1) == velocity;
dot(velocity,1) == -acceleration;
\}
\Invariant\{
height in [0,15];
velocity in [-60,60];
\};
\}
\end{Verbatim}
\end{minipage}
\caption{Class Moving implements interface Dynamic. }
\label{fig:Dynamic_Moving}
\end{subfloat}
\begin{subfloat}
\begin{minipage}[b]{0.45\textwidth}
\begin{Verbatim}[commandchars=\\\{\},fontsize=\fofo,numbers=left,numbersep=0pt,frame=lines]
\ParallelAssignment Jump\{
\Real height,velocity,coefficient;
/*Constructor*/
Jump(\Real height,\Real velocity,\Real coefficient)\{
\this.velocity = velocity;
\this.height = height;
\this.coefficient = coefficient;
\}
\Discrete()\{
velocity = -coefficient * velocity;
height = height;
\}
\}
\end{Verbatim}
\end{minipage}
\caption{Class Jump implements interface ParallelAssignment.}
\label{fig:ParallelAssignment_Jump}
\end{subfloat}
~
\begin{subfloat}
\begin{minipage}[b]{0.48\textwidth}
\begin{Verbatim}[commandchars=\\\{\},fontsize=\fofo,numbers=left,numbersep=0pt,frame=lines]
\Plant Ball\{
\Real height,velocity,k,g;
Ball(\Real height, \Real velocity, \Real k, \Real g)\{
\this.height = height;
\this.velocity = velocity;
\this.k = k;
\this.g = g;
\}
\Dynamic moving = \new Moving(height,velocity,g);
\Assignment jump = \new Jump(velocity,height,k);
\Composition()\{
CompMJ(moving,jump,moving)\{
\Condition\{ moving.height==0; \};
\};
\}
\}
\end{Verbatim}
\end{minipage}
\caption{Class Ball implements interface Plant.}
\label{fig:BouncingBallSystem_Plant}
\end{subfloat}
\begin{subfloat}
\begin{minipage}[b]{0.44\textwidth}
\begin{Verbatim}[commandchars=\\\{\},fontsize=\fofo,numbers=left,numbersep=0pt,frame=lines]
\Controller God\{
\Real mass,height,velocity,k,t,g;
God(\Real mass, \Real height, \Real velocity,
\Real k, \Real t, \Real g)\{
\this.mass = mass;
\this.height = height;
\this.velocity = velocity;
\this.k = k;
\this.t = t;
\this.g = g;
\}
\Dynamic idle = \new \Dynamic()\{
\Continuous()\{ dot(t,1)==1; \}
\};
\Assignment reset = \Skip;
\Composition()\{
CompIR(idle,reset,idle)\{
\Condition\{
height == 0;
Resiliency(mass,velocity,k)>mass*g;\};
\};
\}
\}
\end{Verbatim}
\end{minipage}
\caption{The controller of bouncing ball system, class God implements interface Controller. }
\label{fig:BouncingBallSystem_Controller}
\end{subfloat}
~
\begin{subfloat}
\begin{minipage}[b]{0.48\textwidth}
\begin{Verbatim}[commandchars=\\\{\},fontsize=\fofo,numbers=left,numbersep=0pt,frame=lines]
\System BouncingBall\{
\Real height,velocity,t;
\Real h[] = \{15, 10, 12\};
\Real v[] = \{0, 1, 1.5\};
\Constant \real g=9.8,k=0.6,mass=5;
\Controller god=\new God(mass,height,velocity,k,t,g);
\Plant ball = \new Ball(height,velocity,k,g);
BouncingBall()\{
god.CompIR || ball.CompMJ;
god || ball; //maybe not necessary
\}
\Init()\{
height=h[1],velocity=v[1],t=0;
god.idle.start();
ball.moving.start();
\}
\}
\end{Verbatim}
\end{minipage}
\caption{Class BouncingBall implements interface System. }
\label{fig:BouncingBallSystem}
\end{subfloat}
\caption{Bouncing ball model.}
\label{fig:ModelofBBall}
\end{figure}
\section{Syntax of Apricot}\label{sec:syntax-of-apricot}
\vspace*{-2mm}
In this section we will describe the basic syntax of Apricot.
As a modeling language for hybrid systems, one has to consider the hierarchical
structures of the system to demonstrate the modularity features,
and also has to propose the definitions of system dynamics with
the relations between continuous flow and discrete assignments.
The following recursive definitions have cover the overview of the above ambition.
{\small
\setlength{\jot}{2.5pt}
\begin{align*}
System ::=& ParaPlants \parallel ParaContrs ;
\\
ParaPlants ::=& \parallel_{i=1}^n Plant_i ;
\\
ParaContrs ::=& \parallel_{i=1}^m Controller_i;
\\
Plant ::=& AtomicComp \mid Comp( Dynamic ^+, Assignment ^+, System );
\\
Controller ::=& AtomicComp ;
\\
AtomicComp ::=& Comp( Dynamic ^+, Assignment ^+) ;
\\
Assignment ::=& SequentialAssignment \mid ParallelAssignment .
\end{align*}
}
where $n, m \in \mathbb{Z^+}$(positive integers), symbol `$\parallel$' denotes parallel composition.
`$ { Dynamic} ^+$' represents a set of {\em Dynamic} objects, and `$ {Assignment} ^+$'
has the similar meanings ({\em Assignment} objects).
The system defined here has the point that each system contains one or more plants and controllers. This is different from other approaches or languages such as hybrid automata which do not have this restrict.
\begin{center}
\fbox{\parbox[t]{0.9\textwidth}{
\vspace*{-3mm}
\begin{multicols}{2}
\begin{asparaenum}[(C.1)]
\setlength{\itemsep}{2pt}
\setlength{\itemindent}{2mm}
\setlength{\labelsep}{1mm}
\item \label{syn:continuous}
\hfill$\fofosmall\begin{aligned}[t]
&Continuous()\{\\
& \hspace{0.5cm} dot(Var_1,Nat_1) == MathExp_1;\\
& \hspace{0.5cm} dot(Var_2,Nat_2) == MathExp_2;\\
& \hspace{2.5cm} \cdots\\
& \hspace{0.5cm} dot(Var_n,Nat_n) == MathExp_n;\\
&\}
\end{aligned}$\hfill\null
\item \label{syn:invariant}
\hfill$\fofosmall\begin{aligned}[t]
&Invariant\{\\
& \hspace{0.5cm} Variable_1 ~in~ \lfloor Real_1, Real_1' \rceil;\\
& \hspace{0.5cm} Variable_2 ~in~ \lfloor Real_2, Real_2' \rceil;\\
& \hspace{2cm} \cdots\\
& \hspace{0.5cm} Variable_n ~in~ \lfloor Real_n, Real_n' \rceil;\\
&\};
\end{aligned}$\hfill\null
\item \label{syn:discrete}
\hfill$\fofosmall\begin{aligned}[t]
&Discrete()\{\\
& \hspace{0.5cm} Variable_1 = MathExp_1;\\
& \hspace{0.5cm} Variable_2 = MathExp_2;\\
& \hspace{1.8cm} \cdots\\
& \hspace{0.5cm} Variable_n = MathExp_n;\\
&\}
\end{aligned}$\hfill\null\\
\item \label{syn:condition}
\hfill$\fofosmall\begin{aligned}[t]
&Condition\{\\
&\hspace{0.5cm} MathExp_1 ~Rel~ MathExp_1';\\
&\hspace{0.5cm} MathExp_2 ~Rel~ MathExp_2';\\
&\hspace{2.5cm} \cdots\\
&\hspace{0.5cm} MathExp_n ~Rel~ MathExp_n';\\
&\};
\end{aligned}$\hfill\null
\end{asparaenum}
\end{multicols}
}}
\end{center}
{\em Dynamic} object is an instance of the class that implements the {\em Dynamic} interface. {\em Dynamic} object is refers to flows which are used to model continuous behavior of physical plants. The implementation class of {\em Dynamic} interface defines the continuous valuations of the variables in the system over time. And, it also specifies the invariant of the continuous flow.
The {\em Continuous} method in the {\em Dynamic} implementation class has the form as depicted in (C.\ref{syn:continuous}),
in which, for $1 \leq i \leq n, Var_i$ is the variable of the system, natural number $Nat_i$ represents the derivative order of $Var_i$ that is not equal to 0, $MathExp_i$ is the mathematical expression with the definition:
Let $Vars$ be the set of all variables of system, $\dot{V}ars$ denotes the set of derivative order variables, e.g., if $v \in Vars$, then the first order derivative $\dot{v} \in \dot{V}ars$ ($\dot{v}$ is represented by expression $dot(v,1)$ in Apricot).
{\fofosmall
\begin{align*}
MathExp ::= Function(Vars,\dot{V}ars) ;
\end{align*}
}
where, $Function$ defines the mathematical function defined by the designer or the built-in function in Apricot.
Such as addition, subtraction, multiplication, division, etc. For example, the multiplication in Fig.~\ref{fig:ParallelAssignment_Jump} is an infix form function.
The {\em Invariant} statement specifies the properties of the system during the continuous evolution, as illustrated in (C.\ref{syn:invariant}).
In which, $Real$ denotes the real number, $\lfloor \in \{~ '(', '[' ~\}$, and $\rceil \in \{~')', ']'~\}$. Symbols $'(', ~ ')'$ are used to define open intervals, and $'[',~']'$ for closed intervals. For example, in Fig.~\ref{fig:Dynamic_Moving}, `{\tt \small height in [0, 15]}' clarifies the variable {\tt \small height} evaluates the value within the closed interval [0, 15] during the continuous evolution. Note that, the left-open parenthesis is limited to the special real number {\tt \small -Inf}, and the right-open parenthesis is limited to {\tt \small Inf}, thus intervals like
$(1,2)$,
$({\tt \small -Inf}, {\tt \small Inf}]$,
$[{\tt \small -Inf}, {\tt \small Inf})$ and $[{\tt \small -Inf}, {\tt \small Inf}]$ is invalid.
{\em Assignment} interface has two sub-interfaces, {\em SequentialAssignment} and {\em ParallelAssignment}. Both implementations have a discrete method with the form in (C.\ref{syn:discrete}).
If this discrete method is defied in class implementing the interface {\em SequentialAssignment}, then it is the sequential composition of these $n$ assignment statements. Otherwise, if it is defined in class implementing the interface {\em ParallelAssignment}, then the parallel composition is the semantics that the assignment statements are supposed to represent. Fig.~\ref{fig:ParallelAssignment_Jump} is an example of {\em ParallelAssignment} implementation.
The {\em Composition} statement connects the {\em Dynamic} object and {\em Assignment}
object by a {\em Condition} statement. The {\em Condition} statement has the form in (C.\ref{syn:condition}).
In which, $Rel ~\in \{==,<,>,<=,>=,\text{!=}\}$ is the relation operator, and the expression ``$MathExp_i~Rel~ MathExp_i';$" defines the relation between the evaluations of $MathExp_i$ and $MathExp_i'$. For example, in Fig.~\ref{fig:BouncingBallSystem_Plant}, the {\em Composition} method refers to
{\em Dynamic} object {\tt \small moving} and {\em Assignment} object {\tt \small jump}
with {\tt \small moving.height==0}. Therefore, if the value of the variable
{\tt \small height} in {\tt \small moving} is equal to $0$ (i.e., the ball hits the ground), then the {\em Assignment} {\tt \small jump} will
be executed and the control will move on to {\tt \small moving} after this execution
provided that the invariant is satisfied.
\begin{example}
\label{ex:example_bouncing_ball}
Bouncing ball is a traditional model in hybrid system. The system has a controller named {\tt \small god} and a plant named {\tt \small ball}. The controller has {\em Dynamic} {\tt \small idle}, {\em Assignment} {\tt \small reset} and the {\em Composition} relation {\tt \small CompIR} paralleled with plant's {\tt \small CompMJ}. The plant has {\em Dynamic} {\tt \small moving}, {\em Assignment} {\tt \small jump} and the
{\em Composition} {\tt \small CompMJ} paralleled with controller's {\tt \small CompIR}. The two source-free arrows in the plant
{\tt \small ball} and controller {\tt \small god} represent the initial dynamics. Therefore, {\tt \small moving} and {\tt \small idle} are the initial dynamics of {\tt \small ball} and {\tt \small god}, respectively.
Fig.~\ref{fig:BALLView}--\ref{fig:BouncingBallSystem} are the model code for the bouncing ball system.
Fig.~\ref{fig:BALLView} depicts the ball, when the ball hits the flat horizontal ground, it suffers the gravity {\em F} and the elastic force {\em R}.
The class {\tt \small Moving} (in Fig.\ref{fig:Dynamic_Moving}) is an implementation of the {\tt \small Dynamic} interface.
It declares that the first order derivative of {\tt \small height} over time equals {\tt \small velocity},
and the first order derivative of {\tt \small velocity} over time is equal to {\tt \small -acceleration}.
In Fig.~\ref{fig:BouncingBallSystem_Plant}, an object named {\tt \small moving} is created with the type of class {\tt \small Moving}, and relates the variables {\tt \small height}, {\tt \small velocity}, {\tt \small g} of class {\tt \small Ball} to {\tt \small height}, {\tt \small velocity}, {\tt \small acceleration} in class {\tt \small Moving}, respectively.
\end{example}
\subsection{Class, Object and Relation}\label{sec:class,-object-and-relation}
Class declaration defined reference types. The body of class declaration defines
the implementation details.
All classes are non-nested in Apricot. This means that the class declaration defined
within the body of another class or interface is invalid.
The body of a class consists of fields, methods, instance, relations, and constructors.
Field declarations describe instance variables, each instance of the class holds a new
substantiation of the instance variable.
\noindent
{\bf Class Declaration.} We have three kinds of class declaration:
\begin{asparaenum}[--]
\setlength{\itemsep}{5pt}
\setlength{\itemindent}{2mm}
\item Top-level Class. If the class do not have super class, and do not implements any other interface:
{\fofosmall
\begin{align*}
& Class ~ Identifier\{ \\
& \hspace{1cm} ClassBody\\
&\}
\end{align*}
}
\vspace*{-4mm}
in which, we do not specify the access modifiers (e.g. {\em Public, Protected, Private} in Java).
The keyword {\tt \small this} in the constructor denotes the current instance being constructed. If keyword {\tt \small this} occurs in an instance method then it represents the object for which the method was defined. Most of the time, the keyword {\tt \small this} is employed to distinguish the instance variable from parameter variables when the names of variables in different classes clashed.
\vspace*{2mm}
\item { Interface Implementation}.
If one class implements an interface, the class declaration is:
{\fofosmall
\begin{align*}
& InterfaceType ~ Identifier\{ \\
& \hspace{1cm} ClassBody\\
&\}
\end{align*}
}
\vspace*{-4mm}
It is difference from many other object-oriented languages (e.g., Java, C++), we do not use the keyword {\em implements} to specify the interface type the class implements here.
In example \ref{ex:example_bouncing_ball}, the classes (see Fig.\ref{fig:Dynamic_Moving}--\ref{fig:BouncingBallSystem}) are all interface implementations.
\vspace*{2mm}
\item {Inheritance}.
If one class extends other class (i.e. SuperClass), the class declaration:
{\fofosmall
\begin{align*}
& ClassType ~ Identifier\{ \\
& \hspace{1cm} ClassBody\\
&\}
\end{align*}
}
\end{asparaenum}
\noindent
{\bf Constructor Declaration.}The constructor takes the responsibility for the creation of an instance of a class. Moreover, it weaves the connection between different components in Apricot models. The constructor declaration as follows for the case that formal parameters are presented:
{\fofosmall
\begin{align*}
& Identifier(Formal~Parameters)\{ \\
& \hspace{1cm} ConstructorBody\\
&\}
\end{align*}
}
For example, in Fig.~\ref{fig:BouncingBallSystem_Plant}, the {\tt \small Ball(...)} constructor is:
\vspace*{-2mm}
\begin{Verbatim}[commandchars=\\\{\},fontsize=\fofosmall,frame=single]
Ball(\Real height, \Real velocity, \Real k, \Real g)\{
\this.height = height;
\this.velocity = velocity;
\this.k = k;
\this.g = g;
\}
\end{Verbatim}
The formal parameters are a list of parameter specifiers and separated by the comma symbol `{\tt \small ,}'. Each parameter specifier is a pair of a type and an identifier. The identifier is the name of the parameter. In Fig.\ref{fig:BouncingBallSystem} line 7, it creates a {\tt \small Ball} object using the `{\tt \small Ball(...)}' constructor. Meanwhile, it creates the connection of variables ({\tt \small height, velocity, k, g}) in {\em system} {\tt \small BouncingBall} with the variables ({\tt \small height, velocity, k, g}) in {\em plant} {\tt \small Ball}. The statements in the constructor of {\tt \small Ball}, e.g. ``{\tt \small this.height = height}'' makes the instance variable {\tt \small height} of {\tt \small Ball} and the instance variable {\tt \small height} of {\tt \small BouncingBall} refer to the same entity. All the modification on variable {\tt \small height} take place in {\tt \small Ball} or {\tt \small BouncingBall} will be recognized immediately by each other.
Formal parameters can be absent, for the case of line 8 in Fig.\ref{fig:BouncingBallSystem}.
The line 9 of the constructor denotes that the composition relation {\tt \small CompIR} of controller {\tt \small god} is parallel with the composition reltion {\tt \small CompMJ} of plant {\tt \small CompMJ}.
The line 10 denotes that the controller {\tt \small god} is parallel with the plant {\tt \small ball}.
The initializer is declared by the method ``{\tt \small Init}()\{...\}" at line $12 \sim 16$.
\noindent
{\bf Initializer Declaration.}
The initializer method specifies the initial values of the instance variables in a system.
For example, the line 13 in Fig.\ref{fig:BouncingBallSystem} sets the initial value of {\tt \small height} to the number 15, {\tt \small velocity} the number 0 and the initial value of
{\tt \small t} the number 0.
In addition, it starts the initial dynamics of the components in the system. For instance,
the initial dynamic of {\em controller} {\tt \small god} is {\tt \small idle} and the initial dynamic of
{\em plant} {\tt \small ball} is {\tt \small moving} specified by line 14 and line 15 in Fig.\ref{fig:BouncingBallSystem}, respectively.
\noindent
{\bf Anonymous Class Declaration.}
Anonymous class is an implementation of an interface or an inheritance of a super class.
In Fig.~\ref{fig:BouncingBallSystem_Controller}, the variable {\tt \small idle} declared at line 12 refers to
an instance of an anonymous class which implements the interface {\tt \small Dynamic}.
The method {\tt \small Continuous} defined in the anonymous class denotes the first order time-derivative of variable {\tt \small t} is equal to $1$. Therefore, variable {\tt \small t} takes the role
of a clock.
Moreover, no invariant is defied in the anonymous class, which means that it has an implicit invariant {\tt \small Ture}, variable {\tt \small t} can take any value in real numbers $\mathcal{R}$.
Anyway, as time is not negative, we can specify an invariant that {\tt \small t} is always equal to or greater than the number 0:
\begin{Verbatim}[commandchars=\\\{\},fontsize=\small]
\Invariant\{ t in [0,Inf); \};
\end{Verbatim}
\vspace*{-2mm}
where, `{\tt \small Inf}' denotes the infinity $+\infty$.
\subsection{Interface, Inheritance and Relationship}\label{sec:interface,-inheritance-and-relation}
In Apricot, there are five built-in interfaces, each defines one key element of the Apricot model.
The built-in interface may consist of four parts: method signatures, variable requirements, constraint indications and built-in block statements. From now on, these four parts are abbreviated to MVCB in this paper.
Method signature defines the name and arguments of the method.
Variable requirement holds the relations between the current interface and other interfaces, it also restrict the count of objects of the proper types.
Constraint indication demonstrates the limitation for the behavior of the object which implements the interface.
And, the built-in block statement positioned in the interface emphasizes the structure of the language, and indicates
the right place for the application of the special statement.
\begin{asparaenum}[{\bf --}]
\setlength{\itemsep}{5pt}
\setlength{\itemindent}{2mm}
\item {\bf System Interface} depicted in (I.\ref{itf:system}),
where, `{\em Requires}' is a keyword in Apricot, `$1..*$' denotes at least one entity. Therefore, each {\em System} object contains one or more than one {\em Plant} object, and it also for the objects of type {\em Controller}.
The method signature `$Init()$' indicates that the {\em System} has an initializer that do not contain any argument and no return value for this initializer.
`{\em plants}' and `{\em controllers}' are the names of the variables referring to the proper types behind the colon symbol (`:').
\item {\bf Plant Interface} depicted in (I.\ref{itf:plant}),
where, it indicates that the implementation of this interface holds several objects of the type {\em Dynamic} and {\em Assignment}, and may have a subsystem or not.
The {\em Composition} method is used for defining the composition relationships between {\em Dynamic} (or {\em System}) objects and {\em Assignment} objects.
Each composition relationship with respect to three arguments: the source, action, and the destination.
And, the form `$(dysy[.], ass[.], dysy[.])$' in the composition relationship shows that $dysy[.]$ is the source ({\em Dynamic or System}), ass[.] is the action, and $dysy[.]$ (also can be {\em Dynamic or System}) is the destination, `.' represents the proper index.
The composition relationship denotes the control switch that from the source to the destination under the conditions
defied in the {\em Condition} block statement.
During the control switch the action which is restricted to the {\em Assignment} object (i.e., `$ass[.]$') is executed.
\item {\bf Controller Interface} depicted in (I.\ref{itf:controller}),
where, it is the same as {\em Plant} except the {\em Constraint Indication} and the absent of subsystem.
The {\em clock Constraint Indication} `$Constraint ~~clock$' denotes that the differential equations in the
{\em Dynamic} object of {\em Controller} have the restriction: the derivative assigned to the variable is restrict to
number 1.
\item {\bf Dynamic Interface} depicted in (I.\ref{itf:dynamic}),
where, it indicates that each {\em Dynamic} implementation has a method and an built-in {\em Invariant} block statement.
The method `$Continuous()$' with respect to the continuous evolution of the system states. The form of the method
has been declared before in Sect \ref{sec:syntax-of-apricot}. The {\em Invariant} is applied to define the range of proper
variable concerned for the current {\em Dynamic} object.
\item {\bf Assignment Interface} depicted in (I.\ref{itf:assignment}),
the {\em Assignment} interface only has the method `$Discrete()$'. The {\em Discrete} method
plays the role of the actions that would be executed during the control switch of dynamics.
Moreover, there are two interfaces inherit the {\em Assignment} interface, {\em SequentialAssignment}
and {\em ParallelAssignment}. {\em SequentialAssignment} has the semantics of sequential composition for its assignment statements, and {\em ParallelAssignment} has a parallel composition semantics.
\end{asparaenum}
\vspace*{-3mm}
\begin{center}
\fbox{\parbox[t]{.98\textwidth}{
\vspace*{-3mm}
\begin{multicols}{2}
\begin{asparaenum}[({I}.1)]
\setlength{\itemsep}{3pt}
\setlength{\itemindent}{-1mm}
\setlength{\labelsep}{0mm}
\item \label{itf:system}
\hfill$\fofosmall\begin{aligned}[t]
& Interface ~~ System\{ \\
& \hspace{0cm} Requires ~~ plants[1..*]: Plant;\\
& \hspace{0cm} Requires ~~ controllers[1..*]: Controller;\\
& \hspace{0cm} Init();\\
& \}
\end{aligned}$\hfill\null
\item \label{itf:plant}
\hfill$\fofosmall\begin{aligned}[t]
& Interface ~~ Plant\{ \\
& \hspace{0cm} Requires ~~ dy[1..*]: Dynamic;\\
& \hspace{0cm} Requires ~~ ass[1..*]: Assignment;\\
& \hspace{0cm} Requires ~~sy[0..1]: System;\\
& \hspace{0cm} Composition()\{ \\
& \hspace{0.1cm} Requires ~ coms[1..*] : (dysy[.],ass[.],dysy[.])\\
& \hspace{1cm} \{ ~ Condition\{\} ; ~\};\\
& \hspace{.1cm} \};\\
&\}
\end{aligned}$\hfill\null
\item \label{itf:controller}
\hfill$\fofosmall\begin{aligned}[t]
& Interface ~~ Controller\{ \\
& \hspace{0cm} Constraint ~~ clock;\\
& \hspace{0cm} Requires ~~ dy[1..*]: Dynamic;\\
& \hspace{0cm} Requires ~~ ass[1..*]: Assignment;\\
& \hspace{0cm} Composition()\{ \\
& \hspace{0.1cm} Requires ~ coms[1..*] : (dy[.],ass[.],dy[.])\\
& \hspace{1cm} \{~ Condition\{\};\};\\
& \hspace{0.1cm} \};\}
\end{aligned}$\hfill\null
\item \label{itf:dynamic}
$\fofosmall\begin{aligned}[t]
& Interface ~ Dynamic\{ \\
& \hspace{0cm} Continuous();\\
& \hspace{0cm} Invariant\{\};\\
& \}
\end{aligned}$\hfill\null
\item \label{itf:assignment}
$\fofosmall\begin{aligned}[t]
& Interface ~ Assignment\{ \\
& \hspace{0cm} Discrete();\\
& \}
\end{aligned}$\hfill\null
\end{asparaenum}
\end{multicols}
}}
\end{center}
In addition, as the existence of MVCB in the interface declaration, we claim that the inheritance of class or interface in Apricot should consider to inherit and follow the MVCB in the super-class or super-interface. And, the implementation of interface in Apricot should consider to implement and follow the MVCB in the implemented interface.
\section{Operational Semantics}\label{sec:operational-semantics}
\vspace*{-2mm}
Structural operational semantics (\cite{plotkin1981structural,Plotkin04a}, SOS) was proposed by G.D.Plotkin in 1981. Transition system is the base for structural operational semantics. It takes
the transition relation between configurations to characterize the operational feature of system behaviour. Usually, SOS is applied to the programs and operations on discrete data. In order to deal with continuous data, we need to abstract the continuous features, and then obtain a discrete view of the continuous data for hybrid system. For the semantics and verification of object-oriented languages, some related works can be found in \cite{america1986operational,apt2011verification,jifeng2006rcos}.
\begin{definition}
A Transition System ({\bf TS}) is a structure consists of a set of configurations ({\bf C}) and the relation ($\rightarrow$) between configurations, i.e., $\bf TS \overset{\text{def}}{=} \langle C, \rightarrow \rangle$, where $\bf \rightarrow \subseteq C \times C$.
\end{definition}
\vspace*{-8mm}
\subsection{Configurations}\label{sec:configurations}
\vspace*{-2mm}
Any insight into a hybrid system is obtained through the state of the system.
Each state is a valuation of the variables in the system. After the system start-up, it always accompanied with a state at each time point. All the states compose a state space of the system. Based on the state space, one can
check whether some specific state can be reached by the system for some proper initial states. It is called the reachability analysis. And, various respectable works had been done, e.g., the Hytech \cite{henzinger1997hytech} proposed by Henzinger etc., the Phaver \cite{Frehse08} and SpaceEx \cite{FrehseGDCRLRGDM11} by Frehse etc., the hybrid process algebra approach \cite{cuijpers2005hybrid} by P.J.L. Cuijpers, and Platzer's dynamic differential logic \cite{PlatzerBook}, etc.
Besides system states, to reveal the relation between statement and state,
we also need to pay attention to the statements (control flow) throughout the system execution.
These understanding can be used to check the statement-related properties.
For example, we can check that some particular dynamic method is not reached or executed by the system with the knowledge of both statement and state.
\begin{definition}
We define the set of configurations with statements, states, and types, formally as follows:
{\fofosmall
\begin{align*}
{\bf C}::=& \LRAngle{\mathcal{P}(\Theta), \mathcal{P}(\Sigma), \mathcal{P}({\bf T})},\\
\Theta ::=& \{\vartheta_1.\vartheta_2.\cdots.\vartheta_n \mid \vartheta_{i} \text{ is a statement of Apricot}\},\\
\Sigma ::=& {\bf Vars} \times {\bf Vals},\\
\bf T ::=& {\bf Vars} \times {\bf Types},
\end{align*}}
where $1\leq i \leq n$, $\Theta$ denotes the set of prefix annotated statements, $\mathcal{P}(\Theta)$ is the power set of $\Theta$, $\Sigma$ is consists of all functions that mapping from the set of variables {\bf Vars} to the set of values {\bf Vals}, {\bf T} is a set of functions which relate each variable in {\bf Vars} with a type in {\bf Types}.
\end{definition}
A prefix annotated statement is a linked list
that begins with a variable ($\vartheta_1$) which denotes the system and ended with the statement ($\vartheta_n$) currently executed or expression to be evaluated. Along the list there
will be objects or methods. An Apricot model comprises more than one component, and these components paralleled. As a result, the first element of a configuration is a subset of $\Theta$, consists of the parallel prefix annotated statements. (Fig. \ref{fig:prefixannotatedstatement} illustrates the example prefix annotated statements for bouncing ball system)
\vspace*{-5mm}
\begin{figure}
\centering
\begin{tikzpicture}[scale=0.7]
\tikzstyle{every node}=[scale=0.8]
\path
node at (0,3.5) (system) [scm] {System \nodepart[color=blue]{two} {\em \color{red} system}};
\path
node at (0,0.6) (init) [scm] {init() \nodepart[color=blue]{two} {\em {\bf system}.\color{red}init()}};
\path
node at (7.5,3.5) (assign) [scm] {height=h[1] \nodepart[color=blue]{two} {\em {\bf system.init()}.\color{red}height=h[1]}};
\path
node at (7.5,1) (start) [sc]
{
god.idle.start() \\
ball.moving.start()
\nodepart[color=blue]{two}
{\em {\bf system.init()}.{\color{red}god.idle.start()}\\
{\color{blue} {\bf system.init()}}.\color{red}ball.moving.start()}
};
\draw[rounded corners=2mm,|->,line width=1pt,red!50!black!50] (system) -- (init.north);
\draw[rounded corners=2mm,|->,line width=1pt,red!50!black!50] (init.east) -- +(1,0.4) |- (assign.west);
\draw[rounded corners=2mm,|->,line width=1pt,red!50!black!50] (assign.south) -- (start);
\end{tikzpicture}
\vspace*{-3mm}
\caption{The example of prefix annotated statements for bouncing ball system. The italic statement is the current statement the system executed. }
\label{fig:prefixannotatedstatement}
\end{figure}
\vspace*{-5mm}
Moreover, considering the nondeterminism feature of Apricot, a model of Apricot consists of numerous prefix annotated statements, thus all the possible runs of the model can be
illustrated by a tree structure, and each branch may has a different state space.
\subsection{Axioms and Rules}\label{sec:axioms}
\vspace*{-2mm}
Here, we will give the axioms for Apricot.
Consider single statement $\theta$, for $\{{\bf Pre}.\theta\} \in \mathcal{P}(\Theta)$, $\sigma \in \mathcal{P}(\Sigma)$, and $\tau \in \mathcal{P}(\bf T)$, then $\LRAngle{\{{\bf Pre}.\theta\}, \sigma, \tau} \in {\bf C}$. For simplicity, we take
$\bf Pre.\theta$ for $\{{\bf Pre}.\theta\}$ in the following axioms ({\bf Pre} is the prefix):
\begin{asparaenum}[{\bf --}]
\setlength{\itemsep}{5pt}
\setlength{\itemindent}{2mm}
\item {\bf Arithmetic expression $e$}.
Evaluation of constant numbers:
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.n,\sigma,\tau} \rightarrow n,
\end{align}
}
\text{where $n$ is a constant number.}
Evaluation of variable:
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.v,\sigma,\tau} \rightarrow n,
\end{align}
}
\text{where, $v$ is a variable of number type, and $\sigma(v)=n$.}
Evaluation of addition:
{\fofosmall
\begin{align}
\frac{\LRAngle{{\bf Pre}.e_1,\sigma,\tau} \rightarrow n_1 ~~ \LRAngle{{\bf Pre}.e_2,\sigma,\tau} \rightarrow n_2}{\LRAngle{{\bf Pre}.(e_1+e_2),\sigma,\tau} \rightarrow n}
,
\end{align}
}
where, $e_1$ and $e_2$ are variables or constant numbers, and $n$ is the summation of $n_1$ and $n_2$.
\item {\bf Mathematical function expression}.
Derivative over time $t$ with order $n$:
{\fofosmall
\begin{align}
\label{derivativeovertime}
\LRAngle{{\bf Pre}.dot(v,n),\sigma,\tau} \rightarrow \frac{d^n v}{dt^n},
\end{align}
}
where, $\frac{d^n v}{dt^n}$ is a formula that represents the $n$-th order derivative of $v$
over time. In fact, we can regard the $n$-th order derivative as an attribute or observation of the variable, and
employ a new variable to maintain the value of the derivative. We produce a new variable when it occurs at the
first time, and the name would be $v\_n$. Thus, (\ref{derivativeovertime}) is changed to
{\fofosmall
\begin{align}
\frac{\LRAngle{v\_n,*} \notin \sigma}{\LRAngle{{\bf Pre}.dot(v,n),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.v\_n,\sigma',\tau'}}
,
\end{align}
}
where, symbol `*' stands for any value, $\sigma'=\sigma[v\_n:=null]$, $\tau'=\tau[v\_n:=\tau(v)]$. And, if $v_n$ is already in $\sigma$, then
we have:
{\fofosmall
\begin{align}
\frac{\LRAngle{v\_n,*} \in \sigma}{\LRAngle{{\bf Pre}.dot(v,n),\sigma,\tau} \rightarrow v\_n}
,
\end{align}
}
Derivative over other variable $u$ with order $n$:
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.dot(v,u,n),\sigma,\tau} \rightarrow \frac{d^n v}{du^n},
\end{align}
}
and, if $v\_y\_n$ is new, then we have
{\fofosmall
\begin{align}
\frac{\LRAngle{v\_y\_n,*} \notin \sigma}{\LRAngle{{\bf Pre}.dot(v,y,n),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.v\_y\_n,\sigma',\tau'}}
,
\end{align}
}
otherwise,
{\fofosmall
\begin{align}
\frac{\LRAngle{v\_y\_n,*} \in \sigma}{\LRAngle{{\bf Pre}.dot(v,y,n),\sigma,\tau} \rightarrow v\_y\_n}
.
\end{align}
}
\item {\bf Assignment}.
For single assignment,
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.(v=e),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.skip,\sigma',\tau} ,
\end{align}
}
where, $v$ is a variable, $e$ is for arithmetic expression, and the updated state $\sigma'=\sigma[v:=\sigma(e)]$.
For sequential assignment and parallel assignment,
consider the assignment statements in the {\em Discrete} method $S$:
{\fofosmall
\begin{align*}
Discrete()\{
x = y;
y = x;
\}
\end{align*}
}
\begin{asparaenum}
\setlength{\itemindent}{5mm}
\item As Sequential Assignment: executing $S$ in a state with $x=0$ and $y=1$, $x$ and $y$ are both evaluate to the value $1$. For assignment statements $S_1, S_2$ in Sequential Assignment method,
{\fofosmall
\begin{align}
\frac{\LRAngle{{\bf Pre}.S_1,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.skip,\sigma',\tau}}{
\LRAngle{{\bf Pre}.(S_1;S_2),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.S_2,\sigma',\tau}} ,
\end{align}
}
\item As Parallel Assignment: executing $S$ in the same state, $x$ and $y$ exchange their value, $x$ is changed to $1$, $y$ is $0$. For assignment statements $S_1, S_2$ in Parallel Assignment method, $v_1$ is the variable modified by $S_1$ and $v_2$ of $S_2$,
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\LRAngle{{\bf Pre}.S_1,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.skip,\sigma',\tau},
\LRAngle{{\bf Pre}.S_2,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.skip,\sigma'',\tau} \\
\end{array}
}{\LRAngle{{\bf Pre}.(S_1||S_2),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.skip,\sigma''',\tau} , }
\end{align}
}
where, $\sigma'''=\sigma[v_1:=\sigma'(v_1), v_2:=\sigma''(v_2)]$, `$||$' denotes that the assignments ($S_1,S_2$) in {\em Discrete}
method of {\em ParallelAssignment} object are executed in parallel.
\end{asparaenum}
\item {\bf Method Invocation}.
\begin{asparaenum}
\setlength{\itemindent}{5mm}
\item Zero-Arity-Argument method $m()$:
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.m(),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}'.S,\sigma,\tau},
\end{align}
}
where, ${\bf Pre}'={\bf Pre}.m$ and $S$ is the body of method $m$.
\item Fixed-Arity-Argument method $m(arg[1..n])$:
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.m(exp[1..n]),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}'.S,\sigma',\tau'},
\end{align}
}
where, ${\bf Pre}'={\bf Pre}.m(exp[1..n])$ and $S$ is the body of method $m$,
for $1 \leq i \leq n$, $arg[i]$ is a new variable, and,
{\fofosmall
\begin{align*}
\sigma'=&\sigma[ arg[i]:=\sigma(exp[i]) ],
\end{align*}
}
if $\tau(exp[i])$ is a subtype of the defined type of $arg[i]$, then
{\fofosmall
\begin{align*}
\tau'=&\tau[ arg[i]:=\tau(exp[i]) ],
\end{align*}
}
otherwise, $\tau'(arg[i])$ takes the defined type of the formal parameter.
\end{asparaenum}
\item {\bf Instance variable}. Suppose $var$ is an instance variable of the object $obj$.
\begin{asparaenum}
\setlength{\itemindent}{5mm}
\item Declaration of instance variable without initialization. Consider the declaration $D$:
{\fofosmall
\begin{align*}
Type~~var;
\end{align*}
}
This defines a variable $var$ of type $Type$ and assigns the special value $null$ to $var$.
Thus, we have
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.obj.D,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.obj.Skip,\sigma',\tau'},
\end{align}
}
where, $\sigma'=\sigma[var:=null]$ and $\tau'=\tau[var:=Type]$.
\item Declaration of instance variable with initialization. Consider the declaration $D$:
{\fofosmall
\begin{align*}
Type~~var = val;
\end{align*}
}
This defines a variable $var$ of type $Type$ and assigns the value $val$ to $var$.
Thus, we have
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.obj.D,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.obj.Skip,\sigma',\tau'},
\end{align}
}
where, $\sigma'=\sigma[var:=val]$ and
if $\tau(val)$ is a subtype of $Type$, then $\tau'=\tau[var:=\tau(val))]$, otherwise,
$\tau'=\tau[var:=Type]$.
\end{asparaenum}
\item {\bf Local variable}. Suppose $var$ is a local variable in the method $m$ or block $b$.
The following are demonstrated under the scenario with method $m$.
\begin{asparaenum}
\setlength{\itemindent}{5mm}
\item Declaration of local variable without initialization. Consider the declaration $D$:
{\fofosmall
\begin{align*}
Type~~var;
\end{align*}
}
This defines a variable $var$ of type $Type$ and assigns the special value $null$ to $var$.
Thus, we have
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.m.D,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.m.Skip,\sigma',\tau'},
\end{align}
}
where, $\sigma'=\sigma[var:=null]$ and $\tau'=\tau[var:=Type]$.
\item Declaration of local variable with initialization. Consider the declaration $D$:
{\fofosmall
\begin{align*}
Type~~var = val;
\end{align*}
}
This defines a variable $var$ of type $Type$ and assigns the value $val$ to $var$.
Thus, we have
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.m.D,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.m.Skip,\sigma',\tau'},
\end{align}
}
where, $\sigma'=\sigma[var:=val]$ and
if $\tau(val)$ is a subtype of $Type$, then $\tau'=\tau[var:=\tau(val))]$, otherwise,
$\tau'=\tau[var:=Type]$.
\item End of method $m$.
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.m.End,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.Skip,\sigma',\tau'},
\end{align}
}
where, $\sigma'=\sigma[return:=\sigma(returnExp), rm~vars]$ and $\tau'=\tau[return:=\tau(returnExp), rm~vars]$. `$rm~vars$' represents
the removing of all the mappings related to local variables of the method $m$.
$End$ denotes the end of the method, usually a method is ended by
explicitly a {\em Return} statement or the right brace `\}' positioned at the end of the method body. $return$ is the special variable refers to the result of the method invocation,
$returnExp$ denotes the value of the variable. And, for block $b$, the special variable $return$ is ignored.
\end{asparaenum}
\item {\bf Object Creation}. The procedure of object creation is composed of instance variable initialization and constructor invocation.
\begin{asparaenum}
\setlength{\itemindent}{5mm}
\item Creation by Constructor. If the object creation statement $S$ is
{\fofosmall
\begin{align*}
Type~obj = new~M(exp[0..n]);
\end{align*}
}
where, $exp[0..n]$ represents the list (or array) of actual parameters. $M$
is the name of the instantiated class, also the name of the constructor,
$M(exp[0..n])$ is an invocation of the corresponding constructor in
the class. Suppose the set of instance variable declaration is $Ds$, and constructor $m(arg[0..n])$,
{\fofosmall
\begin{align} \label{objectcreation}
\LRAngle{{\bf Pre}.S,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}'.(Ds;M(exp[0..n])),\sigma',\tau'},
\end{align}
}
where, ${\bf Pre}'={\bf Pre}.obj$, $\sigma'=\sigma[obj:=o]$, $o$ is a new object of $Type$ with all the instance variables refer to the special value $null$, $\tau'=\tau[obj:=Type]$.
\item Creation by Anonymous Class. If the object creation statement $S$ is
{\fofosmall
\begin{align*}
Type~obj = new~Identifier()\{Class~Body\};
\end{align*}
}
Then,
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.S,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}'.(Ds;M()),\sigma',\tau'},
\end{align}
}
where, it is the same as (\ref{objectcreation}) except that it executes the zero-arity-argument constructor.
If there is no zero-arity-argument constructor declares in the class body, the empty one would take the job that doing nothing when it is invoked. The empty constructor is implicitly declared in one class for the case that the zero-arity-argument constructor is missing by the designer.
\end{asparaenum}
\item {\bf Dynamic}.
In Apricot, the {\em Dynamic} object consists of one {\em Continuous} method and an {\em Invariant} block.
The {\em Continuous} method declares the differential equations that the dynamic flow followed with respect to the properties defined within the {\em Invariant} block.
The properties in the {\em Invariant} block indicate the range of the variables during the continuous evolution.
For dynamic, if the dynamic flow reaches the border of the {\em Invariant} and all the conditions of the
compositions from the dynamic can not be satisfied,
then the control is waiting at the border provided that any advancement of
the flow according to the {\em Continuous} method will violate the {\em Invariant}.
\begin{asparaenum}
\setlength{\itemindent}{5mm}
\item Differential Equation.
For one statement $D$ that is declared in the $Continuous$ method, $D$ is a differential equation for the variable $v$.
For variable $v$ and nature number $n$, mathematic expression $me$, the differential equation $D$ is
{\fofosmall
\begin{align*}
dot(v,n) == me;
\end{align*}
}
Suppose that there exists a function $f: I \to \mathbb{R}$, and $I$ is a time-interval $[a, b]$, i.e., the domain of $f$,
and the value of $v$ at time-point $t \in [a,b]$ is $f(t)$.
Here, the start time-point of the continuous evolution following $D$ is at time $a$, the end point $b$ is for some proper time-point greater than or equals $a$.
Then, before the termination of the flow, at some time-point $t \in [a, b]$, we have
{\fofosmall
\begin{align}
\LRAngle{{\bf Pre}.D,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.D,\sigma',\tau},
\end{align}
}
where, $\sigma'=\sigma[v:=f(t)]$. We call $f$ the {\em Real-Function} for $D$, and $t$ the {\em Proper-Time}.
\item Termination of Flow. The dynamic flow reaches the border of the {\em Invariant} and no valid composition relationship exists,
then the control is waiting at the border if the forward flow would violate the {\em Invariant}.
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\forall c \in C,\LRAngle{{\bf Pre}.c,\sigma,\tau} \rightarrow False,\\
\LRAngle{{\bf Pre}.D,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.D,\sigma',\tau},
\exists i \in I, \LRAngle{{\bf Pre}.i,\sigma',\tau} \rightarrow False \\
\end{array}
}{\LRAngle{{\bf Pre}.D,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.(dot(tw,1)=1),\sigma,\tau} },
\end{align}
}
where, the set $C$ is the $Condition$ block related to the current $Dynamic$ object that contains the differential equation $D$. And, $I$ is the $Invariant$ block in the $Dynamic$ object, it is the set of conditions should be satisfied during the continuous evolution. For $\forall t \in (a,b]$, $\sigma'=\sigma[v:=f(t)]$, in which, $f: I \to \mathbb{R}$, $I = [a, b]$, $f(t)$ is the value of $v$ at the time-point $t \in I$.
At last, $tw$ is a specific variable for the waiting time after the flow terminated.
\end{asparaenum}
\item {\bf Invariant}.
An Invariant block $I$ is a built-in block in a {\em Dynamic} object.
Actually, $I$ consists of conditions. Each condition specifies the
range of one variable, and can be evaluated as a Boolean expression.
Suppose $i \in I$, and $i \equiv v ~in~ (e_1, e_2)$, we have
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\LRAngle{{\bf Pre}.(e_1,e_2),\sigma,\tau} \rightarrow (n_1,n_2),
\sigma(v) \in (n_1, n_2)\\
\end{array}
}
{\LRAngle{{\bf Pre}.(v ~in~ (e_1, e_2)),\sigma,\tau} \rightarrow True}
,
\end{align}
}
where, $v$ takes the value in the interval denoted by $(e_1, e_2)$.
And, the opposite situation,
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\LRAngle{{\bf Pre}.(e_1,e_2),\sigma,\tau} \rightarrow (n_1,n_2),
\sigma(v) \notin (n_1, n_2)\\
\end{array}
}
{\LRAngle{{\bf Pre}.(v~in~(e_1, e_2)),\sigma,\tau} \rightarrow False}
.
\end{align}
}
Now, we have the evaluation of an Invariant $I$ based on the up two laws,
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\forall i \in I, \LRAngle{{\bf Pre}.i,\sigma,\tau} \rightarrow True
\end{array}
}
{\LRAngle{{\bf Pre}.I,\sigma,\tau} \rightarrow True}
,
\end{align}
}
where, $I$ is true when all the conditions in it is true. And, if there exists an invalid condition, then
$I$ is false,
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\exists i \in I, \LRAngle{{\bf Pre}.i,\sigma,\tau} \rightarrow False
\end{array}
}
{\LRAngle{{\bf Pre}.I,\sigma,\tau} \rightarrow False}
.
\end{align}
}
\item {\bf Condition}. A {\em Condition} block $C$ consists of a number of Boolean expressions.
Each Boolean expression $c$ involves two mathematic expressions ($me_1, me_2$) and a relational operator $opt$.
Let $c \equiv me_1 ~opt~ me_2$, $opt \in \{==, <, >, <=, >=, !=\}$, and $C$ for the set of all Boolean expressions
in the {\em Condition} block,
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\forall c \in C, \LRAngle{{\bf Pre}.c,\sigma,\tau} \rightarrow True
\end{array}
}
{\LRAngle{{\bf Pre}.C,\sigma,\tau} \rightarrow True}
,
\end{align}
}
where, $C$ is true iff all Boolean expressions in $C$ is true.
\item {\bf Composition Relationship}.
It involves the control switch from one dynamic to another under proper conditions.
Let $D_1, D_2$ represent two {\em Dynamic} objects, they may be the same object, e.g., in
Example \ref{ex:example_bouncing_ball}.
And, let $C$ be one of the {\em Condition} blocks related to $D_1$ and $D_2$.
For {\em Composition Relationship} $CR$, and the corresponding {\em Assignment} object $A$, let
$R$ be the name of the {\em Composition Relationship}, then
{\fofosmall
\begin{align*}
CR \equiv R(D_1,A,D_2)\{C\}.
\end{align*}
}
For convenience, we simplify it to
{\fofosmall
\begin{align*}
CR \equiv R(D_1,A,D_2, C).
\end{align*}
}
Thus, we have the valid composition relationship,
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\LRAngle{{\bf Pre}.C,\sigma,\tau} \rightarrow True,
\LRAngle{{\bf Pre}.A,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.Skip,\sigma',\tau},
\LRAngle{{\bf Pre}.D_2.I,\sigma',\tau} \rightarrow True \\
\end{array}
}{\LRAngle{{\bf Pre}. R(D_1,A,D_2, C),\sigma,\tau} \rightarrow True},
\end{align}
}
where, $I$ is the {\em Invariant} of $D_2$.
And, the control switch from $D_1$ to $D_2$ may occurs when the relationship is valid,
{\fofosmall
\begin{align}
\frac{\LRAngle{{\bf Pre}. R(D_1,A,D_2, C),\sigma,\tau} \rightarrow True}
{\LRAngle{{\bf Pre}. D_1,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}. D_2,\sigma',\tau}}.
\end{align}
}
Note that, the control switch may not take place even though the relationship is valid.
It means that, if the {\em Invariant} of $D_1$ is true and $D_1$ can continue the continuous evolution without to violate the {\em Invariant}, then the choice to switch or continue the flow itself is
nondeterministic.
\item {\bf Start Dynamics}.
For {\em Dynamics} $D_1$ and $D_2$, the composite for start statements, is the parallel evolution of
the continuous flows, let
{\fofosmall
\begin{align*}
D_1||D_2 \equiv D_1.start(); D_2.start(),
\end{align*}
}
then, we have
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\LRAngle{{\bf Pre}.D_1,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.D_1,\sigma_1,\tau},
\LRAngle{{\bf Pre}.D_2,\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.D_2,\sigma_2,\tau} \\
\end{array}
}{\LRAngle{{\bf Pre}.(D_1||D_2),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.(D_1||D_2),\sigma',\tau}},
\end{align}
}
where, $\sigma_1=\sigma[v_1:=f_1(t)]$, and $\sigma_2=\sigma[v_2:=f_2(t)]$, therefore,
{\fofosmall
\begin{align*}
\sigma'= \sigma_1[v_2:=f_2(t)] = \sigma_2[v_1:=f_1(t)] = \sigma[v_1:=f_1(t), v_2:=f_2(t)].
\end{align*}
}
Here, $f_1, f_2$ are the {\em Real-Function}s for $D_1$ and $D_2$, respectively.
And, $t$ is the {\em Proper-Time}.
\item {\bf Parallel Composition Relationship}. For two composition relationships $CR_s$ and $CR_t$,
the parallel composition relationship is defined as follows,
{\fofosmall
\begin{align*}
CR_s ~||~ CR_t \equiv R_s(D_{s_1},A_s,D_{s_2},C_s) ~||~ R_t(D_{t_1},A_t,D_{t_2}, C_t).
\end{align*}
}
First, we have the parallel execution of {\em Assignment} objects $A_s$ and $A_t$,
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\LRAngle{{\bf Pre}.D_{s_1},\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}.D_{s_2},\sigma',\tau},
\LRAngle{{\bf Pre}.D_{t_1},\sigma',\tau} \rightarrow \LRAngle{{\bf Pre}.D_{t_2},\sigma'',\tau}
\end{array}
}
{
\begin{array}{c}
\LRAngle{{\bf Pre}.(A_s || A_t),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}. Skip,\sigma'',\tau} \\
\end{array}
},
\end{align}
}
where, $A_s$ and $A_t$ are symmetrical. The parallel composition relationship is valid,
{\fofosmall
\begin{align}
\frac{
\begin{array}{c}
\LRAngle{{\bf Pre}.(CR_s ~and~ CR_t),\sigma,\tau} \rightarrow True,\\
\LRAngle{{\bf Pre}.(A_s || A_t),\sigma,\tau} \rightarrow \LRAngle{{\bf Pre}. Skip,\sigma'',\tau},
\LRAngle{{\bf Pre}.(D_{s_2}.I ~and~ D_{t_2}.I),\sigma'',\tau} \rightarrow True,
\end{array}
}
{\LRAngle{{\bf Pre}.(CR_s || CR_t),\sigma,\tau} \rightarrow True},
\end{align}
}
where, the Boolean operator $and$ represents the conjunction relation.
\end{asparaenum}
\section{Design by Convention}\label{sec:design-by-convention}
\vspace*{-2mm}
Design by convention is a software design paradigm that is known as convention over configuration (abbreviated as COC).
It evicts the decisions the developers need to make by the conventional usages of the design ingredients, given the simplicity during the modeling process.
In software development, COC is usually used for the least configuration that
the developer should to set down. We apply the idea of COC and utilize it in the design of hybrid systems, and name it as design by convention (abbreviated as DBC) in our language.
\subsection{The composition of statements}
\vspace*{-2mm}
For boolean expressions $A$ and $B$,
{\small
\begin{align*}
Condition\{A;B;\}; \equiv A \wedge B.
\end{align*}}
We do not need to explicitly add the conjunction operation to connect the boolean expressions, the separate expressions in the {\em Condition} block have the conjunction relationship implicitly. It also makes the conditions more
clear and be easy to understand.
For the parallel and sequential assignments, they have the same appearance, but, different execution semantics indicated by the different Interfaces.
{\small
\begin{align*}
ParallelAssignment\{Discrete()\{A;B;\}\}; \equiv A || B,\\
SequentialAssignment\{Discrete()\{A;B;\}\}; \equiv A ; B.
\end{align*}}
The implementation of Interface {\em ParallelAssignment} gives the statements $A$ and $B$ the parallel composition relationship. While, the sequential composition of $A$ and $B$ is prominent for the case of Interface {\em SequentialAssignment}.
In a similar way, the starts of dynamics in the {\em Initializer} method for the {\em System} class have the parallel composition semantics without to employ the parallel operator `$||$'.
{\fofosmall
\begin{align*}
Init\{A.start();B.start();\}; \equiv A || B
\end{align*}}
And, in the constructor of a {\em System} class, we can ignore the parallel indications for plants and controllers if
they have the starts of dynamics in the {\em Initializer}. For instance, the `{\tt \small god||ball}' in Fig.\ref{fig:BouncingBallSystem} can be wiped off.
\subsection{The inexistence}
\vspace*{-2mm}
For True Condition and Invariant,
{\small
\begin{align*}
Condition\{\}; \equiv True, Invariant\{\}; \equiv True.
\end{align*}}
We evaluate the empty {\em Condition} and {\em Invariant} blocks to {\em True}, and the inexistent of these two blocks also considered to the boolean {\em True}.
For {\em Empty} assignment or the non-initialization of the assignment instance variable, we evaluate it to the special statement {\em Skip}.
{\small
\begin{align*}
Comp(Dy_1, , Dy_2) \equiv Comp(Dy_1, Skip , Dy_2),
\end{align*}}
where $Dy_1$ and $Dy_2$ are dynamics and the ` ' (Blank Space) in the LHS denotes the empty assignment.
\section{Conclusions}\label{sec:conclusions}
\vspace*{-2mm}
In this paper, we proposed Apricot as an object-oriented language for modeling hybrid systems and described the syntax and operational semantics of Apricot in detail.
The language combines the features from DSL and OOL, that
fills the gap between design and implementation, as a result, bring about a modeling language with
simple and distinct syntax, structure and semantics.
We also discussed the design by convention features of Apricot.
For the future work, we will focus on the formal verification
for Apricot models, then investigate verification techniques and develop relevant tools.
\bibliographystyle{splncs03}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,758 |
{"url":"https:\/\/uuvsimulator.github.io\/packages\/uuv_simulator\/docs\/packages\/uuv_gazebo_ros_plugins_msgs\/","text":"# uuv_gazebo_ros_plugins_msgs\n\nLink to the uuv_simulator repository here\n\n#### Description\u00b6\n\nThe uuv_gazebo_ros_plugins_msgs package\n\n#### ROS Services\u00b6\n\n##### GetFloat\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#\n# Unless required by applicable law or agreed to in writing, software\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n\n---\nfloat64 data\n\n##### GetThrusterEfficiency\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#\n# Unless required by applicable law or agreed to in writing, software\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n\n---\nfloat64 efficiency\n\n##### SetThrusterState\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#\n# Unless required by applicable law or agreed to in writing, software\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n\nbool on\n---\nbool success\n\n##### SetThrusterEfficiency\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#\n# Unless required by applicable law or agreed to in writing, software\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n\nfloat64 efficiency\n---\nbool success\n\n##### GetModelProperties\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#\n# Unless required by applicable law or agreed to in writing, software\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n\n---\nuuv_gazebo_ros_plugins_msgs\/UnderwaterObjectModel[] models\n\n##### GetThrusterConversionFcn\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#\n# Unless required by applicable law or agreed to in writing, software\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n\n---\nuuv_gazebo_ros_plugins_msgs\/ThrusterConversionFcn fcn\n\n##### GetListParam\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#\n# Unless required by applicable law or agreed to in writing, software\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n\n---\nstring description\nstring[] tags\nfloat64[] data\n\n##### SetUseGlobalCurrentVel\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#\n# Unless required by applicable law or agreed to in writing, software\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n\nbool use_global\n---\nbool success\n\n##### GetThrusterState\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#\n#\n# Unless required by applicable law or agreed to in writing, software\n# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n# See the License for the specific language governing permissions and\n\n---\nbool is_on\n\n##### SetFloat\u00b6\n# Copyright (c) 2016 The UUV Simulator Authors.\n#\n# you may not use this file except in compliance with the License.\n# You may obtain a copy of the License at\n#","date":"2022-08-13 02:26:18","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3597952127456665, \"perplexity\": 7015.921090364132}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882571869.23\/warc\/CC-MAIN-20220813021048-20220813051048-00679.warc.gz\"}"} | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.